> Bhutan is trying to define national welfare
> http://www.physorg.com/news125462439.html
>
> "The main concerns have been identified as psychological well-being,
> health,
> education, good governance, living standards, community vitality and
> ecological diversity."
>
> What concerns would you include? And how would these parts of GDP+ be
> measured?

I'm glad you asked that.

I would include a component to measure self-reported satisfaction.

Now, self-reported satisfaction ("happiness") is notoriously
problematic.  Good fortune doesn't make people as happy as they
predicted it would, and ill fortune doesn't make them as unhappy as
they predict.  Healthy, rich people aren't that much happier.  And so
on.

To counter this, I would explicitly indicate the baseline for
comparison and I would make it clear to survey respondents that
personal circumstantial well-being is what's being asked about.  So
the survey question would be something like "Are you better off than
you were N years ago?" (to nearly paraphrase a certain political
slogan)

There's a dilemma lurking there: If the time interval is too large,
few people can be meaningfully surveyed (Are you better off than you
were 100 years ago?).  If too small, that creates a short time
horizon.

So I'd want to ask about a range of intervals.  That creates issues of
how to weight answers as a function of both N and respondent's age.


Asking only "better/worse" would result in an overly blocky metric.
That is, the system would try to make the majority just a little bit
better off, possibly at the expense of making a minority of citizens a
whole lot worse off.  So I'd offer respondents a range of answers
along the usual lines of "strongly agree" ... "strongly disagree".
How to weight them is an issue here too.


Finally, there's the question of gaming the survey.  If I held a long
position on GDP+, I'd be tempted to say I was better off than I really
was.  I might even fool myself into believing I was.

To counter gaming the survey, I suggest incorporating Drazen Prelec's
"Bayesian Truth Serum" (BTS) - the name perhaps promises too much, but it
is a sound piece of mechanism design.

Tom Breton (Tehom)

david.curran@... (David Curran) writes:
>Bhutan is trying to define national welfare
>http://www.physorg.com/news125462439.html
>
>"The main concerns have been identified as psychological well-being, health,
>education, good governance, living standards, community vitality and
>ecological diversity."
>
>What concerns would you include? And how would these parts of GDP+ be
>measured?

  Life expectancy provides a fairly objective measure that is rather highly
correlated with the concerns that I care about. Some care needs to be taken
to standardize the somewhat variable treatment of infants that die shortly
after birth versus those that aren't counted because they're considered
stillborn, and there's some risk of patients being kept alive when the
patient would rather die, but those affect a pretty small fraction of
political issues.
  I would like to include some measure of psychological well-being, but any
of the measures that come to mind would be abused if they influenced
important decisions.
  I think education, good governance, and possibly more of that list should
be thought of as means we use to increase welfare, not ends.

--
------------------------------------------------------------------------------
Peter McCluskey         | When someone is honestly 55% right, that's very good
www.bayesianinvestor.com| Whoever says he's 100% right is a fanatic

tehom@... (Tom Breton (Tehom)) writes:
>"Peter C. McCluskey" <pcm@...> writes:
>>  Your message implies that all attempts to avoid the opacity problem
>> via human judgment require a single authority. I disagree.
>
>Is that because I said "monarchy"?  I also said "or something else
>depending on how they hold that office".  It's intended to include the
>whole range of possible types of vetoer, {king, oligarchy,
>legislature, judiciary, bureaucracy, or anyone else}.  I'm arguing

  It wasn't just the word monarchy. You also used "someone" and "that office",
which all imply that you're imagining a centralized entity.

--
------------------------------------------------------------------------------
Peter McCluskey         | When someone is honestly 55% right, that's very good
www.bayesianinvestor.com| Whoever says he's 100% right is a fanatic

"Peter C. McCluskey" <pcm@...> writes:

Peter, thank you for answering.  It's good to have feedback to my
(unintentionally so) monologs.

> In futarchy_discuss@yahoogroups.com, "tehom2000" <tehom@...> wrote:
> >* Appointing someone to selectively veto proposals that have already
> >passed. Effectively that gives that office complete authority, both
> >negative authority (by veto) and positive authority (by using the
> >opacity problem themselves). That's not futarchy, that's monarchy (or
> >something else depending on how they hold that office)
>
>  Your message implies that all attempts to avoid the opacity problem
> via human judgment require a single authority. I disagree.

Is that because I said "monarchy"?  I also said "or something else
depending on how they hold that office".  It's intended to include the
whole range of possible types of vetoer, {king, oligarchy,
legislature, judiciary, bureaucracy, or anyone else}.  I'm arguing
that if someone (whoever it may be) holds veto power, then for all
practical purposes they hold *all* the power, unless the opacity
problem is solved.

>  I suspect part of my disagreement reflects a difference in goals. I see
> a broad range of possible ways to partially implement futarchy in
> incremental steps, whereas you seem to focus exclusively on pure
> futarchy.

Yes, perhaps a difference in goals or a difference in focus.

> [...]
>
>  One way to come close to an automated futarchy is to require legislatures
> and administrative agencies to accept any proposal that prediction markets
> approve unless they can articulate clear reasons for rejecting a proposal,
> and to require that whenever they reject such a proposal the issue
> automatically generates a court case to review the rejection. That way
> we have both the partially democratic control that exists over government
> entities plus the checks and balances of two somewhat independent branches
> of government.

An interesting idea.

> [...]
>
>  In any attempt at implementing futarchy, allowing arbitrarily worded
> proposals will cause problems, and something resembling a requirement
> for controlled language seems desirable. I will try to suggest some
> approaches in a future message.

I look forward to seeing that.

>  For those here who don't know me, here are some pieces of information
> about my interest in Futarchy:
> http://www.bayesianinvestor.com/amm/
> http://www.bayesianinvestor.com/blog/index.php/category/econ/if/
> http://www.usifex.com/ (a play money market I wrote 8 years ago)

Thanks for the links.

> --
> ------------------------------------------------------------------------------
> Peter McCluskey         | When someone is honestly 55% right, that's
very good
> www.bayesianinvestor.com| Whoever says he's 100% right is a fanatic

Tom Breton (Tehom)

In futarchy_discuss@yahoogroups.com, "tehom2000" <tehom@...> wrote:
>* Appointing someone to selectively veto proposals that have already
>passed. Effectively that gives that office complete authority, both
>negative authority (by veto) and positive authority (by using the
>opacity problem themselves). That's not futarchy, that's monarchy (or
>something else depending on how they hold that office)

  Your message implies that all attempts to avoid the opacity problem
via human judgment require a single authority. I disagree.
  I suspect part of my disagreement reflects a difference in goals. I see
a broad range of possible ways to partially implement futarchy in
incremental steps, whereas you seem to focus exclusively on pure futarchy.
  I see two important steps toward futarchy as involving voters relying
on market forecasts to choose candidates, and demanding that legislators
rely on market forecasts when deciding how to vote on legislation. I expect
these steps would yield at least half the benefits of completely automated
futarchy, while keeping existing decentralized restraints on the opacity
problem. As long as this is the best that is politically feasible, I suggest
we live with the opacity/ambiguity problems that our legislative processes
currently produce.
  One way to come close to an automated futarchy is to require legislatures
and administrative agencies to accept any proposal that prediction markets
approve unless they can articulate clear reasons for rejecting a proposal,
and to require that whenever they reject such a proposal the issue
automatically generates a court case to review the rejection. That way
we have both the partially democratic control that exists over government
entities plus the checks and balances of two somewhat independent branches
of government.
  And by the time we can hope for widespread support for more
automated versions of futarchy, I see a significant chance that AI will
create choices that will help us see better how to handle the opacity problem.

  In any attempt at implementing futarchy, allowing arbitrarily worded
proposals will cause problems, and something resembling a requirement
for controlled language seems desirable. I will try to suggest some
approaches in a future message.

  For those here who don't know me, here are some pieces of information
about my interest in Futarchy:
http://www.bayesianinvestor.com/amm/
http://www.bayesianinvestor.com/blog/index.php/category/econ/if/
http://www.usifex.com/ (a play money market I wrote 8 years ago)

--
------------------------------------------------------------------------------
Peter McCluskey         | When someone is honestly 55% right, that's very good
www.bayesianinvestor.com| Whoever says he's 100% right is a fanatic

In my last message, I concluded that a futarchy system would benefit
from a mechanism that explicitly considers whether to delay a
promising proposal or not.  This message is a sketch of how that
mechanism might work.  It's longer than I wanted, but hopefully not
too boring.


Desired behavior:

Fix the Railroad Problem.  Ie, let investors expose themselves to
timed outcomes and make the system use that information to better
control the timing of enactment.

Don't ruin the behavior in the levee situation, which works.

Don't favor enactment or non-enactment.

Don't favor any particular enactment time (within a broad range)

Definitions:

I am considering that it is impossible by definition to enact the same
proposal twice.  Other proposals along the lines of "do exactly the
same thing again" don't count as the same proposal.

Overview:

Ingredients overview:

A long trading era.  Maybe 10 years.

Many short trading segments.  Subdivisions of the trading era.  Maybe
a week or a month each.

P(now).  It's the issue P(yes) with respect to a given trading
segment.

P(not_now).  P(no) with respect to a given trading segment.  Ie,
the short side of P(now).

P(sometime).  An option on the P(now) of any future trading segment.
Must be exercised once during the trading era.

P(never).  The short side of P(sometime).


Rules overview:

Enact P just when P is desirable now and now is the best time.

To determine whether P is desirable now, compare price(P(now)) to
price(P(not_now)).

To determine whether now is the best time to enact P, compare
price(P(now)) to price(P(sometime)).

If P is enacted, settle P(now) and P(not_now) with the respective
"enacted" payoffs and call off P(sometime) and P(never).

Each time P is not enacted for a segment, settle P(now) and P(not_now)
with 1/N of the respective "not enacted" payoffs.


Discussion on the ingredients:

Trading era:

Taken literally, "never" enacting P is unknowable.  So of course I
mean that P is not enacted before some time horizon, not never enacted
in the future of the universe.

So the time horizon is a free parameter in my proposal.  It's arguably
a feature, not a bug.  Choice of time horizon permits some degree of
fine-tuning based on features of the proposal.  Eg, a hundred million
dollar proposal had better still make sense 50 years from now, so it
makes sense to use a far time horizon for it, but for a proposal whose
price tag is a few thousand dollars, a nearer time horizon might make
sense.

Trading segments:

I assume that segments are of equal size.  I don't think there's any
serious problem in dynamically subdividing the time, but for now for
simplicity let's say they are all of equal size.

If different segments were to pay out on GDP+ measured at different
future times, their answers might be influenced by different
expectations of GDP+ relative to time, and the relation of P(sometime)
to P(now) would not be the straightforward relation of maximization
that we depend on.

So all trading segments in the same trading era should be keyed to the
same time of measuring GDP+.

One bad consequence: Each successive segment's horizon of prediction
is shorter than the last one's.  We'd probably want future years to
take into account GDP+ predictions that in their turn are farther in
the future.  We certainly don't want the last segment to take into
account only next week's GDP+.

So there should be a significant interval of time between the end of a
trading era and the time when GDP+ is to be measured, maybe 3
or 4 times as long as the trading era itself.

That in turn has a bad consequence: Say a promising proposal P looks
better in the future than it does now and seemingly this trend will
continue past the end of the current trading era.  During the
last segment, it will suffer from the Railroad Problem again.  The
fact that enacting it right now looks good will be the only thing that
counts.

So I further suggest that there be some overlap in time between
trading eras, and when two overlap on an issue P, both of their
current values be used in determining whether to enact P.


P(now), P(not_now):

When a trading segment is finished or P is enacted, P(now) and
P(not_now) both settle up and are gone.

If P is enacted, P(now) holders get the (yes,enacted) payoff and
P(not_now) holders get the (no,enacted) payoff.

If P is not enacted when a trading segment expires, P(now) holders get
1/N of the (yes,not enacted) payoff and P(not_now) holders get 1/N of
the (no,not enacted) payoff, where N is the number of trading segments
in a trading era.

The 1/N scaling factor applies even to {P(sometime),P(never)}'s final
non-enactment payoffs so that exercising is not favored or disfavored.

A pair P(now)+P(not_now) can be created directly or by exercise of
P(sometime), which also converts a P(never).


Why the 1/N scaling factor:

In an earlier draft of this, there was no scaling factor, which caused
a subtle but serious problem.

First, consider what happens to a holder of P(now) if P is enacted a
few segments later.  He's made a bet that GDP+ will not meet
expectations "because P wasn't enacted", but a few weeks later, P is
in fact enacted.  By being just few weeks early, his bet has said
approximately the opposite of what he meant.  Presumably P's effect on
GDP+ is usually not enormously sensitive to when it's enacted, and
it's in nearly-indifferent situations that this situation is most
likely to happen.

An investor would like to be able to mitigate this risk by
diversifying over different P(now)s.  Without a scaling factor, this
strategy only puts him further in the wrong.  For M bets, he will get
M-1 reversed payoffs and only one intended payoff.  With a scaling
factor, the strategy works, because M < N and if the investor has the
slightest clue as to when is a good time to enact, M << N.

Scaling also makes sense balance-wise: Since non-enactment can happen
N times but enactment can happen only once, scaling them like this
makes the payoffs more similar in scale.

If the trading segments were of unequal duration, we'd replace 1/N
with the ratio of the duration of the segment in question to the
duration of the trading era.

P(sometime):

The purpose of P(sometime) is to predict the desirability of the best
future segment for enacting P.

There are two major differences between P(sometime) and conventional
options:

A P(sometime) can be exercised with regard to any one of many
sequential P(now)s.

At the end of the trading era, P(sometime) is converted to P(now)
whether the holder wants to exercise it or not.  That means that on
final non-enactment, any outstanding P(sometime) receives the
(yes,not-enacted) payoff and any outstanding P(never) receives the
(no,not-enacted) payoff.

It also has a strike price of zero; that's not neccessary, it just
makes explanation simpler.

P(never):

Holders of P(never) do not get to choose when to convert to
P(not_now), it follows P(sometime)'s choice; when N shares of
P(sometime) convert to P(now), N shares of P(never) are converted to
P(not_now).  This might appear to disadvantage P(never), but it's
merely making P(never) mean what it says: enacting P will never be a
good idea, within the horizon of predictability.

It's slightly disturbing that a different number of shares of P(never)
are converted to P(not_now) depending on whether P(sometime) holders
collectively "buy N, convert N, buy N, convert N" or "buy 2N, convert
2N" but I suspect that it's not gameable.  I am not familiar with any
existing mechanisms to manage the forced conversion of short positions
on convertible issues, so take this for what it's worth.

Discussion on the rules:

Basically, the mechanism repeatedly considers the proposition that
enacting P right now is a good idea.  The remaining parts exist to
give investors a way to distinguish the positions "no, later" and "no,
never" and to give the system a way to see that information.

Whether now is the best time:

"To determine whether now is the best time to enact P, compare
price(P(now)) to price(P(sometime))."

Yet in any segment except the last, the simplest version of this
option would be strictly more valuable than P(now).  It can be
converted into P(now) of this segment or it can be converted in a
later segment.  Done in the simplest way, the comparison would always
give the answer "no".

We need to separate out the component of P(sometime) that corresponds
to the same segment that's under consideration.  One method is to only
allow conversions at the start of a new trading segment, which removes
the value of P(now) from P(sometime).

In order for P(sometime) to not suffer from the "thin end" problem
(ie, when a price can affect enactment without real risk of being
traded on) the price of P(sometime) that is compared to price(P(now))
should be fixed as the price of P(sometime) immediately after it can
no longer be converted to this segment's P(now).  This solution
appears insecure and a better solution should be found.


Whether P is desirable now:

"To determine whether P is desirable now, compare price(P(now)) to
price(P(not_now))."

This is basically the enactment rules I've talked about before.  The
desirability formula is slightly altered.  in the simple case without
ratioed contingent swaps, it's

       Desirability(P)
	 := (price(P(yes))/((N+1)/N) - (p(P) - 1)GDP+) / (p(P) - p(P)^2)

One point of concern: the mechanism to recover delta GDP+ at very high
or very low probabilities of enactment.  (Recap: The problem is that
if P is almost certain to {be, not be} enacted, a bet contingent on
enactment tells us almost nothing relevant.  A solution I found is to
estimate the probability of enactment, support "ratioed contingent
swaps", and retrieve the true estimate of delta GDP+ by a calculation
that uses those values)

My earlier probability calculations seem unaffected, since they never
were contingent on what causes the apparent probability to take its
value.  My definition of ratioed contingent swaps allowed an arbitrary
ratio, so the 1/N scalar doesn't affect the calculations either.

How can P(sometime) and P(never) convert to ratioed contingent swaps
with values other than 1:1?  A simple but probably suboptimal
solution: Allow P(sometime) and P(never) also to be parameterized by a
ratio, and conversion must keep the ratio the same.  I think this can
be improved on.


Issue: What happens to outstanding P(never) and P(sometime) if P is
enacted?

They are called off.

There appear to be few other options.  The P(sometime) payoff can't be
the P(now) payoff, otherwise P(sometime) holders would have no reason
to ever exercise their option.  It can't be zero, otherwise there is a
risk of stampedes to exercise.  Mixtures of these payoffs don't seem
any better.

How are they called off?  Rather than rolling all their transactions
back to time zero, I suggest rolling them back to the end of the
previous segment.  That's the last time they were able to affect
enactment in this segment.

It's reasonable to call them off because their proper area of concern
is whether in the future it will ever be desirable to enact P.  Since
P is now enacted, this area will never be tested.

Since we fixed the comparison price as price(P(sometime)) from an
earlier time and since price(P(never)) is not a factor in enactment,
insincere wagering at this time cannot affect enactment.

In an enactment situation, price(P(now)) exceeds price(P(sometime)).
We might suppose that this implies that near 100% exercise is likely.
But this requires that all P(sometime) holders anticipate this
near-future situation with great confidence.  What's likely IMO is
that P(sometime) holders diversify by exercising at different likely
times.

This means that both holders of P(sometime) and P(never) will partly
miss out on the large enactment payoff.  Holders of P(never) would
generally prefer to, because (no,enacted) is generally negative, but
they do not control exercise.

Revisiting the desirability formula:

(I'm not going to post the whole derivation again.  Most of it is the
same plus a scaling factor)

	 //In the previous derivation, before rearrangement the equation
	 //is the same up to a scaling factor on one term, so:
       E(P(yes))
	 := E(GDP+(|P - (1/N)|!P))
	 = (p(P)(E(Mixture(p(P))) + (1 - p(P))E(Delta)) -
		 (1/N)(1 - p(P))(E(Mixture(p(P))) - p(P) E(Delta)))

	 //Distributing
	 = (p(P)(E(Mixture(p(P))))
	   + (p(P) - p(P)^2)E(Delta)
	   - (1/N - p(P)/N) E(Mixture(p(P)))
	   + (p(P)/N - p(P)^2/N)E(Delta))

	 //Rearranging, using E(Mixture(p(P))) = GDP+
	 = ((N+1)/N) ((p(P) - 1)(GDP+) + (p(P) - p(P)^2) E(Delta))

So the expected value has merely been scaled by (N+1)/2N.  Nothing
crucial has changed.  The desirability formula merely changes by the
same scaling factor (I've also rearranged it slightly from before)

       Desirability(P)
	 := (E(P(yes))/((N+1)/N) - (p(P) - 1)GDP+) / (p(P) - p(P)^2)

For ratioed contingent swaps, 1/N is just another factor in the ratio
(the ratio that I called M/N before, but that refers to a different N)


Does it fix the problem?:

First, can an investor get exposure to outcomes such as B in the
railroad example?

Yes. If an investor wants exposure to "not now but later", he can buy
P(sometime) and exercise it in a later segment.  If enacting now is
just sub-optimal, he need not play with P(now).  If enacting now is
actually bad, he can buy P(not_now)

If "later" is not an absolute time but a time relative to some
occurence (eg neighboring states standardize railroad track gauge), he
can make himself risk-neutral by making external bets contingent on
that event.  The system doesn't need to know about those, it only
needs to make a sequence of decisions of whether to enact right now or
not.

Second, does the system make the right decision?

We'll assume the following about the original problem:

(a) Some investors understand the situation

(b) "GDP+ given B" > "GDP+ given A" > "GDP+ given C"

(c) Railroads provide an ongoing increase to GDP+ but not so much as
to change relation (b) (so ceteris paribus we prefer to enact early)

(d) There are no other timing concerns (an idealization).


Before neighboring states standardize, by (b), P(sometime) is more
valuable than P(now).  So the enactment conditions would not be met.

After neighboring states standardize, the possible outcomes are B and
C.  So (b) no longer distinguishes P(now) from P(sometime).  By (c)
and (d), P(now) is more valuable than P(sometime) because enacting
during the current segment increases GDP+ more than enacting during
any future segment does.  By (b) and (d), P(now) is more valuable than
P(not_now).  So both enactment conditions are met.

So in the railroad example, this mechanism does the right thing.

	 Tom Breton (Tehom)

An example illustrating the opposite side of the delay question.
Sometimes waiting makes the situation worse.

In a hypothetical city on the gulf coast, everyone knows the following
facts beforehand: A hurricane is 50% likely to strike the city this
year.  If a hurricane strikes the city and the levees have not been
repaired, the expected damage is $1000 million.

The city faces three options:

(a) The levees can be repaired before hurricane season starts at a
cost of $1 million.

(b) The levees can be repaired "in the nick of time", which will cost
the same but offer less certain protection.  The expected cost of that
outcome is $100 million.  B only occurs if a hurricane is headed
towards the city, otherwise there'd be less time pressure and that's
option A.

(c) Do nothing.  If C is chosen, it is not committed to and the city
can still enact B later.  (Or A if no hurricane is imminent)

Proposal P is to repair the levees as soon as P is enacted.


First comment: In the early stage before hurricane season, P's
expected effect on GDP is about $49 million.  So P would be enacted
early, giving outcome A, as it should.  This works.  Whatever
mechanism fixes the railroad situation must not ruin this situation.


Second comment: The example makes it clear what will not work:
Anticipating the intensity of preference for P(yes) and delaying if it
is expected to increase.  (or if you prefer called-off bets, the
intensity of preference for P(yes) - P(no))

In a situation where the city is in the path of the hurricane,
enacting P becomes much more desirable.  Its expected effect on GDP
becomes $900 million.  We said there was a 50% chance of this
happening, so in foresight the expected effect on GDP is at least $450
million (More on average, as P's expected effect on GDP in the other
case ("no hurricane imminent") descends from its original value of $49
million at the beginning of hurricane season to a value of minus the
interest on $1 million)

But option B was not better than A, it was much worse.  If you wait
until a situation is desperate, solving the problem becomes much more
important, but that's not a reason to wait until it's desperate.  So
we can rule out a timing mechanism based on the expected increase of
the price of P(yes).

	 Tom Breton (Tehom)

> Hello
> Imagine a situation where a government was asked to pick between two
> competing standards.
> HD-DVD and Blu-Ray say (this war is now over) .
> Could they really wait and see what format won? If everyone does this
> neither format will win.
> Options do exist for helping to see which format will be successful
> http://ppx.popsci.com/security/view.php?symbol=BLUBY09

That's true, but the example wasn't really about which gauge to choose or
how to choose it.  It was about how a futarchy-type system can know
whether it's better to commit or to wait.  Waiting for a standard is only
one of many concerns that could inform that decision.  All sorts of
factors could bear on whether it's better to commit now or not.  I don't
think it's possible to catalog them all.

I'm sure you get this, I just didn't want lurkers to get the wrong idea.

> I know these points have been made in the original post I am just looking
> for a concrete example. There are many examples of governments picking the
> wrong standards and delaying innovation because of this.

         Tom Breton (Tehom)

An example to motivate concern about timing.  The example is drawn
from the time before railroad gauge was standardized.  In the example,
a region faces 3 possibilities:

(a) Build railroads immediately.

(b) Wait and see what gauge other regions settle on, then build
railroads of the same gauge.

(c) not build railroads.

I'll use the following relative valuations: The best outcome is B, but
A is still better than C.  If outcome A occurs, B is no longer
appealing because it requires the same expenditure but gains a smaller
improvement.

Under the enactment rules we've talked about, as soon as it is
proposed to build railroads, the fact that A beats C would cause the
proposal to be enacted.  B would be missed.

Some investors would recognize that it's actually a choice between A
and a later choice between B and C; presumably the later choice would
choose B.  They still don't have a satisfactory way to expose
themselves to outcome B in the early stage, though.

If they buy "no" early, they appear at first glance to expose
themselves to the difference between outcome (choose C or B) and
outcome A, but as soon as it's known what railroad gauge other regions
will settle on, "no" then means outcome C and it is "yes" that means
outcome B.  So investors who pursue the strategy of buying "no" early
for gaining exposure to B are at risk of being suddenly unwillingly
converted to the opposite of the position they want to hold.  That's a
very risky position.  They might time their sell-and-buy just right,
but it's far more likely they've hurt themselves.

Investors might attempt to expose themselves to outcome B in external
ways, perhaps thru options.  That doesn't seem like it would affect
price of the proposal issue itself.

We might hope that knowledgeable people would notice the situation,
propose B, their proposal be quickly be recognized as competing (in
whatever manner the system recognized competing proposals; that's
another topic), and it would overtake A quickly enough to stop it.
The last two conditions are neccessary because once A happens, B is no
longer appealing.

But that's a lot to hope will happen correctly in a short time.  It
also ignores and recreates some information that never changes: A
proposal is always in competition with its future self.  Delaying is
always an aspect that can be considered (though in particular
circumstances delaying may make no sense)

Therefore I think a futarchy system would benefit from a mechanism
that explicitly considers whether to delay a promising proposal or
not.  I'll write up a suggestion I have in mind, but it's late now.

	 Tom Breton (Tehom)

Another question about futarchy that interests me is this: How can
futarchy handle competing proposals?  This is partly missing
functionality and partly an opportunity not yet capitalized on, and
could become a security hole if it is solved badly.

To give a simple example, there might be two proposals to build a
stadium in a given city.  One proposal says to build it in one
location and the other says to build it a few blocks away.  It would
be folly to enact both.  The proposals are competing with each other.
Futarchy would need a mechanism for dealing with this sort of
situation.


I think that the constraints on the mechanism should include:

* The mechanism can't depend on a trusted omniscient source to tell us
   which proposals compete against each other.

When dealing with a simple example or illustration, it may be tempting
to describe a mechanism for choosing between N competing proposals.
Of course if we knew which proposals competed with each other, it
would be easy to design a mechanism to choose.  But we don't
automatically know that.

It's unsatisfactory to just delegate that determination to a trusted
party.

It would be nice if we could delegate that determination to a reliable
mechanical rule or formula, but no simple such rule suggests itself.


* The mechanism shouldn't be gameable.

No-one should be able to influence outcomes by introducing spurious
alternatives.  A specific threat is that a bad actor who dislikes a
given proposal P would introduce a large number of spurious competing
proposals.

Another version of this threat is that a bad actor would abuse some
mechanism that controls which proposals are considered competitors,
possibly to overwhelm a disliked proposal with fake competitors or to
eliminate competitors to an inferior proposal that the bad actor
likes.

No-one should be able to influence outcomes by controlling when
proposals are respectively introduced.  If earlier proposals are
priveleged, a bad actor, knowing that P will soon be introduced, might
introduce an less desirable variant P' first.  If later proposals are
priveleged, a bad actor might introduce P' later, even at the last
moment.  If introducing a competitor forces a waiting period, a bad
actor might delay enactment of a disliked proposal indefinitely.

No-one should be able to influence outcomes by stopping the
introduction of competing proposals, perhaps on the bureaucratic
pretext that "there's already a similar proposal".  If the general
public may introduce proposals freely, this is solved automatically.

* The mechanism still has to work.

That is, it has to resolve in favor of proposals that maximize the
utility function (GDP+) according to the market's best collective
understanding.

And let's capitalize on opportunity:

* The mechanism should take late structural information into account.

Structural information refers to revised proposals, late alternatives,
new understanding about interaction between proposals, and similar.

It may not be practical to consider new information until the last
instant, but this condition should be approximated.

This condition overlaps with the requirement that the mechanism can't
be gamed by controlling when proposals are introduced.

* The mechanism should allow sensitivity not just to broad
   competition between proposals but to subtle interactions between
   them.

I introduce this idea by talking about competing proposals, but it
applies to subtle interactions just as well.  The difference is merely
a matter of degree.


Situations of interest:

Situation: Proposals Pa and Pb are both promising but they are so
similar that enacting them both would be folly.  Intended outcome:
either Pa or Pb is enacted but not both.  Furthermore, the one that is
enacted should be the better one of the two.

Situation: Proposal Pa is promising, but before it is enacted, new
understanding suggests that a revised proposal Pa' might be superior.
Intended outcome: Pa' is proposed, Pa and Pa' compete in the market,
and the better of the two is enacted.

Situation: Proposals Pa and Pb are mutually dependent: enacting one of
them makes little sense unless the other be enacted.  Together, they
are promising.  Intended outcome: either both are enacted or neither
is.

Situation: More subtly, Pa and Pb are merely somewhat synergistic or
antisynergistic.  Intended outcome: each one's likelihood of enactment
influences the other's value to the appropriate degree.

Situation: Proposal Pc competes with the combination of Pa and Pb,
which are otherwise apparently independent of each other.  (Perhaps Pc
is a revision of both proposals Pa and Pb and they hadn't been
connected before) Intended outcome: Either Pc is enacted and Pa and Pb
are not, or Pc is not enacted.

All the intended outcomes are meant with regard to the microcosm of
the example at hand, not as desired outcomes regardless of any
conflicting larger situation.  But we can't just solve microcosms of
two or three proposals, we need to solve a more general picture.

Seeing a more general picture:

All of these situations may be considered cases of graphs where each
node corresponds to a proposal and each edge corresponds to the degree
of synergy between a pair of proposals.  I will write an edge between
proposals Pa and Pb as:

	 synergy(Pa,Pb).

Clearly one should maximize the total desirability of the set of
proposals enacted.  Neglecting higher-order interaction for the
moment, this means accounting both for proposals' individual
desirability and for the desirability of all the edges between enacted
proposals.  More formally, enact the set {P[i] | member(i,S)} that
maximizes:

	 sum(desirability(P[i]), member(i,S))
	 + sum(desirability(synergy(P[i],P[j]),
	       member(i,S),member(j,S), i < j))

"i < j" is a constraint on the second term only so that we don't
double-count edges or try to count an edge from any proposal to
itself.

Two general strategies present themselves:

* Measure synergy and using the information, mechanically find the
   most desirable set from the graph.

* Elicit single proposals that merely express yes/no on sets of other
proposals and don't allow both a higher-order proposal and members of
the set of proposals it draws from to be enacted.

	 Tom Breton (Tehom)

In the last message, I suggested a formula for extracting Delta, the
effect of P on GDP+, and I pointed out a problem extracting Delta at
extreme values of p(P).  To address that problem, I suggested "Change
the payoff slightly as a function of apparent(p(P)), in order to make
Delta just a little stronger when p(P) has an extreme value."  It
wasn't clear to me how to do so advantageously, but now I think I know
how.

This will require these measuring tools:

* New tool: Ratioed contingent swaps.  On enactment "yes" holders get
M (call - put) and on non-enactment they get N (put - call), for some
numbers M and N.  I will write this as:

	 (yes,M,N)

defined as:

       (call(GDP+) - put(GDP+)) (M|P - N|!P)

They are characterized by a probability of enactment:

	 characteristic probability := N / (M + N)

* As before, an estimate of p(P).

* As before, a measure of GDP+.  This is no longer crucial, but is
still useful.  It's equivalent to "(yes,1,-1)".


Now in principle, any (yes,M,N) could have been calculated from a
linear combination of "yes" and GDP+.  The problem was that when p(P)
was near 0 or 1, this calculation became very inexact.  We'd expect
p(P) to be near 1 (or 0) when enactment is likely (or unlikely).  To
deal with this, we'd like to create issues where the noise terms tend
to cancel.  This happens when true p(P) is exactly the characteristic
probability.

The simplest way would be to use:

       Desirability'(P) :=
	 (price("yes",(1/p(P) - 1),1)) / ((1 - p(P))).

However, p(P) is a moving target.  Worse, when this measurement makes
P more likely to be enacted, that fact changes p(P).

To deal with this problem, we'd like to be able to extract Delta from
some (yes,M,N) whose characteristic probability is close to p(P).  We
could calculate desirability from what we used before and the
disagreement between p(P) and the characteristic probability of
(yes,M,N).

Defining D as:

	 D(M,N) := M/N - (1/p(P) - 1)

Abbreviated as

	 D := D(M,N)

we'd calculate:

       Desirability'(P) :=
	 (price("yes",M,N) - D p(P)(GDP+ - c1))
	 / ((1 - p(P)) + D (p(P) - p(P)^2)).


We can do better by calculating Desirability from two (yes,M,N)s that
bracket p(P).

Using weights Wa and Wb whose ratio is:

	 Wa/Wb := Nb/Na (((Ma/Na - Mb/Nb)/ D(Ma,Na)) - 1)

we'd calculate:

       Desirability'(P) :=
	 (Wa price("yes",Ma,Na) + Wb price("yes",Mb,Nb))
	 / (Wa + Wb)(1 - p(P))

I suspect that by using further (yes,M,N)s, weighting them according
to both distance from apparent(p(P)) and quality of measurement, we
can make the error in the numerator even smaller.  I suggest that GDP+
itself, equivalent to (yes,1,-1), could be used here.  It is in a
sense the cheapest metric of this family because its cost can be
shared by all futarchy issues.

If Ma/Na and Mb/Nb closely bracket p(P), the error in the numerator
gets very small.  However, any error in apparent(p(P)) becomes error
in the denominator, which we can't easily escape from.

Error in the denominator seems tolerable if there is very little error
in the numerator.  We only run the risk of understating or overstating
Delta.  Overstating is the more serious risk, and comparison to a
threshhold needs to account for that.  I suggest that the threshhold
should contain a compensating term of the form:

	 X / (1 - apparent(p(P)))


Issues:

How should these (yes,M,N) issues be provided?

I propose that they be created just-in-time when needed.  Advantages:
Any costs associated with creating them are borne only when they
provide benefit.  Trading is thereby directed to issues that shed more
light on Delta.  If some proposal P has an unexpectedly high or low
apparent(p(P)), an appropriate market can still exist.

Doing so may effectively be required for enactment as p(P) anticipates
enactment and climbs very close to 1.0.

It may make sense to also freeze trading on old (yes,M,N)s whose
characteristic probability is far from apparent(p(P)).  I don't think
it will affect their value, because positions can still be closed by
buying or selling other (yes,M,N)s on P in ratio.  (Again, the
intention is to make the Delta term stand out more clearly above the
noise of the GDP+ term)



What characteristic probability should a (yes,M,N) be given?

There is tradeoff between the precision and regularity.  Precision
would mean setting the characteristic probability as close to p(P) as
possible.  Regularity would mean using only a few well-trodden values.

Precision is to a large extent naturally thwarted by real drift in
p(P) and by any progress P makes towards or away from enactment, so
let's not weight precision too highly.

Regularity would prefer small integer values of M and N.




Wouldn't (yes,M,N)s have long-shot bias like idea futures does at
extreme values, ie when N >> M or M << N?

I suspect that they do for the same reason that other contingent
issues like idea futures do.  There's no experimental data, of course.
But we should suspect the existence of it and not trust extreme ratios
of M/N.  Optimistically, it may be the case that apparent(p(P)) and
(yes,M,N) of the same characteristic probability have identical
long-shot bias and may be made to cancel out its influence.



Random hindsight sampling: I've talked a lot about the perverse
feedback loop where likely enactment makes p(P) high, thus defeating
our ability to measure Delta, thus making enactment impossible.

Perhaps we can avoid some of that feedback by randomly sampling the
recent market in hindsight.  There are crypto protocols that allow
fair public random number generation.  This might be done all at once
or in a few discrete stages - I have no suggestion for which is
better.

It may make sense to focus [the PDF from which the random samples are
drawn] on recent times when apparent(p(P)) was moderate, or when it
nearly co-incided with the characteristic probability of some
(yes,M,N) being traded.

This won't prevent bettors from estimating p(P) themselves, of course,
it will just prevent the enactment process itself from feeding back.



[Just math past here]

First derivation: Estimating Delta from a (yes,M,N) whose
characteristic probability is p(P).

First let's find, for scalars M and N:

       E(GDP+ (M|P - N|!P))

	 //by linearity
	 = (M E(GDP+|P) - N E(GDP+|!P))


	 //By "given" axiom 1
	 = (M E(GDP+ given P|P) - N E(GDP+ given !P|!P))

	 //By "given" axiom 2
	 = (M p(P) E(GDP+ given P) - N p(!P) E(GDP+ given !P))

	 //using definitions of Mixture and Delta and linearity:
	 = M p(P)(E(Mixture(q)) + (1 - q)E(Delta))
	     - N p(!P)(E(Mixture(q)) - q E(Delta))

Setting free parameter q =: p(P),

       E(GDP+(|P - |!P))
	 //Using q = p(P) and p(!P) = (1-p(P))
	 = M p(P)(E(Mixture(p(P))) + (1 - p(P))E(Delta)) -
	   N (1 - p(P))(E(Mixture(p(P))) - p(P) E(Delta))


	 //Rearranging, using E(Mixture(p(P))) = GDP+
	 = ((M + N) p(P) - N)GDP+ +
	    (M + N) (p(P) - p(P)^2) E(Delta)

Now we can find the expected value of ("yes",M,N):

       E("yes",M,N)
	 //definition
	 = E((GDP+ - c1) (M|P - N|!P))

	 //expanding, by linearity of E(), by E(constant) = constant
	 = E(M GDP+|P - N GDP+|!P) - (M c1|P - N c1|!P)

	 //substituting
	 = ((M + N) p(P) - N)GDP+
	   + (M + N) (p(P) - p(P)^2) E(Delta)
	   - (M c1|P - N c1|!P)

	 //Apply probabilities to c1, rearranging
	 = ((M + N) p(P) - N)(GDP+ - c1)
	   + (M + N) (p(P) - p(P)^2) E(Delta)


We can make the (GDP+ - c1) term cancel by choosing M/N such that:

	 M/N = 1/p(P) - 1

This is more symmetrical than it appears.  It's equivalent to:

	 N/M = 1/p(!P) - 1

This gives us:

	 (M + N) p(P) = N


Substituting these values of M/N:

       E("yes",(1/p(P) - 1)N,N)

	 = N/p(P) (p(P) - p(P)^2) E(Delta)

	 //cancelling p(P)
	 = N (1 - p(P)) E(Delta) ; p(P) != 0

So we could define:

       Desirability'(P) :=
	 (price("yes",(1/p(P) - 1),1)) / ((1 - p(P)))

	 = E(Delta)




Second derivation: Estimating Delta from a (yes,M,N) whose
characteristic probability is close to p(P) but not exact.

Introduce D, the difference between M/N and the characteristic
probability:

	 D := M/N - (1/p(P) - 1)

Now

       E("yes",M,N)

         = E("yes",N((1/p(P) - 1) + D),N)

	 = N (((1/p(P) - 1) + D + 1) p(P) - 1)(GDP+ - c1)
	   + N ((1/p(P) - 1) + D + 1) (p(P) - p(P)^2) E(Delta)


	 //Simplifying
	 = N D p(P)(GDP+ - c1)
	   + N ((1 - p(P)) + D (p(P) - p(P)^2)) E(Delta)

So we could define:

       Desirability'(P) :=
	 (price("yes",(1/p(P) - 1) + D,1) - D p(P)(GDP+ - c1))
	 / ((1 - p(P)) + D (p(P) - p(P)^2)).

	 = E(Delta)




Third derivation: Estimating Delta from two (yes,M,N)s whose
characteristic probabilities bracket p(P).

We will consider two (yes,M,N)s,

	 A := ("yes",Ma,Na) and
	 B := ("yes",Nb,Nb)

And define:

	 Da := Ma/Na - (1/p(P) - 1)
	 Db := Mb/Nb - (1/p(P) - 1)

Since we know Ma,Na,Mb,Na exactly, we know (Da - Db) exactly even
though we don't know Da or Db exactly.

	 (Da - Db)
	 //By definition of Da, Db
	 = Ma/Na - (1/p(P) - 1) - Mb/Nb + (1/p(P) - 1)
	 = Ma/Na - Mb/Nb

We will sum A and B with weights Wa and Wb respectively:

       Wa E("yes",Ma,Na) + Wb E("yes",Mb,Nb)

         = Wa E("yes",Na((1/p(P) - 1) + Da),Na)
	   + Wb E("yes",(Nb(1/p(P) - 1) + Db),Nb)

	 //Expanding using the formula derived earlier:
	 = (Wa Na Da + Wb Nb Db) p(P)((GDP+ - c1))
	   + ((Wa Na + Wb Nb)(1 - p(P))
	   + (Wa Na Da + Wb Nb Db) (p(P) - p(P)^2)) E(Delta)

	 //Rearranging
	 = (Wa Na Da + Wb Nb Db) p(P)(GDP+ - c1 + ((1 - p(P))E(Delta)))
	   + (Wa Na + Wb Nb)(1 - p(P)) E(Delta)

We want:

	 (Wa Na Da + Wb Nb Db) ~= 0
	 Wa != 0 or Wb != 0,

So

	 desired(Wa/Wb) := - Nb Db/(Na Da)

	 = -Nb/Na (Db/Da)

	 = Nb/Na (((Da - Db)/Da) - 1)

	 = Nb/Na (((Ma/Na - Mb/Nb)/ Da) - 1)

Turning to the first formula again,

       Wa E("yes",Ma,Na) + Wb E("yes",Mb,Nb)

	 //Using (Wa Na Da + Wb Nb Db) = 0
	 = 0 p(P)(GDP+ - c1 + ((1 - p(P))E(Delta)))
	   + (Wa Na + Wb Nb)(1 - p(P)) E(Delta)

	 = (Wa Na + Wb Nb)(1 - p(P)) E(Delta)

So we can define:

       Desirability'(P) :=
	 (Wa price("yes",Ma,Na) + Wb price("yes",Mb,Nb)) / (Wa + Wb)(1 - p(P))

	 = E(Delta)




Analysis: Sensitivity of the bracketing method to p(P):

We calculate apparent(Da):

	 apparent(Da)
	 = Ma/Na - (1/apparent(p(P)) - 1)
	 = Ma/Na - (1/(p(P) + epsilon) - 1)
	 = Ma/Na - (1/p(P) - 1) + ADaerror

Where

	 ADaerror := (epsilon/(p(P)(p(P) + epsilon)))


Find Wa/Wb

	 //Definition of Wa/Wb
	 Wa/Wb =
	     Nb/Na (((Ma/Na - Mb/Nb)/ apparent(Da)) - 1)

	 //Earlier result about (Da - Db)
	 = Nb/Na (((Da - Db)/ apparent(Da)) - 1)

	 //Substituting apparent(Da)
	 = Nb/Na (((Da - Db)/ (Ma/Na - (1/p(P) - 1) + ADaerror)) - 1)

	 //Definition of Da
	 = Nb/Na (((Da - Db)/ (Da + ADaerror)) - 1)

	 //Using (A-B)/(A + C) + B/A - 1 = (C(B-A))/A(A+C)
	 = Nb/Na
	     ((ADaerror (Db - Da)/(Da (Da + ADaerror))) - Db/Da)

So looking at the term we wanted to minimize:

	 (Wa Na Da + Wb Nb Db) =

	 = Wb(Wa/Wb Na Da + Nb Db) ; Wb != 0

	 //Substituting for Wa/Wb
	 = Wb(Nb/Na ((ADaerror (Db - Da)/(Da (Da + ADaerror))) - Db/Da) Na Da
	      + Nb Db)

	 //Simplifying
	 = Wb Nb ADaerror (Db - Da)/(Da + ADaerror)

Had we calculated this from apparent(Db), the answer would be
essentially the same, swapping all Xa and Xb, and ADaerror would be
unchanged.

So
       Total error
	 = Desirability'(P) - E(Delta)

	 //Substituting
	 =
	 ((Wb Nb ADaerror (Db - Da)/(Da + ADaerror))
	   p(P) (GDP+ - c1 + ((1 - p(P))E(Delta)))
	   + (Wa Na + Wb Nb)(1 - p(P)) E(Delta))
	  / (1 - apparent(p(P)))
	 - E(Delta)

	 //Using definition of apparent(p(P)),
	 //using A/(A-B) - 1 = B/(A-B)
	 //Using definition of ADaerror
	 //Distributing epsilon
	 =
	  epsilon
	 ((Wb Nb (Db - Da)/(Da + ADaerror))
	   (1/(p(P) + epsilon)) (GDP+ - c1 + ((1 - p(P))E(Delta)))
	   + (Wa Na + Wb Nb) E(Delta))
	  / (1 - p(P) - epsilon)

	 //Using definition of apparent(p(P))
	 //Distributing.
	 =
	  epsilon
	  ((Wb Nb (Db - Da))
	      (GDP+ - c1 + ((1 - p(P))E(Delta)))
	      / (Da + ADaerror)(apparent(p(P)) - apparent(p(P))^2)
	    + (Wa Na + Wb Nb) E(Delta)/ (1 - apparent(p(P))))

E(Delta) is indeed a component of the error term, because we scale it
by a noisy term.  To the extent that we scale it wrong, it's noise.

This tells us:

* The error is proportional to epsilon

* Nb and Na just scale the error.

* If Wb is zero (and similarly Wa), which occurs if p(P) happens to be
the characteristic probability of A or of B, the only error is from
the second term.

* The first error term is proportional to (Db - Da), the spacing
between Ma/Na and Mb/Nb.  This is welcome because spacing can easily
be small when p(P) approaches 1.

* When apparent(p(P)) is near 0 or 1, the first error term becomes
large.

* When apparent(p(P)) is near 1, the second error term also becomes
large.

Tom Breton (Tehom)

Having given it some thought, and with thanks to Wei Dai for pointing
out the problem, I think we can extract the desirability of P that we
can meaningfully compare to a threshhold.  It's a bit more
complicated, though.

We'll need to know several things:

* p(P), measured by an idea futures market.  This value will also be
called "apparent(p(P))" when it needs to be distinguished from the
true value of p(P).

* GDP+ itself, measured by yet another market.  This would probably be
measured as put(GDP+) - call(GDP+), equivalent to (c1 - GDP+).

Using that information, compute:

	 Desirability(P) =:
	     (price("yes") + (2 p(P) - 1) (c1 - GDP+)) / 2 (p(P) - p(P)^2)

and if Desirability exceeds the threshhold, enact P.  (But see shortly
below for why this needs help at {0,1})

Desirability(P) corresponds to the real difference between P and !P
outcomes.  A derivation of it is appended below.


You notice, I'm sure, the problem at the endpoints p(P) = 0 and p(P) =
1.  In fact, there are at least three problems related to the
endpoints:

* Division by zero.  This could be addressed by truncating the
effective range of apparent(p(P)), say to (0.01, 0.99).

* Long-shot bias.  Idea futures does not predict probability
accurately near the endpoints because long shots are very cheap there.
If we truncate apparent(p(P)) we probably can't do much about
long-shot bias.

* Third and worst, we don't get a meaningful value for Desirability(P)
near {0,1}.  In common sense terms, if something is a sure thing, you
can't meaningfully bet on whether or not it's a good thing.  This
consideration applies equally well to any other scheme to measure it
by betting markets.

Presumably we don't want to enact if Delta can't be confidently
recovered.  Yet we don't want low p(P) to be inescapable or high p(P)
to be self-defeating.

I don't think it's a problem that at p(P) ~= 0, we might accidentally
enact an improbable proposal due to noise.  The enactment condition
should not be instantaneous in any case, so if P moves towards being
enacted, apparent(p(P)) should respond well before P can be
accidentally enacted.

Several measures I suggest:

* Change the payoff slightly as a function of apparent(p(P)), in order
to make Delta just a little stronger when p(P) has an extreme value.

* Introduce a small random factor blocking enactment, to force p(P)
below 1 - abs(epsilon).  This might happen naturally due to the various
conditions placed on enactment.  I don't think we want to do the reverse
for the reverse case, because it's a lot worse to wrongly enact than to
wrongly not enact.

* When p(P) is takes an extreme value, require the ratio of Delta to
noise to reach a certain value, perhaps by requiring a longer period
of Desirability(P) consistently exceeding the threshhold.

* Introduce just the right amount of latency into apparent(p(P)).  The
right value for this may not be possible to guess in general because
it is sensitive to individuals' actions.


Other issues: The market measuring p(P) might be too thin.  That's
just another liquidity condition we'd need to impose.

Relatedly, I doubt that the direct GDP+ market will have a liquidity
problem because it's shared by all futarchy issues.  I'd impose a
liquidity condition there too but not consider it likely to ever be
invoked.


Derivation:

We're really dealing with two types of contingency: (a) Contingency in
conjunction with the enactment rules of the system and (b) real-world
contingent phenomena.

So let's introduce a new contingency operator, "given", which includes
only the real-world effect of policy and not the effect of any system
rules such as swapping on enactment.  The old contingency operator "|"
includes both effects.  This definition implies the axioms:

	 (A given B)|B = A|B

	 E((A given B)|B) = p(B) E(A given B)

E is the usual expected-value operator.

Let's also define:

	 Delta =: ((GDP+ given P) - (GDP+ given !P))
	 Mixture(q) =: q(GDP+ given P) + (1 - q)(GDP+ given !P)

Delta is the part we're interested in.  We'd like Desirability(P) to
be proportionate to Delta.

Mixture(q) is a linear combination of the outcomes of enacting P and not
enacting P.  It is intended to be used with 0 <= q <= 1.  If q = p(P),

Note that

	 Mixture(A+B) = Mixture(A) + B Delta.

And because a mixture of the outcomes in their relative probailities
has the same expected value as GDP+ itself and GDP+ would be directly
measured:

	 E(Mixture(p(P))) = GDP+


First, let's find E(GDP+|P - GDP+|!P):

       E(GDP+(|P - |!P))
	 //by linearity
	 = (E(GDP+|P) - E(GDP+|!P))

	 //By "given" axiom 1
	 = (E(GDP+ given P|P) - E(GDP+ given !P|!P))

	 //By "given" axiom 2
	 = (p(P)E(GDP+ given P) - p(!P)E(GDP+ given !P))

	 //using definitions of Mixture and Delta and linearity:
	 = p(P)(E(Mixture(q)) + (1 - q)E(Delta))
	     - p(!P)(E(Mixture(q)) - q E(Delta))

Setting free parameter q =: p(P),

       E(GDP+(|P - |!P))
	 //Using q = p(P) and p(!P) = (1-p(P))
	 = (p(P)(E(Mixture(p(P))) + (1 - p(P))E(Delta)) -
		 (1 - p(P))(E(Mixture(p(P))) - p(P) E(Delta)))

	 //Rearranging, using E(Mixture(p(P))) = GDP+
	 = 2 (p(P) - p(P)^2) E(Delta) + (2 p(P) - 1)(GDP+)

Now we can find the expected value of "yes":

       E("yes")
	 //definition
	 = E((GDP+ - c1)(|P - |!P))

	 //expanding, by linearity of E(), by E(constant) = constant
	 = E(GDP+|P - GDP+|!P) - (c1|P - c1|!P)

	 //substituting
	 = 2 (p(P) - p(P)^2) E(Delta) + (2 p(P) - 1)(GDP+)
	    - ((c1|P - c1|!P))

	 //Apply probabilities to c1, rearranging
	 = 2 (p(P) - p(P)^2) E(Delta) + (2 p(P) - 1)(GDP+ - c1)


And find the expected value of "Desirability":

       Desirability(P)
	 = (E("yes") + (2 p(P) - 1) (c1 - GDP+)) / 2 (p(P) - p(P)^2)

	 = (2 (p(P) - p(P)^2) E(Delta) + (2 p(P) - 1)(GDP+ - c1)
	     + (2 p(P) - 1) (c1 - GDP+))
	  / 2 (p(P) - p(P)^2)

	 //cancelling,
	 = 2 (p(P) - p(P)^2) E(Delta) / 2 (p(P) - p(P)^2)


So for p(P) != 0, p(P) != 1,

	 Desirability(P) = E(Delta)

which is what we want.



Sensitivity to apparent(p(P)):

Defining epsilon to represent the (inexact) measured value of p(P)

	 epsilon =: apparent(p(P)) - p(P)

So:
	 apparent(p(P)) = P(P) + epsilon

Note that GDP+ is a mixture on the true value p(P), so we write "GDP+"
and not "E(Mixture(apparent(p(P))))".

	 Desirability(P) =
	 (price("yes") + (2 apparent(p(P)) - 1) (c1 - GDP+))
	    / 2 (apparent(p(P)) - apparent(p(P))^2)

	 //Substituting apparent(p(P)) = P(P) + epsilon
	 = (price("yes") +
	       (2 p(P) + 2 epsilon - 1) (c1 - GDP+))
	     / 2 (p(P) - p(P)^2 + epsilon - 2 p(P) epsilon - epsilon^2 )

	 //Expanding price("yes")
	 //Note that it is a function of true p(P), not apparent(p(P))
	 = (2 (p(P) - p(P)^2) E(Delta)
	      + (2 p(P) - 1)(c1 - GDP+)
	      + (2 p(P) + 2 epsilon - 1) (c1 - GDP+))
	     / 2 (p(P) - p(P)^2 + epsilon - 2 p(P) epsilon - epsilon^2 )

	 //Simplifying
	 = ((p(P) - p(P)^2) E(Delta)
	      + epsilon (c1 - GDP+))
	     / (p(P) - p(P)^2 + epsilon - 2 p(P) epsilon - epsilon^2 )


Which says that:

* The relative contributions of Delta and (c1 - GDP+) are:

	 (p(P) - p(P)^2) / abs(epsilon)

* Most worrisome, the responsiveness to Delta disappears when
   p(P) is near 0 or near 1.

* Small though epsilon is, it dominates when p(P) is near 0 or near 1.

* The error term "epsilon (c1 - GDP+)" motivates choosing c1 to be
   approximately GDP+ to minimize the effect of epsilon.

* If apparent(p(P)) is biased towards 0.5 (long-shot bias), the error
   term moves Desirability(P) in a predictable direction related to the sign
   of (c1 - GDP+).

* The formula blows up when epsilon = 0 and p(P) = 0 or p(P) = 1, ie
   when both true and estimated values are at an extreme.


Tom Breton (Tehom)

> Sorry, I meant to look over your previous post, but forgot to.
>
>> (Proposal 2) So let's change the bundling of "yes" to:
>>
>> "yes" =
>>     ((call(GDP+) + c1 - put(GDP+))|P) -
>>     ((call(GDP+) + c1 - put(GDP+))|!P)
>>
>> In other words, if proposal P is enacted, "yes" holders swap a put for
>> a call and a zero coupon bond, all expiring or maturing at the same
>> time, all for the same strike price or face value, and "no" holders
>> have the opposite side of the swap.  If proposal P is not enacted, the
>> opposite swap is made.
>
> I don't see how this works... Wouldn't the price of "yes" be:
>
> p(P) * ((call(GDP+) + c1 - put(GDP+))|P) -
> (1-p(P)) * ((call(GDP+) + c1 - put(GDP+))|!P)
>
> where p(P) is the probability that P passes? Because if you hold "yes" you
> will payoff ((call(GDP+) + c1 - put(GDP+))|P) if P passes, which occurs
> with
> probability p(P), and you will get payoff ((call(GDP+) + c1 -
> put(GDP+))|!P)
> if P doesn't pass, which occurs with probability 1-p(P). Right?
>
> Since p(P) != 1/2 in general, how could a fixed threshold 'price("yes") >
> threshold' work?

That's a very good point Wei Dai.  My formula worked only when the
probability of enactment was 1/2.  It needs to work for any value of
that and right now it doesn't.

Tom

[In my first attempt at posting this, the head got cut off, so I'm
reposting it. I will delete the old munged post of mine]

The futarchy proposal seems to consider whether a proposal is
implemented to be a condition that is seen in hindsight after the
proposal has been implemented (or has not been).  For instance, this
seems to be assumed in section "You need a way to tell if a proposal
was implemented", page 23 of Robin Hanson's original futarchy paper
and similar section "We need to verify if a proposal was implemented",
page 19, revised version.

I guess that the motivation for this is so that the market has the
benefit of hindsight, but it's not clear to me what this hindsight
hopes to achieve.  There also seems to be no reason that shareholders'
interests would align with the goal of accurately saying in hindsight
whether a given proposal was actually implemented.

In exchange for this non-benefit as far as I can see, the arrangement
seems to invite problems.

* First, Robin anticipates one problem (ops cit).  "You need a way to
tell if a proposal was implemented", a determination that introduces
potential quibbling and legalism. (But he feels no radical change is
called for).

* Second, it seems to alloy (intended) reward for predicting policy
P's influence on GDP+ with (unintended) reward for predicting whether
P will in hindsight appear implemented.

* Third, if the payoff formula is sensitive to the time when a
proposal is enacted then the correct value for the payoff becomes
ambiguous.  Eg a swap between holders of "yes" and "no" that is
triggered by enactment.  (Maybe Robin had this problem in mind when he
proposed the called-off-bet model (See especially Wei Dai's recent
post for problems with that)).

So this arrangement seems to me an unneccessary invitation to
problems.  ISTM these problems stem from lack of a formal "trigger"
that constitutes enactment.

One candidate for a "trigger" is obvious: When it is somehow decided
to go forward with the proposal, this event itself constitutes
enacting the proposal.

My proposed solution introduces two problems.  I think they're both
solvable.

First, if the decision to go forward is a judgement call, the timing
of it could conceivably be used to game the system.  I don't think the
payoff formula I propose (see last message) is susceptible to timing
manipulation, but I'd prefer not to take chances.  Proposed solution:
Make the trigger automatic.  Eg, "The tenth straight day that the
market on P closes above 0.50".

Second, the proposal needs to be self-enacting in combination with
some automatic mechanism drawing on general resources.  It cannot
(say) call on some officeholder to do something, it needs to spell out
what existing control mechanisms are to do.  When you think about it,
a proposal should already do this anyways.

What sort of self-enacting clauses might be supported?  Some
candidates:

* Commission more detailed proposals, perhaps again using the futarchy
mechanism as a way of selecting between them.

* Put out contracts for bid and (if there is some successful bid)
funding the same from the general treasury.

* Create and fund of offices.  The intended use is to provide a means
to oversee the execution of other clauses.

* Fund contingent rewards.  Prizes, bounties, that sort of thing.

* Contingently terminate the proposal.  The intended use is to halt a
proposal if poor conditions become obvious in hindsight.

* Add to or amend formal policy.  (I use the term "policy" to
encompass a broad range of possibilities) So at the moment P is
enacted, X becomes a section of the written policy with the same
standing as any other section.  This does not ensure that officers,
judges (or w/e is governed by the policy) will really act or rule
accordingly, but neither does any act of policy-creation.

This last one is tricky for a number of reasons.  Different proposals
might make inconsistent changes to policy.  The policy might be
quickly amended by some other process, in effect undoing the proposal.
It is open-ended in its potential effect.  I propose it with full
awareness that it has problems that need solving.  I have some ideas
on solving them but I'll flesh them out another time.

Lastly, there should be a canonical form for such clauses, so it's
clear what is being invoked.  There is a side-benefit to this.  We've
discussed proposals whose terms are obscured and turn out to be
outrageous.  This formalism, while it makes nothing impossible, makes
it easy to see exactly what powers would be invoked.  I would guess
that visibility can only help.

Tom Breton (Tehom)

> where p(P) is the probability that P passes? Because if you hold "yes" you
> will payoff ((call(GDP+) + c1 - put(GDP+))|P) if P passes, which occurs
> with
       ^
Sorry, should be a "get" here.

Sorry, I meant to look over your previous post, but forgot to.

> (Proposal 2) So let's change the bundling of "yes" to:
>
> "yes" =
>     ((call(GDP+) + c1 - put(GDP+))|P) -
>     ((call(GDP+) + c1 - put(GDP+))|!P)
>
> In other words, if proposal P is enacted, "yes" holders swap a put for
> a call and a zero coupon bond, all expiring or maturing at the same
> time, all for the same strike price or face value, and "no" holders
> have the opposite side of the swap.  If proposal P is not enacted, the
> opposite swap is made.

I don't see how this works... Wouldn't the price of "yes" be:

p(P) * ((call(GDP+) + c1 - put(GDP+))|P) -
(1-p(P)) * ((call(GDP+) + c1 - put(GDP+))|!P)

where p(P) is the probability that P passes? Because if you hold "yes" you
will payoff ((call(GDP+) + c1 - put(GDP+))|P) if P passes, which occurs with
probability p(P), and you will get payoff ((call(GDP+) + c1 - put(GDP+))|!P)
if P doesn't pass, which occurs with probability 1-p(P). Right?

Since p(P) != 1/2 in general, how could a fixed threshold 'price("yes") >
threshold' work?

> > Answering my own post, I think the solution is to (a) fix the strike
price
> > early, and (b) undo the effect of external fluctuations by making the
> > enactment threshhold dependent on call(GDP+) and put(GDP+).
Specifically,
> > the threshhold should include a term:
> >
> >        2 * (call(GDP+) - put(GDP+))
> >
> > ...evaluated at the fixed strike price.
>
> Are you saying that the proposal will pass if the following is true?
>
> price("yes") - price("no") > 2 * (call(GDP+) - put(GDP+)) + fixed_threshold

Not quite.  I like to think of "yes" and "no" as long and short sides
of the same issue, rather than parallel markets.  That condition is
neccessary for my proposal.  This may have caused confusion; if so I
apologize.  I expect:

	 price("yes") = - price("no")

...so the first part of that inequation is always zero.

In any case, I'm not proposing that corrective term any more.  When I
wrote the math out, I saw that I was trying to cancel the wrong thing.
Now I propose changing the bundle that constitutes "yes", see below.

> If so, are you sure that works out for all four combinations of (proposal
> raises GDP+, proposal lowers GDP+) and (GDP+ fluctuates up, GDP+ fluctuates
> down)?

No, as it happens, when I wrote it out I found I was correcting the
wrong thing.  Let me show you how the first version of my proposal
works out, which will make it clear what the problem is.

I have in mind American-style options, but ISTM there is no reason for
early exercise, because GDP+ wouldn't pay dividends, so the valuation
should the same as for European-style options, so we can use put-call
parity in the analysis.

From the verbal definition I gave, a share of "yes" could be written
as:

	 ((call(GDP+)-put(GDP+))|P) - ((call(GDP+)-put(GDP+))|!P)

...where (X|P) means X contingent on P being enacted, and (X|!P) means
X contingent on P not being enacted.

By put-call parity,

	 put(GDP+) = call(GDP+) + c1 -  c2 * GDP+

c1 and c2 are constants: c1 = the strike price as valued at
expiration, c2 is a scalar, the ratio that we scale GDP+ down by in
order to treat it as one share of stock.  (Or 100 shares if we follow
convention, but let's not complicate the analysis with that).

So we can rewrite price("yes") as:

	 (((c2 * GDP+) - c1|P)) - (((c2 * GDP+) - c1)|!P)

...or equivalently:

	 c2 * ((GDP+|P) - (GDP+|!P)) - (c1|P - c1|!P)

The first term behaves as we want: It has positive value just if GDP+
has more value under P than under !P, negative value under the
reverse, and it's independent of c1.  It's the second term we need to
cancel.

(Proposal 2) So let's change the bundling of "yes" to:

	 "yes" =
	     ((call(GDP+) + c1 - put(GDP+))|P) -
	     ((call(GDP+) + c1 - put(GDP+))|!P)

In other words, if proposal P is enacted, "yes" holders swap a put for
a call and a zero coupon bond, all expiring or maturing at the same
time, all for the same strike price or face value, and "no" holders
have the opposite side of the swap.  If proposal P is not enacted, the
opposite swap is made.

The new bond swap exactly compensates for the second term we had
before, so price should be equivalent to just the first term:

	 price("yes") = c2 * ((GDP+|P) - (GDP+|!P))

So the basic enactment condition can be just:

	 price("yes") > threshold

(Of course the threshold might be informed by other factors, and there
might be other conditions (eg duration and liquidity))

Tom Breton (Tehom)

> Answering my own post, I think the solution is to (a) fix the strike price
> early, and (b) undo the effect of external fluctuations by making the
> enactment threshhold dependent on call(GDP+) and put(GDP+).  Specifically,
> the threshhold should include a term:
>
>        2 * (call(GDP+) - put(GDP+))
>
> ...evaluated at the fixed strike price.

Are you saying that the proposal will pass if the following is true?

price("yes") - price("no") > 2 * (call(GDP+) - put(GDP+)) + fixed_threshold

If so, are you sure that works out for all four combinations of (proposal
raises GDP+, proposal lowers GDP+) and (GDP+ fluctuates up, GDP+ fluctuates
down)?

I wrote:
> One problem is when to calculate the strike price.  If one calculates
> it late, when it's already clear the proposal will (or won't) be
> enacted, current prices of call(GDP+) and put(GDP+) already reflect that
> expectation.
>
> If one calculates it earlier, then the futarchy market will partly be
> tracking the fluctuations of call(GDP+) and put(GDP+).  We don't want to
> enact almost every proposal just because call(GDP+) rises for some
> external reason, or reject [them] just because it falls.

Answering my own post, I think the solution is to (a) fix the strike price
early, and (b) undo the effect of external fluctuations by making the
enactment threshhold dependent on call(GDP+) and put(GDP+).  Specifically,
the threshhold should include a term:

         2 * (call(GDP+) - put(GDP+))

...evaluated at the fixed strike price.

Tom

Good post.  I also had concerns about called-off bets.  I hadn't
thought of that exploit.  I had only thought of a weaker
scenario that may be just theoretical, where a deep-pocketed player
might buy their way out of an impending loss.

To fix the problem, ISTM what's needed is to use a symmetrical form of
payoff.  Instead of contingently zeroing it, contingently reverse it.
I'll flesh that out a bit:

[Proposal]

(I'll assume for the sake of simple exposition that suitable
expiration dates are chosen for options)

If the proposal is enacted, "yes" holders give "no" holders a call
option on GDP+ and in return "no" holders give "yes" holders a put
option on GDP+, same terms.

If the proposal is not enacted, the exhange is the reverse: "no"
holders give "yes" holders a call option on GDP+ and in return "yes"
holders give "no" holders a put option on GDP+, same terms.

In both cases the strike price would be set to be the same as the
strike price where call(GDP+) and put(GDP+) option prices cross over, so
it's a fair exchange.  (In practice, that probably would be
implemented by a mixture of two options at strike prices bracketing
the calculated crossover point)

[End proposal]

I'm sure you already see how that works, Wei Dai, but let me spell it
out for lurkers' benefit:

(Throughout the next few paragraphs, "rise", "fall" etc are relative
to general expectations.  Eg if GDP+ rises less than it should, that is
a case of "GDP+ falls")

If the proposal is enacted, "yes" holders think it will make the GDP+
rise more than expected.  They get call options, which gain value when
it rises, in exchange for put options, which lose value when it rises.
Given their expectations, this looks profitable to them.  "No" holders
think it will make the GDP+ fall, and they get put options in exchange
for calls, so they also expect a profit.

If the proposal is not enacted, the expectations are the opposite and
the rewards are the opposite.  "Yes" holders think a good opportunity
was missed, lowering the GDP+; now they get calls in exchange for puts,
so they again expect a profit.  "No" holders think a mistake was
avoided; they get puts in exchange for calls, again they expect a
profit.

So in every case, bettors do well by betting sincerely.

One problem is when to calculate the strike price.  If one calculates
it late, when it's already clear the proposal will (or won't) be
enacted, current prices of call(GDP+) and put(GDP+) already reflect that
expectation.

If one calculates it earlier, then the futarchy market will partly be
tracking the fluctuations of call(GDP+) and put(GDP+).  We don't want to
enact almost every proposal just because call(GDP+) rises for some
external reason, or reject then just because it falls.

Tom

One feature that distinguishes futarchy with standard prediction markets is
the "call off" feature. For every policy proposed, there are two markets
created, but one of them will always be called off, which means everyone who
traded in that market wasted all of their time and effort. I had thought of
a way to exploit this:

Suppose I propose a policy that says "The government treasury will pay
$1 million to Wei Dai." Then I trade enough futarchy assets so that
the price of "Pays GDP+ dollars if policy is adopted" is higher than
"Pays GDP+ dollars if policy is not adopted" by exactly the amount
necessary to get the policy adopted. At this point, who has incentives
to drive the price of "Pays GDP+ dollars if policy is adopted" back
down? It seems like no one, because if you do, you have to pay
transaction costs, but then the policy would not be adopted and your
trade would be canceled.

I showed this exploit to Robin in April 2003, and we talked a bit back and
forth. I think my experience was better than yours because Robin already
knew me from other discussions, but the end result is that we have different
intuitions. Robin doesn't think this is a big problem, and I do. I think
neither of us can prove what will really happen with a sufficiently
realistic mathematical model.

I guess to survive in academia, as opposed to computer security, it helps to
have a blind spot towards potential exploits. Otherwise one never publishes
one's policy ideas.

In an earlier message I proposed that the Opacity Problem might be
tamed by using controlled language and a complexity metric.

Proposal:

* Require that proposals be expressed in controlled language

* Make the threshhold of enactment a function of a proposal's
   complexity.

* Ban or place extraordinary enactment conditions on proposals whose
   complexity (measured as above) exceeds some high threshhold.

For reference, ACE (Attempto Controlled English) is an example of a
controlled language.  I'm not neccessarily proposing using ACE.  By
complexity here I mean something more akin to cyclomatic complexity
than Kolmogorov complexity.  I'm not neccessarily proposing using
cyclomatic complexity unmodified.

That fact that a proposal is expressed in controlled language makes
measuring its complexity more reasonable.  There's more to be said
about measuring complexity but that's for another time.

The intended results are that:

* To the degree that a proposal is complex, it is difficult to enact,

* There is no way to make a proposal so completely indecipherable that
   other traders are entirely deterred from trading, leaving
   manipulators free to bid an arbitrarily high price.

For the rest of this message, I'm going to focus on an issue that
makes this solution difficult, vocabulary.  Although the use of
suitable controlled language brings structural opacity under control,
vocabulary could still be opaque.

Is opaque vocabulary a serious threat?  Yes. Obscure terms could be
used, or even misleading jargon that misleads non-specialists.  But
the most serious threat is that a proposer/manipulator might arrange
it that they themselves are the defining authority for the terms they
use.  They might stipulate so in the proposal itself or use a
neologism that they can effectively monopolize authority on.

A proposer/manipulator might still be able to create the
"clone"/"gimme" dilemma by copying a proposal structurally but
judiciously substituting terms they are the defining authority on.
This trick might suffice to create proposals that can be flipped to
"clone" or "gimme".  This would recreate the entire Opacity Problem
just using opaque vocabulary.

So vocabulary does need attention.

Some terminology:

A "term" is a word or phrase that is being used.  A term exists in
some specific context.

A "lexeme" is a word or phrase as if from a dictionary.  Terms are
uses of lexemes.

A "presupposition" is a proposition that a given utterance implies and
that its negation also implies.  For instance, "The king of France is
bald" and "The king of France is not bald" both imply there is a king
of France, which is why those statements both seem not so much false
as inadmissible.

The desiderata for vocabulary for futarchy include at least:

* Each term has a definite, stable meaning in the context of the
   proposal it occurs in.

* Terms must not project presuppositions.  A lexeme can (and often
   must) have presuppositions, but then it should only be usable when
   those presuppositions are also directly asserted.  (ie, when
   provably the complete content of the term's lexeme's presuppositions
   is already asserted in the context it occurs in)

* No surprises.  Terms mean what you expect.

* Especially no meta-surprises.  If you don't know what a term means,
   it should be obvious to you that you don't.

* Vocabulary is open-ended.  New lexemes can be added when they are
   needed.

Easy to say, hard to accomplish.  One factor that makes it nasty is
that we're operating on a mapping from lexemes to definitions, and the
terms in the definitions in their turn use lexemes that need
definition.  So the problem is recursive, and at some recursion depth,
it simply requires common understanding as a primitive.

Now, there are plenty of existing lexicons of one form or another that
provide plenty of material.  For now, the problem is what they allow
in, not what they leave out.  So it's more a question of vetting terms
than of creating them.

I propose that in its early stages, futarchy use this quick-and-dirty
solution:

* A proposal must unambiguously specify which lexicon its terms are
   drawn from.

* That lexicon must have been vetted by some mechanism.

* For terms with two or more lexical senses (polysemes), a proposal
   must indicate what sense is meant. It is to do so by a canonical
   mechanism (presumably indexing).

What mechanism can we use to vet the lexicon?  Trusting products
existing institutions is one idea, but:

* That situation seems gameable at least by the institution in
   question.

* Such lexicons seem likely to encode presuppositions that we want to
   at least call into question.

* Such products may have too much inertia in other ways.

* I fear that proposers would tend to use general-purpose lexicons
   (eg, a common dictionary), which violate desideratum #1 (stable,
   definite meaning) and particularly #2 (presuppositions).  Such a
   mistake (or trick) seems impossible to remedy after the fact.  So
   the mere existence of suitable lexicons seems insufficient.

I may try to propose a vetting mechanism in another message, but I've
written enough for this message.

Tom Breton (Tehom)

In an earlier message I proposed that the Opacity Problem might be
tamed by using a parallel market to estimate uncertainty.

How might a parallel market measuring uncertainty work?  Perhaps as a
function from characteristics of derivatives (in the financial sense)
of any given futarchy proposal to a threshhold of enactment for it.

I would like to see a proposal from someone who understands stock
options better than I do.  Until that happens, this sketch by me will
have to do.

During this exposition, I'm going to assume for purposes of simple
exposition that (a) futarchy uses GDP as its utility metric, (b) GDP
is measured on a limited future interval, and (c) the options can only
be exercised during that same interval.

I'll use these notations:

	 call(X)  A call option for issue X
	 put(X)  A put option for issue X
	 X|P  Issue X contingent on proposal P being enacted.
	 U 	 The value of whatever utility metric futarchy uses.

(Sketch of proposal begins here)

Consider a pair of markets for put and call options contingent on
Proposal P being passed.  These options would use U as if it were
their underlying stock.  Ie, if a call is exercised, the seller gives
the exerciser [a predetermined fraction of U] minus the strike price,
and a put does the opposite.  We'll write them as "put(U)|P" and
"call(U)|P".

Just to be clear: contingent on Proposal P being passed, these become
puts and calls on U, the futarchy's utility metric.  This is different
than put and call options on "U|P" (which would be "put(U|P)" and
"call(U|P)").  The {put,call} and contingent-on-P operators do not
commute.

These options could only be exercised during the same future interval
that the underlying issue "U|P" will measure the U on.

Now, when there is more uncertainty about future price, put and call
options are worth more.  So if a given proposal P is unclear, then for
any given strike price, both "put(U)|P" and "call(U)|P" should be
expensive relative to "put(U)" and "call(U)" respectively.  I'm
not going to propose what specific strike price should be used here.
(But I think that it should be out of the money for both options)

The threshhold of enactment of P would be a function of both
respective differences in price.  The function must be monotonically
increasing.  For the sake of simplicity in this exposition, I'll just
say it's a ratio,

	 S * ((put(U)|P + call(U)|P) - (put(U)+ call(U)))

where S is some positive scalar.

The intended behavior is that to the degree that "U|P" is uncertain,
the threshhold of enactment is high.  This seems to be realized.



Of course we need to consider threats to this mechanism.  Several
immediately occur to me:

Threat: If (as discussed in the problem) no-one dares trade "U|P",
manipulators can still set an artificial price that exceeds whatever
threshhold is set by this mechanism.

(Note, this section refers only to the primary issue, "U|P".  The
parallel market has served its purpose)

One countervailing factor that didn't exist in the original situation
is that manipulators would have to make their insincere trades at
prices much more extreme than in the original situation.

Note that the strategy of mixing "gimmes" with "clones" of real
proposals can only deter other traders from trading below the price of
the best known proposal.  Above that price, a proposal is almost
certainly overpriced even if it might be a clone of the best known
proposal.

So when proposer/manipulators make their move, sincere traders have a
favorable situation and more leverage and are not deterred.  But until
then, the situation is the same as the original situation.

Still, the market for an obscured proposal will be thin or
nonexistent, which means both that proposer/manipulators can move the
price and that others are not likely to be tracking the issue.
Proposer/manipulators can strike at a favorable time and give no
warning.  So it's conceivable that an opaque proposal could be enacted
before other traders react to the situation.

One could hope that honest traders have booked offers somewhat above
the price of the best known proposal, and that therefore the market
becomes thick above that price.  But one doesn't expect them to do so
in ordinary markets, so it seems a stretch to rely on it.  That seems
an unreliable defense.

Some counter-rules that might help:

Counter-rule: As a precondition of enactment, require that the
enactment price be exceeded for a set period of time, not
instantaneously.  That's a good idea in general, but especially
important for this situation.

Counter-rule: As a precondition of enactment, require a certain amount
of average liquidity for the period of time mentioned in counter-rule
#1.  Again, a good idea in general, especially important here.

Counter-rule: High prices that meet high enactment threshholds should
be singled out for publication so they are not likely to be missed.

Still, it seems premature to rule out that this attack might succeed.
Therefore, this mechanism seems able to supplement another mechanism
but should not be relied on to do the job by itself.


Threat: Manipulators might try to influence these options' prices too.

In this case, unlike before, other traders can profit by correcting
out-of-line prices.  So it's not a threat.


Threat: If these options markets are too thin, they don't say much of
anything, thus blinding this mechanism.  A manipulator/proposer might
simply not make a market.

Counter-rule: Require liquidity in the options too.  Either as a
precondition of enactment, or by requiring a certain amount and kind
of market-making.  Honest proposals shouldn't be disadvantaged by
this, because they benefit from accurate uncertainty (ie, low
uncertainty).


In sum, this mechanism seems helpful but should not be relied on to do
the job by itself.

Tom Breton (Tehom)

In the last post I described the Opacity Problem, a serious problem
with futarchy.  If you haven't read it, you will need to have read it
to understand this post.

The purpose of this forum is constructive, so participants shouldn't
just point out flaws, we should also try to fix them.  That includes
me.

First, I don't believe the opacity problem can be tamed by any of the
following:

* Forbidding proposals that are encrypted, or opaque in other obvious
ways.  There are plenty of other ways of being obscure.

* Appointing someone to selectively veto proposals that have already
passed.  Effectively that gives that office complete authority, both
negative authority (by veto) and positive authority (by using the
opacity problem themselves).  That's not futarchy, that's monarchy (or
something else depending on how they hold that office)

* Just tightening the rules for enacting a proposal.  Eg, requiring a
certain volume of trade or that the price remain high for a certain
period of time.  This does not stop this attack.

What might work?  I suggest disadvantaging proposals that are not
obviously transparent.  How?  I suggest two general approaches.  Both
approaches raise the threshhold of enactment to compensate for
unclarity.

* Using the market to measure certainty.

* Controlled language + a complexity metric.

Because this problem is so serious and the two approaches are
compatible, I believe both approaches should be used.  I will talk
about each in more detail later.

Tom Breton (Tehom)

This description is borrowed from an earlier email I wrote.

The scenario I worry about is that, under the futarchy mechanism,
someone (call her Alice) makes a deliberately obscure self-serving
proposal.  Since other traders can't easily figure out what they're
trading, they are scared off, turning the market into a non-market.
Since no-one else is trading, Alice's bid or her trade with a
confederate effectively dictates the price.  She sets a price
sufficiently high to enact her self-serving proposal.

Of course that's a simplified version that doesn't consider
counter-rules and countermoves to those rules.  Other than what I
proposed wrt controlled language, I believe most counter-rules are
defeatable, but we can talk about that another time.

Here's a version with more detail:

Alice proposes the following:

	 Enact the proposal described in the plaintext corresponding to
	 this cyphertext #..dkegs4fr inscrutable cyphertext here
	 df4ix5ufh ..# as decrypted by an asymmetric RSA key whose
	 public component is #...PGP key here..#".

Of course only Alice knows what the proposal says.  By revealing the
corresponding private key later, she can reveal the corresponding
plaintext at a time of her choosing, or never reveal it at all.

Alice repeats this procedure with different keys upon a mix of
proposals, some of which are identical to promising recent proposals,
some of which are pure "gimme"s diverting public resources to her own
interests.

To the general public, these opaque proposals appear all essentially
the same.

Before revealing a proposal's content, she buys "yes" shares in it.
Regardless whether others will trade with her, she does well.  If many
do, she holds a fair amount of "yes" purchased at a moderate price
(unless the price is already higher than that, which diminishes her
profit on her "clones" but brings her that much closer to enacting her
"gimme"s) If nobody at all will trade, she effectively dictates the
price.  If just a few do, she has a mix of the two benefits.

When a "gimme" issue's price rises high enough to cause it to be
enacted, she reveals it.  She also sporadically reveals some "clone"
proposals and cashes in on the subsequent rise in price - presumably
up to the level of the claim it's a clone of.  If it doesn't rise in
price - perhaps she is boycotted - she wins anyways when the real
original claim is enacted.

This does not exhaust Alice's possible tricks.  She could also clone
some unpromising ones, thus defeating any counterstrategy that's based
on public knowledge that she wants all her proposals priced high.  But
I've written enough that you can see that.

Tom Breton (Tehom)

First, you need to be familiar with Idea Futures in order to make
sense of this.  If you're not, please read "Put Your Money Where Your
Mouth Is" Meets The Stock Market, a non-technical intro to Idea
Futures.

Let The Market Really Decide

A non-technical introduction to Futarchy in the form of a narrative.

By Tom Breton (Tehom)

================

Coston is a city with traffic problems.  Big, persistent traffic
problems that have given it a state-wide reputation as the place to
avoid.

The Coston Transit Authority has a plan, which the papers call The
Dig That's Big.  They promise that this time there will be absolutely no
cost overruns at all, and no delays either.  Nobody believes them.

The decision, however, belongs to Mayor Tommy Meno.  In his office, he
and his assistant Alan are talking.

Tommy: Alan, I'm getting old and this is probably my last term
anyways.  Forget the politics, I just want to do the right thing.  If
the Dig That's Big is the right thing, I want to go ahead.  If it's just
going to get out of hand, forget it.

Alan: Sounds like we'll all have our hands full managing it.

Tommy: No, I only get to decide whether to go ahead or not.  If I okay
it, the Transit Authority will be in charge of it.  This office
couldn't oversee construction work anyways, not effectively.

The Transit Authority has already drawn up the plans.  They estimate
that the traffic problem costs city residents $50 million a year, in
terms of an elevated accident rate, wasted fuel from idling in stalled
traffic, and late delivery charges.

My thinking is, even if there are a few cost overruns, wouldn't it be
worth it?

Alan: That depends.  How big would these overruns be?

Tommy: I have no idea.  But if they're more than $20 million, it's
unacceptable.

Alan: And how long would the delays be?

Tommy: No idea either.

Alan: So to decide whether The Dig That's Big makes sense, you need to
know
the real costs and benefits and how much it will be delayed before
committing to it.  After it's done, it will be obvious what it really
cost and how much it was delayed.

Tommy: That doesn't help me at all.  I can't jump into my time machine
and grab a copy of next year's financial report.

Alan: It helps you a little.  There are millions of people in Coston.
Some of them must be able to estimate the overruns and delays pretty
well.

Tommy: Problem is, most of them are working for construction firms.
If I poll them, they're not gonna tell me "Oh, it's really going to
cost $20 million more than I told you it would yesterday."

Alan: I don't think polling will do much for you here.  What I propose
instead is that we use Idea Futures.

Tommy: Idea Futures?  I've heard about that.  So what?

Alan: You want to know how much the Dig That's Big would really cost,
and there are people out there who know.  So you create an Idea
Futures issue about how much the Dig That's Big will cost.  The
proposition could be "The Dig That's Big will overrun estimates by $20
million or more".

Then if its going price is more than $0.50, that means its odds are
better than 1:1, which means there's a better than even chance that
the Dig That's Big will overrun by $20 million or more.

Tommy: In which case I won't go ahead with it.  But if the price is
less than $0.50, there's less than a 50% chance of an unacceptable
overrun, so I will go ahead.

It's worth a try.  I'll meet you this time tomorrow at Gator's Idea
Futures Market.

Alan: It's not that simple...

Tommy: We'll work out the details when we get there.

==

Salient points:

* It really isn't that simple, as we'll see in part 2.

* This is not Futarchy yet.  The issue itself won't decide anything,
   it just feeds one factor into a decision.

* This is not even really Idea Futures yet, because Tommy doesn't yet
   realize he's going to have to act as market maker for it to work.

* Futarchy is meant for proposals whose costs and benefits are easy to
   measure afterwards, but difficult to estimate well beforehand.

* Futarchy depends on the assumption that some people out there know
   the information, but either don't want to reveal it for free or
   can't be distinguished from people who think they know but don't.

* Costs and benefits aren't neccessarily monetary.  Delay was a cost
   too.

Points that won't carry over:

* The veiled parallels to Boston's Big Dig.  That's a motif, it's not
   subject matter.  Boston's Big Dig was actually decided and funded at
   the US federal level and managed by a state agency.

* I left out many costs for the sake of simplicity.  For instance, the
   quality of the work, safety issues, and maintainability.

* That there is only one plan being considered.  That's not
   neccessarily the case in general.  There might be multiple competing
   futarchy proposals for the same project.

* At this point they are actually measuring the wrong thing, the
   chance of an unacceptable overrun.  In the end they won't use this,
   so I'm glossing over that complication.

========

Part 2: Adding a missing piece of Idea Futures.

==

Alan enters Gator's Idea Futures Market.  Tommy is already here,
talking to a clerk.

Tommy: Alan, I just tried to create an Idea Futures issue, but the
clerk wants $10,000 to do it.  It's the city's money but I guard it
like it was my own.

Carol, the clerk: I *suggested* $10,000.

Tommy: I suggest zero.

Carol: You don't want to do that.  Look, Sal here is a contractor and
a potential player in your market.  Try to see it from his point of
view.

Sal: Mayor Meno, why should I want to bet my money on this?

Tommy: For the honor of the thing, I guess.  That's not going to work,
is it?

Sal: Nope.  Honor don't pay the bills.

Tommy: But if I pay you for playing, that's not Idea Futures at all.
So how exactly do I do this?

Carol: I've been trying to tell you.  You gotta be the market maker.
That means something different here than it means in AMEX or NYSE or
NASDAQ.  It means you create a series of pre-existing bets.  You
expect those bets to be lost.

Tommy: I expect to lose money?

Carol: Your downside exposure is limited.  In English, you can't lose
more than the $10,000 you put in.

Tommy: So if I do that, how does that make Sal want to play?

Sal: Suppose, I'm not saying this is what I really think, but suppose
your issue is trading for $0.60 and I think that there's less than a
50/50 chance of that much of a cost overrun.

Alan: You do?  Now I *know* it's a fictional example.

Sal: Heh heh.  Anyways, that means the market thinks a share of "Dig
That's Big overrun > 20mil" is worth more than I think it is.  So I
sell "yes" or if I don't own any "yes", I buy "no".

If there's an offer for, say, $0.54, I'd accept it.  But what if there
isn't an offer I like?  What if the highest offer is, say $0.40?

Carol: Then you wouldn't trade.  But you could still ask $0.54 for
it.

Sal: I might.  Or I might not want to commit myself.  Or more likely,
I wouldn't bother paying attention to your market if there's no way to
make money.

Tommy: If I did see an ask of $0.54, I'd know that the probability, as
the market estimates it, was less than 0.54.  So why shouldn't I save
my money?

Sal: Because you couldn't have much confidence in that estimate.  Most
of the people out there like me who know the score have tuned out,
because there's no profit.

That estimate also wouldn't be very precise.

Alan: But what if the going price is already about right?  What's your
incentive then?

Sal: Nothing, and in that situation I probably wouldn't trade.  But
the price is right, so you'd be all set.  You'd have the reliable
information you wanted.

Salient points:

* Market maker means something different in Idea Futures than it means
   in the ordinary stock market, but related.  In both senses, it's
   someone who assures that an issue remains "liquid".  An issue is
   liquid if you can buy it without moving the price significantly.  In
   Idea Futures, the market maker is an issue's patron, who wants to
   see it succeed so he can get the information.  In AMEX and NYSE,
   it's a firm that does so in return for special access to the market.
   ("market maker" has another less special sense too)

* The one who creates an issue generally acts as market maker too.

* Now it's really Idea Futures.  It's still not Futarchy, though.

Points that won't carry over:

* We glossed over what sort of bets the market maker should place.
   Carol just handled that.  In practice a patron would probably want
   more control.

========

Part 3: We finally talk about Futarchy ... sort of

==

Tommy: OK, I'm sold.  Let's do it.

Carol: (Ready to write) Proposition?

Alan: "The Dig That's Big will overrun estimates by $20 million or more".
No, wait!  What about the construction delays?

Tommy: Oh, the delays.  I forgot about them.  Add "The Dig That's Big
will take more than 18 months" - the Transit Authority estimated 14
months, so that will estimate the likelihood of a 4-month delay.

Carol: So you want two issues.  One about the cost overruns, one
about the delays.

Alan: Yes.  No, wait again!  Safety is an issue too.

Carol: Three.

Alan: Wait, it needs to be four.  Maintainability.  Oh, and whether
they cut corners and use substandard materials. And what about the
issues we've forgotten?

Tommy: Which issues we've forgotten?

Alan: How should I know?  But there are bound to be issues we've
forgotten.  They'll probably be obvious in hindsight.

Tommy: That's true.

Carol: Well, it doesn't help me.  What am I supposed to write as the
proposition, "Whatever issues Alan has forgotten go badly?"

Alan: Something else occurs to me.  The actual breakeven point is a
function of all those issues: cost, delays, safety, etc.  If the
delays are just barely acceptable by themselves and the cost overruns
are just barely acceptable by themselves, the situation as a whole
probably isn't acceptable.

Tommy: This is getting out of hand anyways.  I don't want to play
market-maker for a hundred issues!  That's too much and too
complicated!  I came here to create one - ONE! - issue.

Carol: But I can't write "Mayor Meno is satisfied with the Dig That's
Big" as the proposition.

Alan: Sure you can ... kind of.  Only that's subjective.  All we
really need is a metric that captures the total desirability of the
result.  Like the gross domestic product of the city.

Tommy: How does it capture all that?

Alan: Each of these issues, even safety, affects the city's GDP.
Accidents lower productivity.  So do traffic delays.  And cost
overruns take money away from where it could be used more
productively.

Tommy: So where does the Dig That's Big figure into it?

Alan: You make the payoff contingent on whether you go forward with
the Dig That's Big.  If you don't go forward, the bets are called off.
So I propose this:

	 "Scaled claim: If the Dig That's Big goes forward, each Yes
	 pays $0.01 per 1 million of Coston's GDP, and each No pays $1
	 minus the value of a Yes.  If the Dig That's Big does not go
	 forward, all transactions are rolled back."

Tommy: Do it.

Carol: So you want a called-off bet on a scaled claim.

Tommy: Yes.

Carol: Contingent on Coston's GDP.

Tommy: Yes.

Carol: Done.

Salient points:

* MAYBE treating GDP as the utility measure.  This was the measure
   Robin suggested in his earliest futarchy paper, but he also
   suggested flexibility on what the utility measure should be.  As I
   write this in October 2007, he seems to want to use national wealth.
   For that and other reasons, I don't consider this point settled.

* MAYBE called-off bets.  Robin proposed this means of making
   contingent bets, but didn't commit to it.  I have reservations about
   this being the best means.

Points that won't carry over:

* There was no date set for measuring the GDP.  Obviously the GDP is
   different in different years.  I glossed over that complication.

* The payoffs are still limited to between $0 and $1 per share.
   That's only because this explanation borrows on Idea Futures and I
   didn't want to add a complication.  Robin has never said that should
   be the case with futarchy, and I think there could at least be
   multiple ranges bracketed by pairs.

* The formula relating the payoff to Coston's GDP is unnaturally
   simple for this situation.  But the complication above cancels out
   this one.  Because the range is adapatable, the formula that links
   GDP and payoff numerically can be just a scalar multiplier.

========

Part 4: Let the market decide.  REALLY decide.

==

The futarchy issue was a success.  The price of "Dig That's Big:
effect on GDP" dropped so far that mayor Meno had no trouble deciding
not to proceed with The Dig That's Big.  He feels it was well worth
the $10,000 he spent as market-maker.

There was one other result.  Alan, feeling confident because of the
succeess, ran for next mayor.  His platform: Futarchy.  His speech
went like this:

	 Since it always makes sense to go ahead with a city project if
	 the market thinks it will improve the GDP, and it never makes
	 sense to if the market thinks it won't, why not always let the
	 market decide?  Let's automatically enact whichever proposal
	 is currently trading at the highest price, then the next, and
	 so forth down to the breakeven point.

	 And it shouldn't be just me making proposals.  Why shouldn't
	 anyone at all introduce proposals?  If they're lousy, they'll
	 do lousy in the market.  If they're good, let's enact 'em!

But this was not an idea whose time had come.  Almost nobody
understood it, and in consequence Alan lost the mayoral race.

Salient points:

* Now it's really futarchy.

* Though Alan didn't mention it, in order for him to pick the best via
   price, the issues have to all use the same formula to convert GDP
   (or w/e) to payoff, which implies they have to all be based on GDP
   (or all on the same thing)

* The public can make proposals.

* Although Alan and Tommy's earlier proposal was straightforward and
   in good faith, there's no guarantee that all others' proposals will
   be.  One has to expect that some people will try to game the system
   if they can.

* DISPUTED: Whether this situation can be abused by clever proposals.
   Robin Hanson firmly believes that it can't be.  I firmly believe it
   can.

Points that won't carry over:

* Alan is vague on how often to pick a proposal off the top of the
   market and enact it, and on where the breakeven point is.  Those
   details are not difficult, though.

================
Let The Market Decide
By Tom Breton (Tehom)
The End

It's easier to explain futarchy if I first explain Idea Futures,
another idea Robin Hanson had.  So without further ado,

"Put Your Money Where Your Mouth Is" Meets The Stock Market.

A non-technical introduction to Idea Futures in the form of a
narrative.

By Tom Breton (Tehom)

================

In the bar, two patrons are arguing.

Mike: "Nope.  No way could you eat a live catfish."

Gator: "I could so!"

Mike: "Oh yeah? Put your money where your mouth is!"

Whereupon Gator and Mike bet that if Gator eats a live catfish, Mike will
pay him $50, and if Gator fails to eat it, he will pay Mike $50.

Salient points:

* The 1:1 odds of the bet are probably more realistic than either Mike
   or Gator's estimates alone.

* It's fairly resistant to insincere participation.  It's conceivable
   but unlikely that Mike bet someone else $100 earlier tonight that
   Gator would try to eat a live catfish.

* In the short term, it does not neccessarily demonstrate rational
   belief, but in the long term, it does.  If Gator wins, Mike won't
   take another bet that involves Gator eating small animals.  Either
   he will know better or he will be too broke.  If instead Gator pays
   $50 for the privilege of proving that he can't eat a live catfish
   like he thinks he can, he'll learn better or go broke.

Points that won't carry over:

* It's just a bar bet.

* Exactly two people were involved.

* The bet is about performance by one of the people involved in the
   bet.  Idea Futures bets are more commonly about future events or
   revelations that the bettors can't influence.

* The people who want to know the outcome are the same people who
   placed bets.  In general, that need not be the case.  Commonly,
   someone wants to learn the answer but has no strong opinion
   himself. To use Idea Futures, he'd act as a market maker, which is a
   topic for another time.

* The amount being bet is symmetrical; the odds are 1:1.  Either would
   pay the other the same amount, $50.

* Each behaved as if his belief was all-or-nothing.  No probabilities
   were contemplated.

* They couldn't find a live catfish and the next morning nobody
   even remembered the conversation.


========

Part 2: The odds change.

Starting here in part 2, I'll introduce some issues about idea
futures, even though it makes the scenario less realistic.

==

The other patrons of the bar had noticed Gator and Mike's bet.

Steve: $50 says he can do it.

Peter: Don't do it, Steve.  Gator's just full of himself.  He's not
gonna eat a catfish.

Steve: So will you bet $50 with me?

Peter: No.

Gator: Cause you know I can do it.

Peter: No way you can eat another catfish.

Steve: "Another" catfish?  So he's done it before?  (pause) I still
don't think he can do it, but maybe he can.  Gator, I'll bet $10 to $50
that you can't eat a live catfish.  If you win, I give you $10.  If
you lose, you give me $50.

Gator: I'll take that bet.  Know why?  Because you figure my odds of
winning are worse than one to five.  I figure they're better than that
CAUSE I KNOW I CAN FREAKIN' DO IT!  YEAH!

Steve:  You're on!

Salient points:

* The price reflects the odds (and therefore the probabilities) as
   participants estimate them.

* The price aggregates information.  The current odds of 1:5 reflect
   new information about Gator's catfish eating proficiency.

* When someone's betting behavior is different from his comments, as
   Peter's was in the story, we have grounds to suspect that they are
   insincere, or at least not as certain as they appear.

Points that won't carry over:

* They aren't using a consistent unit of betting extent.  Steve and
   Gator's bet makes a difference of $70, but Mike and Gator's makes a
   difference of $100.

* They're ignoring a possible situation of asymmetric information.
   They think they know Gator's limitations better than he does, and
   maybe they do, but if he knows what he's doing then they are fools
   to bet at any odds that he will accept.

========

Part 3.  Buying and selling

==

Steve: I like those 5:1 odds.  Gator, I'll buy another $10 to $50 bet.

Gator: I'd love to take your money, Steve, but I just bet my last $100
to you and Mike.

Mike: And now I regret it.  Steve, how about I give you my bet?  If
Gator wins, you pay him my $50 plus your $10, and if he loses, he pays
you my $50 plus your $50.

Steve: I don't want it at those odds.  I want it at my own odds: If
Gator wins, I pay twice $10, if he loses, I get twice $50.

Gator: No way!  I have a 50/50 bet with Mike.  Your idea is just that
I get $40 less when I win.

Steve: Both Mike and I want to transfer his bet to me.  There's gotta
be some way we can do it.

How about I bet with Mike, the same amount that he already bet with
Gator.  Then Mike's old and new bets will mostly cancel each other
out.  So if Gator wins, Mike pays him $50 and gets $10 from me, so he
only loses $40.  If Gator loses, Mike gets $50 and gives it to me.

Mike: Look, I know that I was probably overconfident when I made the
bet, but I still don't think the odds are as bad as 5:1.  When I think
about what trouble he would have getting those whiskers down his
throat, I think the odds are more like fifty-fifty, which is 1:1.

Peter: Know what the problem is?  You're trying to transfer the bet as
a single unit.  That doesn't work at Mike's odds or at Steve's odds,
or even at Mike's new odds.

Stop thinking of it as a single indivisible unit.  Instead, think of
the bet as a combination of two parts: A Yes part and a No part.  A
Yes gets you paid if Gator can do it.  A No gets you paid if he can't.

It's as if when Gator and Mike made the first bet, they swapped
50 Yeses for 50 Noes.  Then Gator and Steve swapped 10 Yeses for 50
Noes.  Steve got a better deal, obviously.

Mike: So where did these valuable Yeses and Noes come from?  Since
apparently I can create them at will, why can't I pay my bar tab with
them?

Peter: (clearly doesn't know the answer) I guess they come from the
same place that Mike's Noes would go back to if he made the bet that
Steve just proposed.

Mike: So really, I own 50 of No.  Since I think it's a fifty-fifty
shot, my total Noes are worth to me ... mmm, fifty times a half, $25.

Steve: And I own 50 Noes too, but I value each No less than you do
... at somewhat more than one sixth of $50, mmm ... $8.33.

Gator: You guys don't just own Noes, you also own what I guess you
could call negative Yeses.  I own 100 Yeses, which are gonna be worth
$100 when I win, and that's $100 that you guys are gonna hafta pay me.

Peter: Aha!  So that's where the Yeses and Noes come from.  They're
balanced by negative Yeses and Noes that someone else holds.

Mike: From what you said earlier, Steve, I calculated that you value
each $1 of No at $0.17, and I value it at about $0.50.  So I oughta be
buying from you, not the other way around!  But that makes no sense.
I want out, I don't want further in.

Steve: So sell some of those negative Yeses that you have.  No, wait,
that's gotta be wrong.  They're worth less than zero.

Mike: Wait, I see it.  I buy 50 Yeses from you.  They cancel out the
negative Yeses I have.

Gator: And Steve pays me $100 when I win, because he holds 100
negative Yeses.

Mike: As for the price ... I value each Yes at $0.50 and I presume you
value a Yes at $1 minus the $0.17 you say a No is worth, that's $0.83.
Let's just split the difference and say $0.66 per Yes.  So I'll buy 50
Yeses from you for $33.25.

Steve: That makes sense to me.  Done.

(Mike gives Steve $33.25)

Salient points:

* Bets are decomposed into pairs of Yes and No.

* Yeses and Noes are transferrable, whole bets generally aren't.

* Even though a Yes or No is a sort of possession, it doesn't
   relate to any property outside the circle of bettors.  Gator, Mike,
   and Steve collectively own nothing they didn't own before.

* The price continues to change.  As we said, the price aggregates
   information, and Mike just contributed new information in his trade
   with Steve.

* The price can now be understood as the price of a Yes that would pay
   $1, or equivalently as $1 minus the price of a No that would pay $1.
   So the price can also be understood as a probability.

* It's possible to lose or gain money before the bet is settled.  Mike
   lost money because he bet overconfidently before.

Points that won't carry over:

* Negative Yeses and negative Noes.  They are in effect conditional
   IOUs.  These people seem to trust each other with $50 IOUs.  In
   general that trust wouldn't be there.

* Yeses and Noes in terms of dollars.  They need not be denominated
   in dollars.

* Steve lost 25 cents because Mike rounded the price in his own favor.

========

Part 4: The danger of negative holdings

==

Steve: And now I'll buy Yeses from Crazy Ethel and close out my
position.  Watch me bargain her down to a nickel.

Gator: No way! That would mean I'd have to get $100 from Crazy Ethel,
and that's never gonna happen.

Steve: But it's the same thing as before with me and Mike.

Gator: No it isn't.  When you sold Yeses to Mike, I sorta agreed to
let you take on his debt.  I know you're good for it.  But Ethel
isn't.

Salient points:

* A bet isn't worth much if it wouldn't be paid off.

Points that won't carry over:

* Gator's approval was needed to transfer Yeses.  In general this
   wouldn't be practical or desirable.

========

Part 5: Remove alcohol, add financal institutions.

==

Gator: You know what?  I changed my mind.  $100 is more than I trust
Steve for.  But the bet's still on.

Steve: Sounds like you've got a real dilemma, my friend.

Mike: Yeah, how are you going to have it both ways?

Gator: I've got an idea.  It's 10:30, the bank's closed.  But tomorrow
morning I'm going down there and set up a very special account.

Mike: What makes you think the bank is so much better than Ethel?
Banks sometimes go broke.

Gator: I'll take that chance.

Steve: So how's setting up an account going to help?

Gator: Because here's how I'm going to set it up: We're all going to
give the bank all of these Yeses and Noes, and the bank is going to
hold onto them.  And then whoever wins the bet - ME! - the bank's
going to give it to them.

Steve: How are we going to give the bank Yeses and Noes?  They're not
even real objects.

Gator: I thought of that.  We just give them what all the Yes and
Noes are worth.

Mike: But what they're worth changes all the time.  Believe me, I'd be
$33.25 richer right now if it didn't.

Gator: OK, OK, gimme a moment.  What doesn't change?

Peter: The price of a Yes plus a No.  Together they're always worth
$1, no matter what the bet is.

Gator: OK, I got it now.  Instead of letting you guys make Yeses and
Noes out of thin air, everyone who wants to make, say, a $1 bet gives
a dollar to the bank, and gets back a pair.

Peter: Right.  $1 and a pair are worth the same.

Gator: So then what?

Peter: Then you can sell somebody a No, and you'll have a Yes and zero
Noes plus what they paid you, instead of a Yes and minus one Noes.  So
you and the other guy only hold positives, never negatives.

Gator: Aha!  I get it now.

Steve: So, when Gator and Mike made that first bet, Mike would have
given the bank $50, and ...

Mike: Why me?  Gator should pay the $50.

Gator: Fine by me.  I got it figured out.  Since I would own 50 pairs,
you'd pay me $25 to get 50 Noes, which is half of them what I paid.

Peter: It's only exactly half in this case because it's a 1:1 bet.  In
general, he'd pay you whatever you both agree that 50 Noes are worth
at the moment.

Gator: Even more than $50?

Peter: It wouldn't be.

Mike: So regardless whether I buy the pairs or he does, we both give
$25 and the bank holds $50.  And it's the same because our odds were
1:1.

Steve: But then when I bet with Gator, we agreed on 1:5 odds.  How
many pairs should we have traded?  I get 30, but that can't be right.

Peter: Your bet with Gator was more complicated.  I'll just give you
the answer: It's the same as buying 30 pairs and trading 30 Yeses at a
little over $0.83 per Yes, plus Gator unconditionally giving you $20.
There's also an equivalent in Noes.

Gator: I unconditionally gave him $20?

Peter: You might make $30, which still leaves you with $10 profit.

Steve: Which was the deal.  $10 from me to Gator if he wins.

Gator:  OK, so it works out right.

Mike: But when I had negative 50 Yeses before, I bought 50 Yeses
from Steve so that I would have exactly zero Yeses.  If we did things
your way, I wouldn't have bothered.  My money would be in the bank and
Gator would get it when he won.  If he won.

Steve: You were holding 50 Noes and you bought 50 Yeses.  That gives
you 50 pairs.

Mike: So?

Steve: Since a pair and $1 are the same, you could take your 50 pairs
to the bank and they'd give you $50.  Right?

Gator: I guess I could set it up that way, so that the bank gave back
$1 when you gave them a pair.

Mike: And I would have paid $25 plus $33.25 to get $50 back, so even
though I got $50 back I'd still have lost money.

Steve: Wait.  Gator happens to be holding all the positive Yeses, so
if he wins it's fair he would get the whole bank account.  But what if
we did this and he lost?  I hold Noes and Mike holds Noes.  Do we
split the money or something?

Peter: Then the bank pays $1 per No.  You hold 50 so you'd get $50,
Mike also holds 50 so he gets the other $50.  Yeses really work the
same way, just Gator is holding all of them.

Mike: What if there are more Noes than there are dollars in the
account?

Peter: There can't be.  There are exactly as many Noes and Yeses as
there are pairs, and we put in $1 for every pair that was created.

Steve: And destroyed a pair for every $1 we took out.

Gator: So it works out perfect.  I like it.  Now let's go find a live
catfish.

Salient points:

* Even though a bank is a lot more reliable than Crazy Ethel,
   questions can still be raised about the winner actually getting the
   payoff.  "You can not pay off bets if the earth is destroyed".

* No holding negative Yeses or Noes.

* There are always an equal number of Yeses and Noes in existence,
   and the same number of underlying units (dollars or whatever unit is
   used) on deposit.  It's very zero-sum.

* A pair can always be created for $1 or redeemed for $1 (again, in
   whatever units)

* When the bet is settled, either Yeses or Noes pay off, contingent on
   which way the bet was settled.

Points that won't carry over:

* The use of a real bank.  That's mostly a handy expository device,
   but there are any number of complications a real bank would
   introduce, because they don't know about Idea Futures yet.

* Yeses and Noes in terms of dollars again.  They need not be
   denominated in dollars.

* We ignored interest, fees, etc.  In the fake-money web versions of
   Idea Futures we can ignore them too.  With real money, they are
   complications.

* These people have no good way of tracking who holds Yeses and Noes.
   But with computers it's easy.

* It's still among a group of people who know each other and who know
   how each other bet.  In practice, it'd be mostly anonymous, like the
   stock market.

* There being just one type of bet, binary Yes or No.  There are other
   possible types of bets, all based on mutually exclusive collectively
   exhaustive (MECE) sets.

* Payoffs being always $0 or $1.  There are also scaled bets, whose
   payoff is between $0 and $1.

====
"Put Your Money Where Your Mouth Is" Meets The Stock Market.
By Tom Breton (Tehom)
The End

Welcome!  This group exists to discuss futarchy, Robin Hanson's idea.

He summarizes it as "Vote on values but bet on beliefs".  For a
non-technical introduction, see the first few posts in the forum, from
October 2007.  There are links in the links section and papers in the
files section.

I'm sorry to report that its creator, Robin Hanson, is either not
willing or not able to see certain flaws in futarchy.  I say this with
certainty after a long and frustrating discussion with him.

It seems a shame to me to let such a promising idea die because of its
creator.  I would like those flaws to be recognized and fixed.  They
won't be if we pretend they don't exist.

That's why I created this group.  Its purpose is to discuss futarchy,
flaws and all, in a constructive manner.

Tom Breton (Tehom)