Strong FBC

[Forest Simmons]

On Sat, 4 May 2002, Adam Tarr wrote:

> At 05:23 PM 5/3/02 -0700, you wrote:
> >The Gibbard-Satterthwaite result doesn't rule out Alex's SVM (Small Voting
> >Machine) when you take into account that the voting machine is supposed to
> >apply the OPTIMAL strategy, which is sometimes a probabilistic mixture of
> >pure strategies requiring coin tosses, die throwing, or needle spinning.
>
> I'm still very skeptical that the SVM could work in theory.  The problem is
> that, in essence, this is nothing but a voting system.  Probabilistic or
> not, all this is is a system that takes in a set of preference ballots and
> produces a result.  As such, I find it extremely difficult to believe that
> some voter might not be able to achieve a better result by falsifying their
> input to the SVM.

What you say is certainly true if the utilities are not evenly
distributed.

Actually, I had in mind Lorrie Cranor's DSV (Declared Strategy Voting)
machine more than the Small Voting Machine when I wrote the above.

The DSV machine takes as inputs the voters' utilities (and the utilities
are supposed to include every value that might be considered as a basis
for making decisions).

The ideal DSV machine calculates everybody's optimum strategies based on a
complete knowledge of everybody's (submitted) utilities.

What you are asking below is, "What if some folks don't submit their
sincere utilities?"

Good question, but it has nothing to do with the G-S theorem.


>
> The G-W theorem only works when every voter knows every other voter's
> sincere preferences.  It doesn't necessarily follow that you can't spoof
> the SVM by falsifying your preferences; if everyone else thinks you are
> less likely to support the true Condorcet winner, then that can affect
> their optimal strategies.

The G-W theorem "only works" in the form, if a method is deterministic,
then it can be manipulated (except for dictator).

It says nothing about non-deterministic methods.

>
> The beauty of a method like CRAB is that it relies on the nature of
> equilibria to eventually steer the result toward a Condorcet winner.  It
> won't always work, but it usually does.  A SVM couldn't really simulate
> this, since it only has one set of preferences to work with.  If voters are
> insincere in what they enter, then they never have a chance to budge from
> this insincere position.
>
> >The beauty of Cumulative Repeated Approval Balloting is that the
> >randomness required for non-manipulability is approximated by the pseudo
> >randomness inherent in the chaos of the cyclic patterns.  So the method is
> >absolutely deterministic, but random enough to thwart insincere voting.
>
> It's not absolutely deterministic, although I admit it is close.

Actually, as Rob LeGrand said, a version of his isn't, but mine is. Mine
has a cutoff quota.  You keep going until one or more candidates has
accumulated a pre-set quota of approval, say 1001 times the number of
voters. The candidate that has surpassed that amount the most wins.

To be practical for such large quotas this method has to be automated
(i.e. simulated) and that is what I called CRAB_DSV several months ago.

I'll look up the posting when I get a chance.

For Demorep, don't worry, this method will always give the win to the
majority first choice if there is one.  The temporal proportionality comes
into play only when their is no CW.

Forest

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