Strong FBC

[Adam Tarr]

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.

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 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.  Alex came 
up with this example where Approval voting can settle in a rut:

25 A>B>C
49 B>A>C
26 C>A>B

Now suppose the initial approval votes are

25 AB
49 B
26 C

So B wins, 25-74-26, even though A is the Condorcet winner.  No voter has a 
clear incentive to change their vote; the vote combination is a Nash 
equilibrium, when factions are considered players.  Now this rut is very 
tenuous, and one could certainly imagine the voters breaking out of 
it.  But they will not certainly break out of it.

Don't get me wrong; I think CRAB is a fabulous procedure for committees and 
other settings that can support repeated balloting.  I just don't believe 
that it is completely deterministic.

Has anyone tried to simulate a repeated approval balloting election where 
some voters use insincere strategy - that is, they approve a candidate who 
they like less than a candidate they do not approve?  Obviously, there is 
no incentive to do so in a normal approval vote, but in a repeated approval 
vote, such disinfestation may help you by convincing other voters to 
approve your favorite as a compromise.

-Adam

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