[EM] Strong FBC

[Forest Simmons]

On Mon, 6 May 2002, [iso-8859-1] Alex Small wrote:

> Forest 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.
>
> If we bloc all people who have similar preference orders and consider each
> to be a single player, couldn't we model such strategies as saying the bloc
> divided over strategy?  e.g. In a plurality race, some fraction of Nader
> supporters might hold fast and vote for him, while others may strategically
> vote insincerely for Gore.  This is equivalent then to a single
> player "dividing his vote."
>
> It would seem that such probabilistic strategies could then be modeled as
> single players dividing up their available votes in different ways.  In a
> ranked method the player might hand in a million sincerely marked ballots
> and a million insincere ballots to represent the fact that the people in
> his bloc were divided on whether to vote sincerely or strategize for a
> better outcome.
>
> The method then becomes deterministic again, and it would seem like the
> theorem should hold.
>
> Of course, there could easily be an error in my argument...
>
> Alex

That was my intuition, too, the last time I played around with trying to
use game theoretic strategies.  I never pinned it down, completely,
though.

Richard was working on this at the same time.  He might have a
counter-example.

But assume now (for the sake of argument) that if the game theoretic
oracle told your block to approve down to C7 six thirteenths of the time
and otherwise approve down to C8, then you could accomplish the same thing
by having six thirteenths of your block approve down to C7 and the rest
approve down to C8.

For this to work out exactly, you would need a multiple of thirteen voters
in your block.

Suppose that all of the blocks had exactly the right number of voters to
carry out the corresponding modifications of their oracle's instructions.

I believe that would likely result in an approval tie between two or more
candidates (assuming the oracle only recommends stochastic strategies to a
block when all deterministic block strategies are non-optimal, e.g. the
case of no Condorcet Winner).

If blocks don't have the right number of voters to split up in the
recommended proportions, then they will need to spin needles to decide
which way their "odd" person votes, if they want to optimize.

So the SVM would still be non-deterministic.

Forest


----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em