[EM] Strong FBC

[Alex Small]

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

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