re: [EM] strong FBC

[Alex Small]

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>D- What is the voodoo math model that produces the fractions ???

Voodoo math?  Try this:

In 2000, say that 6% of the voters actually liked Nader more than Gore (not
an unreasonable number).  Nonetheless, some of them may have given their
one and only vote to Gore to make sure that Bush lost.  So, say half of the
Nader faction votes (insincerely) for Gore and half votes (sincerely) for
Nader.

Is this voodoo math?

Or, if the voting machine (which I named Small Voting Machine only as a
joke, although some are now using the name) used IRV, we know that
sometimes in IRV giving more votes to the winner can cause him to lose, or
taking votes away from a loser can cause him to win.  Simple monotonicity
violation.  Some fraction of a camp might decide to vote insincerely to
make their favorite win.  If he lost ALL of his supporters he'd of course
lose, even in IRV.  But if just a few split off he might win.

Remember that the idea of the voting machine is that if a faction has an
incentive to follow an insincere strategy it assigns that strategy to the
faction.  Not because we actually want to use this machine, but to test
whether you can still have an incentive to lie to the machine.  If so, then
strong FBC is impossible.  Forest, as is usually the case, has explained it
better than I have.

Point is, a faction dividing up so that some members vote insincerely might
be part of an optimal strategy in some voting systems.  Although we'd
prefer that the voting machine not use systems that encourage such
strategies, to keep things as general as possible we're not completely
disallowing such strategies at the moment.  Especially since such "mixed
strategies" play an important role in game theory.

Or maybe game theory is just "voodoo math."  Let's ask Russell Crowe, who
won a Nobel Prize for it (this is after his stint as a Roman
gladiator)...  ;)

Alex

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