[EM] Some myths about voting methods

[Raph Frank]

On Fri, Jun 5, 2009 at 11:54 PM, Warren Smith<warren.wds at gmail.com> wrote:
> --true.   This actually sounds like a good way to perturb the Nash equilibrium
> notion/definition to make it become more sensible than the official
> definition.

Ok, so we are in agreement  :).

> So the new improved Raphfrk+Nash notion would be, assume each player will
> play whatever strategy they select, or with probability epsilon they play
> a random strategy.   Now we only have equilibrium if no player can
> improve their expected reward, and this includes improvements by very
> tiny amounts
> proportional to epsilon^4 or whatever.

This could also be uncertainty from the perspective of the voters
about what strategy the other voters are using.  Even a tiny
uncertainty is enough to unbalance the effect.

> Here's another nasty Nash equilibrium which still applies for the
> Raphfrk-Nash version:
> In a plurality election consider say, "all vote for Gore or Bush about 50-50"
> but a higher reward would come if Nader won.   In this scenario  I guess
> you cannot improve expected reward, and in fact will worsen it, by
> switching your vote to Nader.

Right, that is the point, under plurality, if everyone is using a
strategy of "vote for Gore or Bush", then your optimal strategy is
also "vote for Gore or Bush".

However, with approval, Nader voters would use "vote for Nader and
(Gore or Bush)" and achieve a result that is better than simple "vote
for Gore and Bush".

Thus it shows  the difference between approval and plurality.

With a 50/50 situation, Bush and Gore supporters would probably also
approve Nader, at least the ones who rate him as better than the
average of Bush and Gore.  This gives a more range like result than a
condorcet one.

In practice, it is unclear what would actually happen.  I wonder if
polls would ask "which candidates do you approve", or would they still
stick with plurality polling.  Plurality polling is much easier to
collect.