[EM] How to fix the flawed "Nash equilibrium" concept for voting-theory purposes

[Jameson Quinn]

2010/4/14 Thomas von der Elbe <ThomasvonderElbe at gmx.de>

> Hello,
>
> Warren Smith wrote:
>
>> For example, consider a 2-way election Gandhi vs Hitler in which everybody
>> votes
>> for the (unanimously agreed to be) worst choice: Hitler.
>>
>> Well, that is a "Nash equilibrium" because no single voter can change
>> the election result!
>>
>> Indeed, essentially every possible vote pattern in every possible
>> large election, is a Nash equilibrium.
>>
>
> If the election-method is proxy-voting, then a Nash equilibrium seems to
> not exist. Because you can then vote for a voter of Hitler. This in itself
> is already a payoff (because Hitler gets less direct votes). But even
> further it's possible to vote for a voter of Hitler who says something like:
> I delegate all my votes to Hitler until I have 50% of all votes, then I
> delegate them to Gandhi.
>

What do you think?
>

Doesn't work. Everybody (bizarrely) voting Hitler is still an equilibrium,
as long as there is no individual majority-holder among those who directly
vote for Hitler. (For instance, three proxy groups at the second-to-top
level.)

JQ
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