[EM] Nash equilibrium for voting?

[Alex Small]

> For a particular situation (configuration of candidates, voters, and
> voters' utilities for the candidates), a voting Nash equilibrium is a
> configuration of votes such that no group of voters having the same
> candidate-utilities, and who have voted in the same way, can improve
> the outcome for themselves by changing their voting strategy in the
> same way.
>
> [end of definition]


I'd say that you should replace "no group of voters having the same
candidate-utilities" with "no group of voters having the same preference
orders."  If I think Gore is slightly better than Bush, and somebody else
thinks Gore is a LOT better than Bush, and we can help Gore win by
changing strategies, the different intensities of preference don't change
the fact that we'd both be happier with Gore instead of Bush.


So, as long as equilibrium is based on nobody being able to improve his
outcome while everybody else's strategies remain constant, cardinal
utilities are irrelevant, and only relative utilities matter.


One caveat:  Those of us who support third parties might be happier
seeing our favorite candidate put in an unusually strong showing, even if
it means that our lesser evil loses to our greater evil.  For instance,
Libertarians have at times threatened to use the "spoiler effect" to
punish legislators who support tax increases.  In 2002 they're hoping to
use the "spoiler effect" to defeat especially egregious "drug warriors."


These calculations based on the long-term fortunes of a political idea or
party might complicate defining Nash equilibria, and should probably be
ignored for practical purposes.




Alex



-- 
The first thing we do, let's kill all the lawyers!

Of course, that's just my opinion.  I could be wrong.


-- 
The first thing we do, let's kill all the lawyers!

Of course, that's just my opinion.  I could be wrong.


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