[EM] Plurality equilibria

[Rob LeGrand]

Forest wrote:
> Very informative examples, but the existence of different equilibria
> doesn't quite answer the original question, which was formulated in
> terms of near optimal strategy given near perfect information.

Zero-sum games always have optimal strategies, whether simple or mixed,
for each player, but non-zero-sum games, which include most elections,
are more complicated.  Knowing the other voters' sincere preferences
just isn't enough.  You have to know their thought process too.

> Given the sincere preferences of your example it seems more likely to
> me that optimal (and near optimal) strategy for plurality would lead
to
> the other equilibrium that you mentioned:
>
> 45:Anderson   <--- insincere
> 35:Carter
> 20:Anderson

Depends.  What if the Anderson voters know that the Reagan and Carter
voters will stick to their favorites?  You might say that that's
irrational, but in non-zero-sum games rationality can be elusive. 
Consider the game of chicken, where two trucks drive straight at each
other on a skinny road.  You can swerve at the last second or not.  The
best outcome is to watch your opponent swerve while you don't; next
best is for both to swerve; third best is to swerve and give your
opponent the glory; worst is to die together in a ball of flame.  One
extremely effective strategy is to convince the other driver that
you're insane.  Scream, drink beer, throw the steering wheel out the
window.  The other driver will realize that swerving is a good
strategy, even if he loses face.  Being known as a rational player can
be to your disadvantage.  The game of chicken is symmetrical and has
two mutually exclusive equilibria.

There's an excellent treatment of zero-sum and non-zero-sum games in
Philip Straffin's Game Theory and Strategy.  Straffin also analyzes the
above election under plurality; he gives three equilibria.

=====
Rob LeGrand
robl at aggies.org
http://www.aggies.org/robl/
for Texas State Representative, District 50

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