[EM] Re: group strategy equilibria: no sincere CW

[Steve Eppley]

Anthony Duff asked:
> I am interested in the question of the frequency 
> of non-existence of a sincere CW.  I personally 
> do not know that it is probable.

Here's another reason to occasionally expect 
sincere cycles at the top, when we're electing 
candidates to offices: Candidates want to win!  
In other words, they'll position themselves on 
the issues in such a way as to give themselves 
a good shot at winning.  Assuming a Condorcetian 
voting method, there figures to be a bunch of 
candidates competing to be the most popular 
centrist compromise, adopting positions similar 
to each other.  I think this implies simulations 
using random electorates provide a reasonable 
estimate of the frequency of sincere cycles 
at the top.

Peter Ordeshook's book, Game Theory and Political
Theory, has a table on p.58 listing such estimates.
Here are its percentages assuming a large number 
of voters:

   #alternatives       noCW fraction
  ---------------     ---------------
         3                 .088
         4                 .176
         5                 .251
         6                 .315
         7                 .369

(Interpret the #alternatives column as the number 
of alternatives competing to be the centrist 
compromise.)

--Steve