[EM] Better than Condorcet?

[Colin Champion]

A few weeks ago I argued that Bayesian decision theory was the right 
approach to voting (assuming sincere voters). I then went away and 
implemented a semi-Bayesian voting method to test my claim, comparing it 
against Condorcet methods under a carefully selected spatial model. The 
semi-Bayesian method gives 95.7% accuracy where Condorcet methods must 
fall in the range from 90.5% to 91%.

My model uses an infinite population of voters whose distribution is a 
mixture of 3 components, each of which is uniform over a unit circular 
disc. There are 4 candidates drawn randomly from the voter distribution 
(which was probably a bad decision).

The semi-Bayesian method is not very Bayesian at all; it simply solves 
the equations relating the model parameters to the ballot frequencies, 
and elects the best candidate under the implied model. It would be 
possible to improve on it by using prior information to choose between 
alternative solutions. A truly Bayesian method would integrate over the 
solution space.

I can's say that I think this proves very much. It may be of some 
interest to have an example in which Condorcet methods are beaten by a 
non-Condorcet method under a spatial model, but not many people would 
regard this as impossible. I wouldn't dream of suggesting that any 
Bayesian method was worth considering in practice, and I doubt than a 
reasonable approximation can be derived.

Anyone interested in the gory details will find them on a web page:
http://www.masterlyinactivity.com/condorcet/semibayes.html

CJC