[EM] Better than Condorcet?

[Kristofer Munsterhjelm]

On 01.02.2022 11:13, Colin Champion wrote:
> 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

There's a result that if the method X is of the form where a majority
can force an outcome, then Condorcet,X is no more strategically
susceptible than X. But no such result has (to my knowledge) been found
for VSE, and I would be surprised if there is any at all.

The best VSE-wise method I know of is Sinkhorn, which is not Condorcet
either. Perhaps you could compare your semi-Bayes method performance to
its performance?

The Sinkhorn method is implemented in Warren Smith's IEVS:
https://rangevoting.org/IEVS/IEVS.c

-km