[EM] Yee diagrams and Condorcet (was Centrist vs. non-Centrists (was A distance based method))

[Kristofer Munsterhjelm]

Bob Richard wrote:
> On 7/13/2011 11:14 AM, fsimmons at pcc.edu wrote:
> 
>> Jameson, I'm surprised that you consider a Condorcet method to be too 
>> extremist or apt to suffer center
>> squeeze.
>>
>> Think Yee diagrams; all Condorcet methods yield identical diagrams, 
>> while center squeeze shows up
>> clearly in methods that allow it.
> 
> This is a sidebar in this thread, but worth pointing out anyway.
> 
> The reason all Condorcet-compliant methods yield the same Yee diagrams 
> is that Yee's model guarantees that there will always be a Condorcet 
> winner. This is the because the two dimensions on which voters and 
> candidates vary are forced to be orthogonal. In fact, Yee's 
> computational method (at least in in the version I looked at a long time 
> ago) doesn't even count votes, much less care what completion method is 
> used. It just picks the candidate closest to the median (and mean) 
> voter, relying on theorems in social choice theory.

Not all voting methods are equally well-behaved. IRV, for instance, can 
be chaotic. Thus I think Yee's originally code counted the ballots 
instead of trying to find the right shape directly; at least that is 
what Warren's IEVS does, as does my simulator.

I have thought about ways to speed up the actual ballot generation by 
considering Gaussian integrals instead of sampling from the Gaussians, 
but the implementation would be tricky.

(Though if one had a "which criteria does this method pass" field in 
one's simulator, it would be relatively simple to just reproduce the 
Voronoi diagram for all Condorcet-compliant methods. The Voronoi diagram 
can even be calculated in n log n time with fancy data structures.)