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

[Bob Richard]

After looking up some old email threads, it now seems to me that I made 
a significant mistake in the post below. It is true that the model 
underlying Yee diagrams guarantees that there will always be a Condorcet 
winner. But apparently that has nothing to do with the two dimensions 
being orthogonal. It results from the fact that voters are normally 
distributed on both dimensions.

--Bob Richard


On 7/13/2011 2:19 PM, Kristofer Munsterhjelm wrote:

> 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.)
>
>

-- 
Bob Richard
Executive Vice President
Californians for Electoral Reform
PO Box 235
Kentfield, CA 94914-0235
415-256-9393
http://www.cfer.org