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

[Bob Richard]

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.

fsimmons hints at this in the fourth paragraph below, in the comment 
about symmetric distributions and different definitions of "center".

In the real world, of course, dimensions of political beliefs are not 
orthogonal, and the Condorcet criterion sometimes fails to elect anyone 
without the help of a rule for handling cycles.

--Bob Richard

>
> Of course if we have a multiwinner method, we don't want all of the winners concentrated in the center of
> the population.  That's why we have Proportional Repsentation.
>
> Also the purpose of stochastic single winner methods ("lotteries") is to spread the probability around to
> avoid the tyranny of the majority.
>
> But if we want a deterministic single winner method, then we want the winner to be as representative of
> the population as possible, i.e. as close to the "center" of the population as possible.
>
> Of course there are many possible definitions of "center."  But in the centrally symmetric distributions
> used in Yee diagrams all of these definitions coincide.  So if Yee diagrams of the method fail to yield
> Voronoi polygons, the method is not centrist enough.
>
> Have Badinski and Laraki subjected their method to Yee analysis?
>
> I know it's boring for all of the politicians to posture as centrists; no matter where the polls tell them that
> it is, they will lie just as freely as they always have.  The task of the voter is still the same: to discern
> who is telling the worst lies, and who has been bought off by which interests the most.
>
> The only case in which Badinski and Laraki have a leg to stand on is the case of a bi-modal distribution
> of voters with two prominent humps.  If that is a permanent feature of the electorate, then it is important
> to replace the single winner institution with a more representative multi-winner one, or to use a lottery
> method.  Think of the Hutus and Tutsis of Rwanda.
>
> It seems to me that in most cases it is more likely that the double hump is an artifact of the divisiveness
> of a method that doesn't elect centrists.
>