On 7/13/2011 11:14 AM, [email protected] 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.
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