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, fsimm...@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
----
Election-Methods mailing list - see http://electorama.com/em for list info
