[EM] Statistical analysis of Voter Models versus real life voting

[Leon Smith]

On Fri, Jan 28, 2011 at 3:08 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> One could generalize Yee diagrams to other distances than Euclidean, but
> AFAIK, there's a theorem that says that with any centrosymmetric
> distribution, the Yee diagram for a Condorcet method is the L2 Voronoi
> diagram. Warren used this to argue that Range is better than Condorcet
> because it would make more sense for voters with L1 (Manhattan distance)
> utility functions to yield L1 win regions (which Range does) and not L2
> (Euclidean) win regions, as Condorcet methods do.

Interesting,  but wouldn't you need slightly more stringent conditions
than "merely" a centrosymmetric voter distribution?    For example,
consider  four identical gaussian distributions added together,  with
the peaks placed at four corners of a square.   Then place four
candidates,  one at each peak,  and rotate the candidates around the
center of the square by 20 degrees or so.   Now you have a
centrosymmetric voter distribution and a condorcet paradox.    If your
condorcet method resorts to IRV to resolve the ambiguity,  for
example,  you certainly won't get a Voroni diagram.   (And I presume
some of the other Condorcet methods would exibit the same behavior.)

>> Given access to enough data of fully-ranked,  it seems to me that it
>> should be possible,  especially with a Yee model,  to somehow
>> determine how well that model fits real life.   Is a 2-d euclidean
>> plane a with voters ranking based on distance from the candidates a
>> reasonable model?   How would you analyze this?
>
> You may want to check Tideman's paper "The Structure of the
> Election-Generating Universe". See
> http://www2.lse.ac.uk/CPNSS/projects/VPP/VPPpdf/VPPpdf_Wshop2010/Workshop%20Papers/duBaffy2010_Plassmann.pdf
> . The paper suggests that a spatial model is the most accurate given the
> election data examined.

That paper looks interesting and very relevant,  thanks!   I haven't
examined the other links too much yet.


- Leon