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

[Kristofer Munsterhjelm]

Leon Smith wrote:
> There are a couple different (honest) voter models that have commonly
> been used.   The two used in Warren's Bayesian Regret simulations and
> ranked Yee diagrams come to mind, of course.

I think Warren's Bayesian Regret simulations use a number of models, 
averaging together the results over all the IEVS models. I'm not sure of 
this, however.

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.

> 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.

There's also http://politics.beasts.org/ which did a PCA type 
decomposition on survey answers to determine the number of preference 
axes for issues, rather than for political candidates themselves. This 
site suggests the dimensionality is somewhat above 1 - there's a strong 
"right/hard versus left/soft" axis, and a weaker "pragmatic" axis. I 
don't know the distribution, though.

Similar clustering attempts have been done with regards to British MPs 
(http://www.publicwhip.org.uk/mpsee.php). I think Warren did one with 
regards to United States senators, but I can't find the link at the moment.