Re: [EM] Statistical analysis of Voter Models versus real life voting
Hi Kevin, On Fri, Jan 28, 2011 at 11:01 AM, Kevin Venzke step...@yahoo.fr wrote: The 2D Yee diagrams cast voters around a point without any bias in favor of one dimension or the other, as far as I know. I don't think that is likely to be realistic. I think a 1D Yee diagram would be more realistic. Or else have 2D, but the second dimension is much narrower. Well, I don't see why you couldn't create a Yee diagram that doesn't use a rotationally-symmetric gaussian distribution; or even some kind of double- or triple- humped distributions. Of course interpreting a diagram would probably be a bit harder. I don't know how to prove that some approach is realistic though. In real life we tend to see a single dimension for single-winner seats, but that could be a product of nomination disincentive produced by the particular method (or political framework) being used. Well, that is true. New Hampshire's legislature is considering a bill that would introduce approval voting state-wide; I do hope it passes, and if it does I can't help but think most voters will continue voting for a single candidate because they won't be aware of the changes, or they'll see it as somehow cheating or otherwise view it with suspicion.(Or even irrationally believing that voting for their most preferred candidate in addition to a Republican or Democrat would somehow be a waste of a vote, helping their least preferred choice win, etc.) I suspect that it will take a generation or two before voting patterns really change in New Hampshire. But maybe I'm a little overly cynical and pessimistic; some time ago I do remember seeing two otherwise identical polls in the UK conducted with vote for one versus vote for many rules, and support for a few of the smaller parties grew quite dramatically. It seems to me a government vs. opposition mindset causes voters to think in terms of a single dimension. I also don't think Yee diagrams based on sincere voting are all that compelling. I remain rather unconvinced that Yee diagrams are a good argument for Approval or Condorcet, but I sure do think they are a compelling argument against Instant Runoff Voting. Best, Leon Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Statistical analysis of Voter Models versus real life voting
On Fri, Jan 28, 2011 at 3:08 PM, Kristofer Munsterhjelm km-el...@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 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Statistical analysis of Voter Models versus real life voting
Simplified models can be used to prove something about real life if one assumes that the model is accurate enough for the situation in question. 2D models are often very good in demonstrating and visualizing some properties of voting methods. But they can thus not be assumed to prove some generic results (with no assumptions on the applicability of the used model). For many cases Yee and 2D models, with some chosen voter distribution etc. may work very well, but one has to check and justify their applicability well before drawing any strong conclusions. Juho Laatu On 28.1.2011, at 15.49, 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. 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? Best, Leon Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Statistical analysis of Voter Models versus real life voting
Leon Smith wrote: On Fri, Jan 28, 2011 at 3:08 PM, Kristofer Munsterhjelm km-el...@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.) I recalled it incorrectly. The actual version is that if you draw a Yee diagram with voters clustered centrosymmetrically around each pixel, whose utility is a function of Lp distance (for p = some L-norm, p = 1 Manhattan, p = 2 Euclidean, etc) between the candidate and voter in question, then a Condorcet method renders the Lp Voronoi diagram, but when p is not equal to 2, the social optimal method may not be the Lp Voronoi diagram. See the bottom of http://rangevoting.org/BlackSingle.html for an example. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] An interesting real election
Here is an unusual case from a real poll run recently by a group using CIVS. Usually there is a Condorcet winner, but not this time. Who should win? Ranked pairs says #1, and ranks the six choices as shown. It only has to reverse one preference. Schulze says #2, because it beats #6 by 15-11, and #6 beats #1 by 14-13. So #2 has a 14-13 beatpath vs. #1. Hill's method (Condorcet-IRV) picks #6 as the winner. -- Andrew 1. 2. 3. 4. 5. 6. 1. - 13 15 17 16 13 2. 9 - 13 14 17 15 3. 11 11 - 13 15 14 4. 9 10 10 - 14 13 5. 11 10 9 10 - 13 6. 14 11 11 13 10 - Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] An interesting real election
Hallo, over a long period of time, the Simpson-Kramer method was considered to be the best Condorcet method because this method minimizes the number of overruled voters. However, the Simpson-Kramer method has recently been criticized e.g. for violating the Smith criterion, reversal symmetry, and independence of clones. Therefore, my aim was to find a method that satisfies the Smith criterion, reversal symmetry, and independence of clones and that chooses the Simpson-Kramer winner wherever possible. In your example, candidate #2 is the Simpson-Kramer winner. Therefore, candidate #2 should be elected. See section 1 of my paper: http://m-schulze.webhop.net/schulze1.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
