While I was away from the list, I implemented VSE and OUF simulators for my voting tool, quadelect. OUF is my term for the utility measure James Green-Armytage used in his papers; it's short for "Optimal Utility Fraction", i.e. the fraction of the time the method in question elects the highest utility winner. (One benefit to OUF is that it converges faster and is more discriminating than VSE in the spatial model setting I used. But purists would probably prefer VSE.) And then I thought I would check how much quality is lost by insisting on resistant set compliance. In line with JGA's Smith-IRV results, my simulations seem to indicate that there's not much of a loss. Which is fortunate if we want something that's highly strategy resistant. Here are the results: OUF: Number of voters: 99, number of candidates: 3 Gaussian spatial distribution, 8 dimensions, sigma = 1 Ext-Minmax 0.950199 Resistant,Ext-Minmax 0.949857 Plurality 0.918477 IRV 0.945945 Smith,IRV 0.949666 Resistant,Eurovision 0.950432 Relative resistant set compliance cost: 0.035% (Minmax) Number of voters: 99, number of candidates: 6 Gaussian spatial distribution, 8 dimensions, sigma = 1 Ext-Minmax 0.923995 Resistant,Ext-Minmax 0.923015 Plurality 0.813871 IRV 0.9066 Smith,IRV 0.921964 Eurovision 0.937177 Resistant,Eurovision 0.927298 Relative resistant set compliance cost: 0.1% (Minmax), 1.05% (Eurovision) VSE: Number of voters: 99, number of candidates: 6 Gaussian spatial distribution, 8 dimensions, sigma = 1 Ext-Minmax 0.994717 Resistant,Ext-Minmax 0.994538 Plurality 0.965466 IRV 0.991495 Smith,IRV 0.994306 Eurovision 0.996406 Resistant,Eurovision 0.995076 Relative resistant set compliance cost: 0.02% (Minmax), 0.13% (Eurovision) The Eurovision method is a weighted positional method that gives the highest ranked candidate 12 points, then 10, then 8 down to zero: (12, 10, 8, 7, ..., 1, 0, 0, 0...) So for methods that already pass majority, it doesn't seem that we lose much in terms of utility. The main costs of resistant set compliance are instead, in my opinion, that we lose monotonicity and summability, and that calculating the set is quite complex. -km

This is great, thanks for your work on this km! I'm a bit confused on the IRV results—doesn't IRV already elect from the resistant set? On Tue, Jul 23, 2024 at 4:09 PM Kristofer Munsterhjelm < km-elmet@munsterhjelm.no> wrote: > While I was away from the list, I implemented VSE and OUF simulators for > my voting tool, quadelect. OUF is my term for the utility measure James > Green-Armytage used in his papers; it's short for "Optimal Utility > Fraction", i.e. the fraction of the time the method in question elects > the highest utility winner. > > (One benefit to OUF is that it converges faster and is more > discriminating than VSE in the spatial model setting I used. But purists > would probably prefer VSE.) > > And then I thought I would check how much quality is lost by insisting > on resistant set compliance. In line with JGA's Smith-IRV results, my > simulations seem to indicate that there's not much of a loss. Which is > fortunate if we want something that's highly strategy resistant. > > Here are the results: > > OUF: > > Number of voters: 99, number of candidates: 3 > Gaussian spatial distribution, 8 dimensions, sigma = 1 > > Ext-Minmax 0.950199 > Resistant,Ext-Minmax 0.949857 > Plurality 0.918477 > IRV 0.945945 > Smith,IRV 0.949666 > Resistant,Eurovision 0.950432 > > Relative resistant set compliance cost: 0.035% (Minmax) > > Number of voters: 99, number of candidates: 6 > Gaussian spatial distribution, 8 dimensions, sigma = 1 > > Ext-Minmax 0.923995 > Resistant,Ext-Minmax 0.923015 > Plurality 0.813871 > IRV 0.9066 > Smith,IRV 0.921964 > Eurovision 0.937177 > Resistant,Eurovision 0.927298 > > Relative resistant set compliance cost: 0.1% (Minmax), 1.05% (Eurovision) > > VSE: > > Number of voters: 99, number of candidates: 6 > Gaussian spatial distribution, 8 dimensions, sigma = 1 > > Ext-Minmax 0.994717 > Resistant,Ext-Minmax 0.994538 > Plurality 0.965466 > IRV 0.991495 > Smith,IRV 0.994306 > Eurovision 0.996406 > Resistant,Eurovision 0.995076 > > Relative resistant set compliance cost: 0.02% (Minmax), 0.13% (Eurovision) > > The Eurovision method is a weighted positional method that gives the > highest ranked candidate 12 points, then 10, then 8 down to zero: (12, > 10, 8, 7, ..., 1, 0, 0, 0...) > > So for methods that already pass majority, it doesn't seem that we lose > much in terms of utility. The main costs of resistant set compliance are > instead, in my opinion, that we lose monotonicity and summability, and > that calculating the set is quite complex. > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

On 2024-07-27 22:03, Closed Limelike Curves wrote: > This is great, thanks for your work on this km! > > I'm a bit confused on the IRV results—doesn't IRV already elect from the > resistant set? Yes, both IRV and Smith,IRV do. The IRV results are intended to show: - Smith,IRV is better than plain IRV (as expected), and - There exist other resistant set methods that are better than Smith,IRV. -km