[EM] Some utility results for resistant set methods

[Closed Limelike Curves]

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 at 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
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>
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