[EM] Manipulability stats for every tested method (plus Approval Sorted Margins)

[Ted Stern]

I suspect that Margin Sort Approval doesn't perform as well with mean
utility cutoff.

Chris Benham's proposal was that by default the cutoff should be one rank
below top. In general, this is a good rule of thumb to follow.

Strategically, I think the cutoff should be just below the voter's
highest ranked candidate who has a chance (who would be in the Smith set if
some other faction strategically tries to induce a cycle). I.e.,

Long-shot-1 > Long-shot-2 > Contender-1 *>>* Contender-2 > etc.

On Fri, May 10, 2024 at 3:43 PM Closed Limelike Curves <
closed.limelike.curves at gmail.com> wrote:

> I do want to ask though, do you think the rate of manipulable elections
>> is a good measure of the "general strategy resistance" of an electoral
>> method? The resistant set certainly seems to reduce that rate, but for all
>> I know that 7.5% is all turkey-elections.
>
>
> On Fri, May 10, 2024 at 12:29 PM Kristofer Munsterhjelm <
> km_elmet at t-online.de> wrote:
>
>> Here are the manipulability stats that I've checked, for methods
>> cardinal and ordinal. I've also added Approval Sorted Margins (or MSA),
>> as I ran that test last night. As usual, asterisks mark non-poll methods.
>>
>> 0.937    *Range(0-5, absolute scale)
>> 0.928    Approval (absolute scale)
>>
>> 0.710    *Range (0-10, normalized)
>> 0.708    *Range(0-5, normalized)
>> 0.705    Smith//Range(0-5, absolute scale)
>>
>> 0.698    *Borda
>> 0.666    Approval (mean utility cutoff)
>> 0.655    Smith//Range(0-10, absolute scale)
>> 0.645    STAR
>>
>> 0.564    Smith//Range (0-5, normalized)
>> 0.557    Smith//Range (0-10, normalized)
>> 0.545    Condorcet//Borda (Black)
>> 0.514    Smith//Approval (explicit, mean utility cutoff)
>> 0.508    Approval Sorted Margins (mean utility cutoff)
>> 0.490    Smith//Approval (implicit, mean utility cutoff)
>>
>> 0.480    Copeland//Borda (Ranked Robin)
>> 0.443    Smith//DAC (mean utility truncation)
>>
>> 0.417    Plurality
>> 0.412    *BTR-IRV
>>
>> 0.350    Baldwin
>> 0.333    Raynaud (Gross Loser Elimination)
>> 0.333    Schulze(wv)
>> 0.332    Minmax(wv)
>> 0.321    Ranked Pairs(wv)
>>
>> 0.075    Woodall, Schwartz-Woodall
>> 0.074    RCIPE
>> 0.074    IRV
>> 0.074    Benham
>>
>> -km
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>>
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