[EM] Detailed stats for the ordinal methods
Richard, the VoteFair guy
electionmethods at votefair.org
Thu May 9 09:08:05 PDT 2024
Bravo Kristofer! Thank you for doing these valuable calculations!!
IMO it reveals two important points:
* The methods that get the highest resistance to strategic/tactical
voting are methods that combine pairwise vote counting with IRV-style
counting. Specifically the lowest failure rates are for:
** RCIPE (IRV with pairwise eliminations)
** Benham (IRV except stop when pairwise winner)
** Smith-IRV (Woodall)
** Schwartz-IRV (Schwartz-Woodall)
** IRV.
* When a method is designed to achieve a zero failure rate for a
fairness criterion, the method develops weaknesses regarding other kinds
of failures. For example, the Schulze method achieves zero clone
failures at the expense of being less resistant to strategic/tactical
voting.
I'm excited that we are now looking deeper into election methods instead
of just looking for zero-versus-nonzero failure rates!
Again, thank you Kristofer for doing this valuable work!
Richard Fobes
The VoteFair guy
On 5/8/2024 5:56 PM, Kristofer Munsterhjelm wrote:
> I said I was going to either put up a link to or just post the detailed
> manipulability stats for the methods. Due to current simulator
> limitations, the per-category breakdown can be considerably off for
> cardinal and approval methods (as well as their hybrids), so I won't
> post those. (Namely, it may register burial or compromising as "other".)
> But for the ordinal methods, the per-category information should be
> correct. So here goes!
>
> There are a few points to note: each run for a single method starts with
> the RNG set to a fixed seed. This means that two methods that behave
> identically will have the exact same result.
>
> In addition, Ranked Pairs and the elimination methods have non-neutral
> tiebreaks: they break ties in favor of earlier numbered candidates.
> However, since the spatial generator doesn't care about the order it
> generates its candidates, this is in effect the same thing as a random
> ordering tiebreak.
>
> These effects mostly explain why Smith//IRV and Schwartz//IRV have the
> same results, and why the elimination methods (as well as RP) have zero
> ties. The thing they don't explain is how the Smith and Schwartz sets
> seem to coincide (to get the identical behavior), and I'm not sure why
> that happens.
>
> There are four strategy types:
> - Burial: every voter in the strategic coalition tries to get the
> candidate X they all prefer to the current winner W, to win, by ranking
> W uniquely at bottom.
> - Compromising: every voter in the coalition tries to get X to win
> by raising X to the top, above every other candidate.
> - Two-way: Both burial and compromising at once.
> - Other: everything else.
>
> Taking the report for Schulze as an example:
>
>> 11: Schulze
>> Ties: 0.001724 (862) Of the non-ties:
>> Burial, no compromise: 124456 0.249342
>> Compromise, no burial: 751 0.00150459
>> Burial and compromise: 1003 0.00200946
>> Two-sided: 39359 0.0788539
>> Other coalition strats: 695 0.0013924
>> ===============================================
>> Manipulable elections: 166264 0.333102
>>
>> Worked in 166264 (0.3324, 0.3338) out of 499138 for Schulze(wv) ties: 862
>
> This says that there were 862 elections where the honest outcome was a
> tie, which thus were skipped. Of those that did not have a honest tie,
>
> 24.93% of the elections were vulnerable to burial but not compromising,
> 0.15% of the elections were vulnerable to compromising but not burial,
> 0.20% of the elections were vulnerable to both compromising and burial,
> 7.89% of the elections were vulnerable to two-sided strategy but
> neither burial nor compromising on their own,
> and
> 0.14% of the elections were immune to the above strategies but
> vulnerable to something else.
>
> In total that gives 33.31% of the non-tie elections being vulnerable to
> some kind of strategy: or 166264 out of 499138.
>
>
>
>
> The detailed stats are, in no particular order, and with non-poll
> methods marked with an asterisk as before:
>
> Using ballot domain Gaussian, sigma = 1
>
> 0: *BTR-IRV
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 63778 0.127556
> Compromise, no burial: 2397 0.004794
> Burial and compromise: 198 0.000396
> Two-sided: 104608 0.209216
> Other coalition strats: 34603 0.069206
> ==========================================
> Manipulable elections: 205584 0.411168
>
> Worked in 205584 (0.4105, 0.4119) out of 500000 for
> BTREliminate-[ER-Plurality]/fd ties: 0 (0)
>
>
> 3: *Borda
> Ties: 0.007576 (3788)
> Of the non-ties:
>
> Burial, no compromise: 149385 0.301051
> Compromise, no burial: 33338 0.067185
> Burial and compromise: 77412 0.156006
> Two-sided: 84390 0.170068
> Other coalition strats: 1766 0.00355896
> ==========================================
> Manipulable elections: 346291 0.697869
>
> Worked in 346291 (0.6972, 0.6985) out of 496212 for ER-Borda ties: 3788
>
> 4: Smith//IRV (Woodall)
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 15443 0.030886
> Compromise, no burial: 2427 0.004854
> Burial and compromise: 114 0.000228
> Two-sided: 3262 0.006524
> Other coalition strats: 16050 0.0321
> ==========================================
> Manipulable elections: 37296 0.074592
>
> Worked in 37296 (0.0742, 0.075) out of 500000 for [Smith]//[ER-IRV/fd]
> ties: 0
>
> 5: Schwartz//IRV (Schwartz-Woodall)
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 15443 0.030886
> Compromise, no burial: 2427 0.004854
> Burial and compromise: 114 0.000228
> Two-sided: 3262 0.006524
> Other coalition strats: 16050 0.0321
> ==========================================
> Manipulable elections: 37296 0.074592
>
> Worked in 37296 (0.0742, 0.075) out of 500000 for
> [Schwartz]//[ER-IRV/fd] ties: 0
>
> 6: Benham
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 15627 0.031254
> Compromise, no burial: 2572 0.005144
> Burial and compromise: 70 0.00014
> Two-sided: 3062 0.006124
> Other coalition strats: 15724 0.031448
> ==========================================
> Manipulable elections: 37055 0.07411
>
> Worked in 37055 (0.0737, 0.0745) out of 500000 for
> Benham-Meta[ER-IRV/fd] ties: 0
>
> 7a: Copeland//Borda (Ranked Robin)
> Ties: 0.000498 (249)
> Of the non-ties:
>
> Burial, no compromise: 181882 0.363945
> Compromise, no burial: 449 0.000898447
> Burial and compromise: 1823 0.00364782
> Two-sided: 53215 0.106483
> Other coalition strats: 2460 0.00492245
> ==========================================
> Manipulable elections: 239829 0.479897
>
> Worked in 239829 (0.4792, 0.4806) out of 499751 for
> [Copeland]//[ER-Borda] ties: 249
>
> 7b: RCIPE
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 16077 0.032154
> Compromise, no burial: 2456 0.004912
> Burial and compromise: 282 0.000564
> Two-sided: 2765 0.00553
> Other coalition strats: 15571 0.031142
> ==========================================
> Manipulable elections: 37151 0.074302
>
> Worked in 37151 (0.0739, 0.0747) out of 500000 for Eliminate-[[Condorcet
> non-loser],[ER-Plurality]]/fd ties: 0 (0)
>
> 8: Minmax
> Ties: 0.00165 (825)
> Of the non-ties:
>
> Burial, no compromise: 123185 0.246777
> Compromise, no burial: 731 0.00146442
> Burial and compromise: 1000 0.00200331
> Two-sided: 38597 0.0773216
> Other coalition strats: 1971 0.00394852
> ==========================================
> Manipulable elections: 165484 0.331515
>
> Worked in 165484 (0.3309, 0.3322) out of 499175 for Minmax(wv) ties: 825
>
> 9: Plurality
> Ties: 0.020924 (10462)
> Of the non-ties:
>
> Burial, no compromise: 0 0
> Compromise, no burial: 204344 0.417422
> Burial and compromise: 0 0
> Two-sided: 0 0
> Other coalition strats: 0 0
> ==========================================
> Manipulable elections: 204344 0.417422
>
> Worked in 204344 (0.4167, 0.4181) out of 489538 for ER-Plurality ties:
> 10462
>
> 10: IRV
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 0 0
> Compromise, no burial: 21348 0.042696
> Burial and compromise: 0 0
> Two-sided: 0 0
> Other coalition strats: 15789 0.031578
> ==========================================
> Manipulable elections: 37137 0.074274
>
> Worked in 37137 (0.0739, 0.0747) out of 500000 for ER-IRV/fd ties: 0
>
> 11: Schulze
> Ties: 0.001724 (862)
> Of the non-ties:
>
> Burial, no compromise: 124456 0.249342
> Compromise, no burial: 751 0.00150459
> Burial and compromise: 1003 0.00200946
> Two-sided: 39359 0.0788539
> Other coalition strats: 695 0.0013924
> ==========================================
> Manipulable elections: 166264 0.333102
>
> Worked in 166264 (0.3324, 0.3338) out of 499138 for Schulze(wv) ties: 862
>
> 12: Baldwin
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 106015 0.21203
> Compromise, no burial: 72 0.000144
> Burial and compromise: 2527 0.005054
> Two-sided: 11253 0.022506
> Other coalition strats: 54895 0.10979
> ==========================================
> Manipulable elections: 174762 0.349524
>
> Worked in 174762 (0.3489, 0.3502) out of 500000 for ER-Baldwin/fd ties: 0
>
> 13: Condorcet//Borda (Black)
> Ties: 0.000266 (133)
> Of the non-ties:
>
> Burial, no compromise: 176214 0.352522
> Compromise, no burial: 2215 0.00443118
> Burial and compromise: 195 0.000390104
> Two-sided: 79258 0.158558
> Other coalition strats: 14555 0.0291177
> ==========================================
> Manipulable elections: 272437 0.545019
>
> Worked in 272437 (0.5443, 0.5457) out of 499867 for
> [Condorcet]//[ER-Borda] ties: 133
>
> 14: Raynaud
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 107385 0.21477
> Compromise, no burial: 131 0.000262
> Burial and compromise: 2576 0.005152
> Two-sided: 10936 0.021872
> Other coalition strats: 45583 0.091166
> ==========================================
> Manipulable elections: 166611 0.333222
>
> Worked in 166611 (0.3326, 0.3339) out of 500000 for
> Eliminate-[Minmax(wv)]/fd ties: 0
>
> 15: *Smith//DSC
> Ties: 0.001368 (684)
> Of the non-ties:
>
> Burial, no compromise: 141718 0.283824
> Compromise, no burial: 1246 0.00249541
> Burial and compromise: 674 0.00134985
> Two-sided: 62796 0.125764
> Other coalition strats: 1565 0.00313429
> ==========================================
> Manipulable elections: 207999 0.416568
>
> Worked in 207999 (0.4159, 0.4173) out of 499316 for [Smith]//[DSC] ties:
> 684
>
> 16: Ranked Pairs
> Ties: 0 (0)
> Of the non-ties:
>
> Burial, no compromise: 128541 0.257082
> Compromise, no burial: 759 0.001518
> Burial and compromise: 1901 0.003802
> Two-sided: 27418 0.054836
> Other coalition strats: 1846 0.003692
> ==========================================
> Manipulable elections: 160465 0.32093
>
> Worked in 160465 (0.3203, 0.3216) out of 500000 for Ranked Pairs(wv)
> ties: 0
>
> That should be right.
>
> -km
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