Detailed stats for the ordinal methods
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
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
Election-Methods mailing list - see https://electorama.com/em for list info
On 2024-05-09 18:08, Richard, the VoteFair guy wrote:
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.
In particular, strategy resistance seems to be linked to the resistant
set I defined last year. https://electowiki.org/wiki/Resistant_set
Here's a rough example showing just that, with Resistant,Borda. 5k
elections so it won't take so long to calculate, but the other details
are as in my previous simulations: 99 voters, 4 dimensions, and 4
candidates:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
Worked in 391 (0.0752, 0.0828) out of 4995 for [Inner burial
set],[ER-Borda] ties: 5
Going from 0.70 to 0.08 by restricting to a particular set is pretty
respectable.
The IRV hybrids you listed elect from the resistant set because they
pass a "proper order criterion": if X disqualifies Y, then X is never
eliminated before Y.
I don't quite know why electing from the resistant set seems to grant
general strategy resistance. I've only been able to prove burial
resistance, though in practice it limits other strategies too.
-km
Hi Kristofer! Thanks for this :)
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 Thu, May 9, 2024 at 10:49 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2024-05-09 18:08, Richard, the VoteFair guy wrote:
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.
In particular, strategy resistance seems to be linked to the resistant
set I defined last year. https://electowiki.org/wiki/Resistant_set
Here's a rough example showing just that, with Resistant,Borda. 5k
elections so it won't take so long to calculate, but the other details
are as in my previous simulations: 99 voters, 4 dimensions, and 4
candidates:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
Worked in 391 (0.0752, 0.0828) out of 4995 for [Inner burial
set],[ER-Borda] ties: 5
Going from 0.70 to 0.08 by restricting to a particular set is pretty
respectable.
The IRV hybrids you listed elect from the resistant set because they
pass a "proper order criterion": if X disqualifies Y, then X is never
eliminated before Y.
I don't quite know why electing from the resistant set seems to grant
general strategy resistance. I've only been able to prove burial
resistance, though in practice it limits other strategies too.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
On 2024-05-09 23:56, Closed Limelike Curves wrote:
Hi Kristofer! Thanks for this :)
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.
The narrow sense of turkey elections - exploiting nonmonotonicity to do
pushover - must, for ordinal methods, belong to the "Other" strategy
category. Not every Other strategy need to be pushover, but pushover
must be an Other strategy. Let's consider Resistant,Borda again:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
There's only one out of 4995 elections with "other" strats. So pushover
manipulability is very low. (I've designed resistant set methods that
seem to have no pushover at all, even though they fail monotonicity. I
haven't been able to prove why certain resistant set constructions make
pushover impossible, though.)
I can think of two ways to formalize the broader category of
turkey-raising as mentioned on Electowiki. They would be:
- Supporters of candidate A encourage a candidate C to enter, so that
C>B>A voters express their honest opinion; but that makes A win instead.
- By making C appear to have more support than he actually does,
supporters of candidate A trick strategic B>C>A voters to compromise for
C. As a result, the winner changes from B to A.
Neither effect is captured in my simulations: the first would be a form
of strategic nomination, and the second is a strategic play under
imperfect information. As the number of candidates doesn't change, and
the simulation involves a fully honest election followed by
full-information strategy, it doesn't capture either.
Strategic nomination can indeed be a problem and should be investigated
more closely. James-Green Armytage showed that IRV has greater exit
incentive than the Condorcet-IRV methods do, for instance. I haven't
written code to do this, and thus my stats don't provide any information
about strategic nomination.
Taking the second effect into account would be very difficult, as we're
then moving into a repeated game of imperfect information. But, as a
heuristic, if the voters know that the method has low (ordinary)
manipulability, then it would probably be harder to get them to engage
in a self-destructive strategy as well, since it would be harder to get
them to engage in strategy in general.
And a final caveat: if you combine a strategy resistant method with
primaries or other parts, the composition could have turkey strategies.
I imagine that the likelihood of this happening depends on the strategic
nomination incentives for the method: so you could see it with IRV but
it would be less likely with Smith-IRV.
-km
Strategic nomination can indeed be a problem and should be
investigated more closely. James-Green Armytage showed that IRV has
greater exit incentive than the Condorcet-IRV methods do, for instance.
Kristofer,
Can you please point me to this?
Chris
On 12/05/2024 6:18 am, Kristofer Munsterhjelm wrote:
On 2024-05-09 23:56, Closed Limelike Curves wrote:
Hi Kristofer! Thanks for this :)
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.
The narrow sense of turkey elections - exploiting nonmonotonicity to
do pushover - must, for ordinal methods, belong to the "Other"
strategy category. Not every Other strategy need to be pushover, but
pushover must be an Other strategy. Let's consider Resistant,Borda again:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
There's only one out of 4995 elections with "other" strats. So
pushover manipulability is very low. (I've designed resistant set
methods that seem to have no pushover at all, even though they fail
monotonicity. I haven't been able to prove why certain resistant set
constructions make pushover impossible, though.)
I can think of two ways to formalize the broader category of
turkey-raising as mentioned on Electowiki. They would be:
- Supporters of candidate A encourage a candidate C to enter, so
that C>B>A voters express their honest opinion; but that makes A win
instead.
- By making C appear to have more support than he actually does,
supporters of candidate A trick strategic B>C>A voters to compromise
for C. As a result, the winner changes from B to A.
Neither effect is captured in my simulations: the first would be a
form of strategic nomination, and the second is a strategic play under
imperfect information. As the number of candidates doesn't change, and
the simulation involves a fully honest election followed by
full-information strategy, it doesn't capture either.
Strategic nomination can indeed be a problem and should be
investigated more closely. James-Green Armytage showed that IRV has
greater exit incentive than the Condorcet-IRV methods do, for
instance. I haven't written code to do this, and thus my stats don't
provide any information about strategic nomination.
Taking the second effect into account would be very difficult, as
we're then moving into a repeated game of imperfect information. But,
as a heuristic, if the voters know that the method has low (ordinary)
manipulability, then it would probably be harder to get them to engage
in a self-destructive strategy as well, since it would be harder to
get them to engage in strategy in general.
And a final caveat: if you combine a strategy resistant method with
primaries or other parts, the composition could have turkey
strategies. I imagine that the likelihood of this happening depends on
the strategic nomination incentives for the method: so you could see
it with IRV but it would be less likely with Smith-IRV.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
On 2024-05-12 05:35, Chris Benham wrote:
Strategic nomination can indeed be a problem and should be
investigated more closely. James-Green Armytage showed that IRV has
greater exit incentive than the Condorcet-IRV methods do, for instance.
Kristofer,
Can you please point me to this?
Sure :-)
That's from his paper, "Four Hare-Condorcet Hybrids", which can be found
at http://www.mcdougall.org.uk/voting-matters/ISSUE29/I29P1.pdf. See
page 10, table 3; as well as Figure 3 on page 11.
For instance, with a spatial model with 99 voters, 4 dimensions, 9
initial candidates, Benham's strategic exit fraction is 0.015, while
IRV's (marked "AV" for "alternative vote") is 0.151.
The calculation is described in section 6 from page 8 onwards.
-km
The narrow sense of turkey elections - exploiting nonmonotonicity to do
pushover - must, for ordinal methods, belong to the "Other" strategy
category.
Right, that makes sense. I was thinking of turkeys just in the sense of
"very bad candidates who win because of strategic voting". So my
real question is, what happens if voters actually play strategically? We
know for score the answer is "we end up with a Condorcet method" (from
Myerson and Weber). By contrast, I'd conjecture no plurality-Condorcet
method (pairwise defeats of <50% are allowed) is actually Condorcet in the
presence of strategy.
On Sat, May 11, 2024 at 1:48 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2024-05-09 23:56, Closed Limelike Curves wrote:
Hi Kristofer! Thanks for this :)
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.
The narrow sense of turkey elections - exploiting nonmonotonicity to do
pushover - must, for ordinal methods, belong to the "Other" strategy
category. Not every Other strategy need to be pushover, but pushover
must be an Other strategy. Let's consider Resistant,Borda again:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
There's only one out of 4995 elections with "other" strats. So pushover
manipulability is very low. (I've designed resistant set methods that
seem to have no pushover at all, even though they fail monotonicity. I
haven't been able to prove why certain resistant set constructions make
pushover impossible, though.)
I can think of two ways to formalize the broader category of
turkey-raising as mentioned on Electowiki. They would be:
- Supporters of candidate A encourage a candidate C to enter, so
that
C>B>A voters express their honest opinion; but that makes A win instead.
- By making C appear to have more support than he actually does,
supporters of candidate A trick strategic B>C>A voters to compromise for
C. As a result, the winner changes from B to A.
Neither effect is captured in my simulations: the first would be a form
of strategic nomination, and the second is a strategic play under
imperfect information. As the number of candidates doesn't change, and
the simulation involves a fully honest election followed by
full-information strategy, it doesn't capture either.
Strategic nomination can indeed be a problem and should be investigated
more closely. James-Green Armytage showed that IRV has greater exit
incentive than the Condorcet-IRV methods do, for instance. I haven't
written code to do this, and thus my stats don't provide any information
about strategic nomination.
Taking the second effect into account would be very difficult, as we're
then moving into a repeated game of imperfect information. But, as a
heuristic, if the voters know that the method has low (ordinary)
manipulability, then it would probably be harder to get them to engage
in a self-destructive strategy as well, since it would be harder to get
them to engage in strategy in general.
And a final caveat: if you combine a strategy resistant method with
primaries or other parts, the composition could have turkey strategies.
I imagine that the likelihood of this happening depends on the strategic
nomination incentives for the method: so you could see it with IRV but
it would be less likely with Smith-IRV.
-km
On Sun, May 12, 2024 at 19:56 Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
[quote]
I’d conjecture no plurality-Condorcet method (pairwise defeats of <50%
are allowed) is actually Condorcet in the presence of strategy.
[/quote]
A very safe conjecture, if you’re conjecturing that the CW won’t win every
strategic circular tie. :-)
How would anyone expect the CW to always win in every strategic
circular-tie?
But the Condorcet Criterion doesn’t require that.
In one form, it’s defined for sincere voting & certain preferences. In
another form, it’s defined by who should win if someone pairbeats everyone
else, by the ballots. The latter definition requires a specification about
the balloting.
So you’re expounding to us about what’s Condorcet-complying, based on your
confusion about what the Condorcet Criterion says.
No method is guaranteed to elect the CW if someone makes a strategic
circular-tie.
But the wv Condorcet methods deter offensive-strategy so well that they
achieve the ideal of no need for defensive-strategy.
If you’re the one who said that people might do offensive strategy anyway,
an analysis of the likely result is the strategist’s business.the whole
point of strategy.
On Sat, May 11, 2024 at 1:48 PM Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 2024-05-09 23:56, Closed Limelike Curves wrote:
Hi Kristofer! Thanks for this :)
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.
The narrow sense of turkey elections - exploiting nonmonotonicity to do
pushover - must, for ordinal methods, belong to the "Other" strategy
category. Not every Other strategy need to be pushover, but pushover
must be an Other strategy. Let's consider Resistant,Borda again:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
There's only one out of 4995 elections with "other" strats. So pushover
manipulability is very low. (I've designed resistant set methods that
seem to have no pushover at all, even though they fail monotonicity. I
haven't been able to prove why certain resistant set constructions make
pushover impossible, though.)
I can think of two ways to formalize the broader category of
turkey-raising as mentioned on Electowiki. They would be:
- Supporters of candidate A encourage a candidate C to enter, so
that
C>B>A voters express their honest opinion; but that makes A win instead.
- By making C appear to have more support than he actually does,
supporters of candidate A trick strategic B>C>A voters to compromise for
C. As a result, the winner changes from B to A.
Neither effect is captured in my simulations: the first would be a form
of strategic nomination, and the second is a strategic play under
imperfect information. As the number of candidates doesn't change, and
the simulation involves a fully honest election followed by
full-information strategy, it doesn't capture either.
Strategic nomination can indeed be a problem and should be investigated
more closely. James-Green Armytage showed that IRV has greater exit
incentive than the Condorcet-IRV methods do, for instance. I haven't
written code to do this, and thus my stats don't provide any information
about strategic nomination.
Taking the second effect into account would be very difficult, as we're
then moving into a repeated game of imperfect information. But, as a
heuristic, if the voters know that the method has low (ordinary)
manipulability, then it would probably be harder to get them to engage
in a self-destructive strategy as well, since it would be harder to get
them to engage in strategy in general.
And a final caveat: if you combine a strategy resistant method with
primaries or other parts, the composition could have turkey strategies.
I imagine that the likelihood of this happening depends on the strategic
nomination incentives for the method: so you could see it with IRV but
it would be less likely with Smith-IRV.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
I'm thinking more along the lines of Burt Monroe's nonelection of
irrelevant alternatives. He shows Nanson, Baldwin, and any system
equivalent to Minimax in the 3-candidate case fails the Condorcet criterion
with strategic voting.
On Sun, May 12, 2024 at 8:27 PM Michael Ossipoff email9648742@gmail.com
wrote:
On Sun, May 12, 2024 at 19:56 Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
[quote]
I’d conjecture no plurality-Condorcet method (pairwise defeats of <50%
are allowed) is actually Condorcet in the presence of strategy.
[/quote]
A very safe conjecture, if you’re conjecturing that the CW won’t win every
strategic circular tie. :-)
How would anyone expect the CW to always win in every strategic
circular-tie?
But the Condorcet Criterion doesn’t require that.
In one form, it’s defined for sincere voting & certain preferences. In
another form, it’s defined by who should win if someone pairbeats everyone
else, by the ballots. The latter definition requires a specification about
the balloting.
So you’re expounding to us about what’s Condorcet-complying, based on your
confusion about what the Condorcet Criterion says.
No method is guaranteed to elect the CW if someone makes a strategic
circular-tie.
But the wv Condorcet methods deter offensive-strategy so well that they
achieve the ideal of no need for defensive-strategy.
If you’re the one who said that people might do offensive strategy anyway,
an analysis of the likely result is the strategist’s business.the whole
point of strategy.
On Sat, May 11, 2024 at 1:48 PM Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 2024-05-09 23:56, Closed Limelike Curves wrote:
Hi Kristofer! Thanks for this :)
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.
The narrow sense of turkey elections - exploiting nonmonotonicity to do
pushover - must, for ordinal methods, belong to the "Other" strategy
category. Not every Other strategy need to be pushover, but pushover
must be an Other strategy. Let's consider Resistant,Borda again:
Ties: 0.001 (5)
Of the non-ties:
Burial, no compromise: 123 0.0246246
Compromise, no burial: 72 0.0144144
Burial and compromise: 147 0.0294294
Two-sided: 48 0.00960961
Other coalition strats: 1 0.0002002
---===============
Manipulable elections: 391 0.0782783
There's only one out of 4995 elections with "other" strats. So pushover
manipulability is very low. (I've designed resistant set methods that
seem to have no pushover at all, even though they fail monotonicity. I
haven't been able to prove why certain resistant set constructions make
pushover impossible, though.)
I can think of two ways to formalize the broader category of
turkey-raising as mentioned on Electowiki. They would be:
- Supporters of candidate A encourage a candidate C to enter, so
that
C>B>A voters express their honest opinion; but that makes A win instead.
- By making C appear to have more support than he actually does,
supporters of candidate A trick strategic B>C>A voters to compromise for
C. As a result, the winner changes from B to A.
Neither effect is captured in my simulations: the first would be a form
of strategic nomination, and the second is a strategic play under
imperfect information. As the number of candidates doesn't change, and
the simulation involves a fully honest election followed by
full-information strategy, it doesn't capture either.
Strategic nomination can indeed be a problem and should be investigated
more closely. James-Green Armytage showed that IRV has greater exit
incentive than the Condorcet-IRV methods do, for instance. I haven't
written code to do this, and thus my stats don't provide any information
about strategic nomination.
Taking the second effect into account would be very difficult, as we're
then moving into a repeated game of imperfect information. But, as a
heuristic, if the voters know that the method has low (ordinary)
manipulability, then it would probably be harder to get them to engage
in a self-destructive strategy as well, since it would be harder to get
them to engage in strategy in general.
And a final caveat: if you combine a strategy resistant method with
primaries or other parts, the composition could have turkey strategies.
I imagine that the likelihood of this happening depends on the strategic
nomination incentives for the method: so you could see it with IRV but
it would be less likely with Smith-IRV.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info