[EM] The best voting methods with honest voters

[Warren Smith]

IEVS ran for a few days using honest voters and random normal utilities.
I have now also implemented Venzke's "vote for and against" method (which is not 
the same as mine) under the name "VenzkeDisqPlur"; and 
Condorcet//Approval and UncoveredSet, bringing us up to 39 voting methods.
(Your contributions will be welcomed...)
But none of those were written when I ran this sim. 
[It appears with honest voters VenzkeDisqPlur is better than Plurality but
worse than Top2Runoff, becoming the same as Plurality if there are a lot of candidates;
UncoveredSet is better than the Smith and Schwartz sets, but not by much.]

Strategic voting is not yet ready to roll.  However, you can for example regard
"honest-approval" as the same thing as "strategic range voting" 
(which by the way is not quite true...)  and hence are
in a position to make some comparisons.  You will find, for example, that
under the sim conditions strategic zero-info range is superior to honest Bucklin, 
honest DMC, honest Raynaud, honest SmithIRV,
and honest IRV, which seems a severe indictment of those systems
and is contrary to many peoples' intuition.  For example (just to rub that in),
Chris Benham has at various times informed me that ER-Bucklin, SmithIRV, and DMC
were his favorite methods and he disliked Range voting because of its strategic properties,
in particular the fact zero-info strategic range voting is not the same as honest range
voting.  But the sim shows that even with fully honest voters, all of those Benham-favored
systems perform worse than Range even with 100% strategic (zero-info) voters.
I conclude from this that the zero-info honesty criterion can and does mislead you!

Source code:
Here are some results.

(NumVoters=1535, NumCands=7, NumElections=1999999, IgnoranceAmplitude=0.001000)
The voting methods with BayesianRegret < 10 have * and those with BR<6 have **.
Method, & BayesianRegrets & #Agreements with Condorcet Winner (when CW exists)
0=SociallyBest                  0         909726   **
1=SociallyWorst            105.95            115
2=RandomWinner            52.9372         180594
3=Plurality               21.0808         572465
4=Borda                   4.54339         1063164  **
5=IRV                     11.4525         1071832
6=Approval                9.57248         820661   *
7=Range                   2.34923         968687   **
8=SchulzeBeatpaths        7.65854         1262175  *
9=SmithSet                15.1901         1262175
10=SchwartzSet            15.1545         1262175
11=CondorcetLR            7.34944         1262175  *
12=Top2Runoff             14.0468         860532
13=SimpsonKramer          7.80134         1262175  *
14=Bucklin                12.3466         835287
15=Copeland                8.2384         1262175  *
16=SimmonsCond            7.94824         1262175  *
17=SmithIRV                9.7471         1262175  *
18=BTRIRV                 9.18064         1262175  *
19=DMC                    10.8252         1262175
20=Dabagh                 13.9448         747406
21=VtForAgainst           11.6002         757580
22=AntiPlurality          21.7252         550365
23=PlurIR                 14.0468         860532
24=Black                   5.6356         1262175  **
25=RandomBallot           51.6386         191308
26=RandomPair              37.874         334004
27=NansonBaldwin          9.50171         1262175
28=Nauru                   10.427         835902
29=TopMedianRating        8.95933         775247
30=LoMedianRank           52.9952         180459
31=RaynaudElim            10.3868         1262175
32=ArrowRaynaud           8.03927         1254525  *
33=Sinkhorn               4.54255         1061707  **
34=KeenerEig              4.54734         1066258  **
35=MDDA                   7.56647         1262175  *

(NumVoters=1535, NumCands=3, NumElections=1999999, IgnoranceAmplitude=0.001000)
The voting methods with BayesianRegret < 6 have *.
Method, & BayesianRegrets & #Agreements with Condorcet Winner (when CW exists)
0=SociallyBest                  0         1353746   *
1=SociallyWorst           66.2759          79391
2=RandomWinner            33.1834         607348
3=Plurality               8.78614         1389914
4=Borda                    5.0884         1644984   *
5=IRV                     6.82907         1757694
6=Approval                 5.1228         1381587   *
7=Range                   3.81388         1528868   *
8=SchulzeBeatpaths        6.00479         1825359
9=SmithSet                6.69801         1825359
10=SchwartzSet             6.6996         1825359
11=CondorcetLR            6.00539         1825359
12=Top2Runoff              6.8306         1757781
13=SimpsonKramer          6.00364         1825359
14=Bucklin                8.92371         1374589
15=Copeland               6.69666         1825359
16=SimmonsCond            6.51225         1825359
17=SmithIRV               6.51254         1825359
18=BTRIRV                 6.19843         1825359
19=DMC                     6.6959         1825359
20=Dabagh                 5.10445         1645045   *
21=VtForAgainst           5.06958         1645046   *
22=AntiPlurality          8.92968         1374611
23=PlurIR                  6.8306         1757781
24=Black                  5.78931         1825359   *
25=RandomBallot           32.3044         629469
26=RandomPair             21.4056         1014263
27=NansonBaldwin          6.44418         1825359
28=Nauru                  6.17584         1551182
29=TopMedianRating        5.12254         1381527   *
30=LoMedianRank           33.3714         602651
31=RaynaudElim            6.70031         1825359
32=ArrowRaynaud           6.00212         1825359
33=Sinkhorn               5.08644         1636869   *
34=KeenerEig              5.09094         1653486   *
35=MDDA                   5.65242         1825359   *

Warren D Smith
http://rangevoting.org