Hello,
I've set up my simulation to be able to run repeatedly, and randomly toss
the candidates out. I've changed distance to be taxicab. As the issues
seem to be more independent than I first was thinking, I got rid of the
voters having to be cast within a certain distance of the origin, which
means they lie in a square (in 2D elections) rather than a circle.
There are a few new methods here. I found that I mistakenly implemented
sincere CdlA rather than truncated CdlA, so I renamed the old one
"CdlASnc" and added the correct method as "CdlA".
I added back Raynaud(wv), 2-slot MMPO, and sincere Majority Favorite//
Antiplurality (MAP), as well as sincere Antiplurality.
The program dumps all the results to a file that I've loaded into a
database in order to look at "pairwise comparisons" of methods, and
similarity of methods, and attempt to figure out what causes them to
differ.
I don't have a lot of trials (a few thousand, though each trial is made
up of thousands of elections) so I wouldn't take these as the final
word necessarily...
The format is:
Method, % elect best, % elect worst, % of times the method ranked in the
top third of all methods, then middle third, and final third, average
distance, average normalized distance.
The reason I note how often each method was in the top/middle/bottom
third is that I noticed some methods were all over the place in where
they ranked, while other methods didn't move around much.
Note that a method having superior average distance to another method
doesn't necessarily have superior average normalized distance.
The sort order is increasing average distance (which is the utility
metric here).
One-dimensional elections:
Method BestC WorstC Top Middle Bottom Dist DistN
CdlASnc 91.8% 1.1% 87.3% 10.4% 2.2% 52.978 1.306
MMstrict 91.8% 1.1% 97.2% 2.6% 0.1% 53.010 1.314
Bucklin 90.4% 1.4% 79.0% 10.2% 10.8% 53.044 1.453
DAC 89.6% 1.4% 61.8% 29.6% 8.7% 53.049 1.481
MAP 91.8% 1.1% 94.1% 4.8% 1.2% 53.155 1.359
RangeNS 83.3% 0.4% 46.4% 21.8% 31.8% 53.237 2.083
ApprPoll 81.2% 1.3% 52.0% 19.7% 26.9% 53.442 3.060
QR 84.1% 2.0% 33.2% 66.1% 0.7% 53.471 2.831
DSC 83.0% 1.5% 53.1% 40.5% 6.4% 53.474 2.656
C//A 81.0% 1.8% 13.3% 78.9% 7.8% 53.510 3.074
MMWV 81.0% 1.8% 17.3% 72.7% 10.1% 53.510 3.075
CdlA 82.5% 1.5% 25.1% 62.1% 12.8% 53.585 2.786
ApprZIS 77.0% 0.9% 58.5% 13.2% 28.2% 53.593 3.841
2sMMPO 81.1% 1.3% 42.6% 28.6% 28.8% 53.602 3.004
MMmarg 78.1% 3.0% 5.9% 62.4% 31.7% 53.762 3.983
IRV 79.1% 3.6% 1.1% 67.9% 31.0% 53.851 4.216
SPST 78.3% 2.5% 27.0% 44.1% 28.9% 53.996 4.245
MMPO 76.7% 4.4% 4.4% 34.8% 60.8% 54.017 4.877
IRV-tr 76.3% 4.1% 0.1% 42.7% 57.2% 54.110 4.924
Raynaud 76.8% 4.4% 1.6% 34.4% 64.0% 54.139 4.841
QR-tr 76.0% 4.5% 0.1% 39.2% 60.7% 54.200 5.221
VFA 73.3% 4.0% 11.3% 21.0% 67.6% 54.377 5.630
DSC-tr 71.8% 5.4% 13.1% 20.0% 66.9% 54.796 6.735
FPP 70.4% 8.2% 7.9% 12.8% 79.3% 55.249 8.487
Antip 44.8% 0.0% 8.8% 16.3% 74.9% 60.119 26.835
Two-dimensional elections:
Method BestC WorstC Top Middle Bottom Dist DistN
RangeNS 86.1% 1.1% 81.1% 7.4% 11.5% 113.559 2.470
ApprPoll 83.6% 2.2% 72.6% 13.0% 14.2% 113.948 3.696
Bucklin 83.9% 2.4% 76.7% 16.1% 7.1% 113.954 3.651
DAC 83.9% 2.4% 71.6% 23.8% 4.7% 113.966 3.653
ApprZIS 82.4% 1.7% 66.3% 16.0% 17.7% 114.009 3.641
MMstrict 83.1% 2.4% 77.4% 18.6% 4.0% 114.089 3.961
CdlASnc 82.3% 2.8% 58.6% 27.0% 14.4% 114.247 4.309
MAP 81.4% 2.9% 51.9% 20.7% 27.4% 114.362 4.695
CdlA 81.1% 3.3% 20.6% 61.0% 18.3% 114.370 4.686
QR 81.1% 3.3% 26.1% 65.5% 8.4% 114.456 4.839
DSC 79.9% 2.8% 43.4% 37.0% 19.5% 114.536 4.882
C//A 80.5% 3.6% 17.4% 73.0% 9.6% 114.561 5.033
IRV 79.8% 3.8% 12.8% 70.2% 17.1% 114.668 5.359
MMWV 79.9% 4.0% 12.5% 59.2% 28.3% 114.701 5.343
MMmarg 79.7% 4.2% 15.9% 59.7% 24.4% 114.746 5.477
IRV-tr 78.5% 4.7% 5.9% 56.2% 37.9% 114.985 6.057
QR-tr 78.3% 4.9% 6.1% 51.7% 42.2% 115.062 6.284
Raynaud 78.5% 5.3% 4.4% 37.9% 57.8% 115.089 6.261
SPST 77.0% 4.1% 19.9% 33.9% 46.3% 115.143 6.300
VFA 75.9% 4.5% 17.8% 25.8% 56.3% 115.325 6.754
MMPO 76.9% 7.3% 3.9% 22.5% 73.6% 115.827 7.857
DSC-tr 74.3% 6.0% 15.4% 16.8% 67.8% 115.832 7.961
FPP 73.6% 7.0% 10.3% 13.2% 76.5% 116.080 8.770
2sMMPO 77.0% 8.5% 25.6% 13.2% 61.2% 116.310 8.874
Antip 62.5% 4.0% 16.7% 12.3% 71.1% 119.050 16.697
I also tried out a hybrid, where the second dimension wasn't as large
as the first, but it didn't seem to have unique results beyond being a
compromise between the results of the 1D and 2D simulations.
Kevin Venzke
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