[EM] Sims with random candidate allocation, 1D and 2D

[Kevin Venzke]

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