[EM] Two scenarios and 11 Condorcet methods

[Kevin Venzke]

Hi,

This follows from the discussion on strategy-resistant Condorcet methods.
I ran these 11 methods in my simulation: AWP(implicit), BPW (the "Beats 
Plurality Winner" cycle-breaker proposed by Stensholt), C//A(implicit), 
C//FPP, C//IRV, C//KH (KH being King of the Hill), DMC, FPL75 (this is 
the joke method I proposed to Juho), margins, TACC, and WV.

I did two scenarios: Spectrumless ("aspectral"?), and a 1D spectrum with
candidates and voting blocs randomly distributed. I did 7 blocs for both.

In the spectrumless scenario there seems to be a lot more strategy
incentive across the board, with worsened sincere Condorcet efficiency.
Every method improves at "SCE" in the 1D scenario, and only C//IRV has
better overall sincerity with spectrumless.

So, starting with the spectrumless scenario:
Compromise (percentage of voters doing it): BPW was the worst at 13.3%.
Then C//FPP 12.0%, FPL75 11.5%, margins 8.7%, C//KH 8.1%, DMC 8.1%,
C//IRV 8.0%, AWP 6.5%, C//A 6.2%, TACC 2.8%, WV 1.2%.

In the 1D scenario all %s were within 5.5% and the ranking was C//FPP
as worst, C//IRV, C//KH, BPW, FPL75, margins, TACC, DMC, AWP, C//A, WV.

Spectrumless again:
Compression: WV was highest at 15.4%, then TACC 12.4%, C//A 5.6%, AWP
4.7%, margins 3.5%, DMC 0.2%, and 0 for the five methods that don't
allow equal ranking (because they care about first preferences).

With 1D the ranking only changes a little. Figures are within 9.3% (for
TACC).

Spectrumless again:
Truncation (bullet-voting really): TACC 17.1%, C//A 14.5%, C//KH 12.4%,
C//IRV 5.3%, C//FPP 4.2%, FPL75 3.9%, DMC 3.7%, AWP 3.7%, margins 0.9%,
BPW 0.5%, WV 0.1%.

In the 1D scenario TACC actually gets worse, at 19.0%. It's not the
only one. The overall ranking isn't that different though.

I can't currently explain the low truncation rate for WV. Perhaps the
"random-fill to beat your opponents" conventional wisdom is more accurate
than the "many will and should truncate" school of thought that I
personally consider realistic.

Spectrumless:
Burial: Margins was surprisingly worst at 14.4%, then BPW 14.2%, WV 
12.4%, C//FPP 12.4%, DMC 12.2%, FPL75 10.3%, AWP 8.4%, C//A 5.5%, C//IRV
3.3%, TACC 2.8%, and, the winner, C//KH with 2.1%.

The 1D figures are better all around except for C//IRV. The order is
C//FPP worst at 7.9%, C//IRV 5.4%, margins 5.1%, WV 4.6%, FPL75 4.4%, BPW
4.2%, AWP 3.6%, DMC 3.4%, C//KH 3.3%, C//A 2.4%, TACC 2.1%.

I'm disappointed I can't confirm that BPW is a good way to deter burial.

As far as "pushover" (ranking worst first) I got zero for almost 
every method in both scenarios. I did get a small number (tenths of a
percent) for C//KH in both scenarios, so that's probably legitimate. I 
got a much smaller blip from TACC in the spectrumless scenario; that 
might be a fluke.

As far as overall sincerity (no strategy use at all), in the spectrumless
scenario: The winner is C//IRV with 83.4%. Then C//KH 77.4%, AWP 76.8%,
DMC 75.7%, FPL75 74.3%, margins 72.5%, BPW 72.0%, C//FPP 71.5%, WV 70.8%,
C//A 68.2%, TACC 64.9%.

In the 1D spectrum the ranking is DMC 94.8%, AWP 93.3%, BPW 91.9%, FPL75
91.9%, margins 90.4%, C//A 89.1%, WV 87.0%, C//FPP 84.3%, C//IRV 81.3%,
C//KH 78.0%, TACC 68.2%.

So you can see that C//IRV and also C//KH take a major hit in relative
ranking when you go to the 1D scenario.

Finally, I want to look at the sincere Condorcet efficiency in the
spectrumless scenario:
C//FPP wins with 95.4%, then DMC 95.3%, C//KH 95.1%, WV 94.9%, C//IRV
94.6%, margins 94.3%, TACC 94.2%, AWP 93.8%, C//A 93.7%, BPW 91.8%,
FPL75 91.7%.

In the 1D scenario the numbers are even higher: AWP 99.8%, C//A 99.8%,
DMC 99.7%, FPL75 99.6%, margins 99.1%, WV 99.1%, BPW 99.0%, TACC 98.0%,
C//IRV 98.0%, C//FPP 97.8%, C//KH 97.2%.

It's not quite clear how important this score is, since you can get
quite a good score if the weakest candidate's supporters just dump him
all the time and vote for second best.

I wasn't going to remark on the "% of voters who feel the race was
spoiled" metric, but at a glance its order agrees completely (in the
opposite direction) with the sincere Condorcet efficiency.

It is a bit ironic that, if we succeed in getting people to vote for
more than two candidates (FPP-style), it's hard not to expect that we
would see *more* spoiled elections than under FPP.

Kevin Venzke