[EM] Stats on HBH and a few others

[Kevin Venzke]

Hi Forest,

I ran some small batches of simulations under a handful of scenarios
(1D and also aspectral) to try to get a sense of general trends. Then
I averaged the numbers.

Hopefully I didn't implement anything incorrectly.

Definitions:
HBH3 and HBH4 are three- and four-slot HBH.
ELMDP is the "eliminate loser of most distant pair" method, 3-slot.
ELLDP is the "eliminate loser of least distant pair" method, 3-slot.
Appr and WV are what you'd guess.
MinAvt is the Condorcet method that picks the outcome that minimizes
the number of voters that could and would "avert" it. (Average of two
versions' scores, but they are quite close)
SC is the currently best version of my Single Contest method that I
won't define just yet. (If I can still improve it I want to wait.)

Finally, MAIRO or "Majority Approval//Instant Runoff" is an irritating
method that tests well but has obvious clone concerns. It's a rank 
ballot with explicit cutoff. If zero or one candidate has maj approval,
the AW wins. Otherwise, take the pairwise comparison between the top two
approval candidates.

(I wish I had included the Approval-Weighted Pairwise methods as well.
They are usually stiff competition.)

For "percentage of polls won by the candidate who won in the fewest
polls (in a given scenario)" aka "method that comes closest to Random
Candidate," the ranking goes:
Appr 0.80%, ELLDP 0.47%, HBH3 0.44%, ELMDP 0.34%, HBH4 0.34%, 
MinAvt 0.23%, SC 0.22%, WV 0.22%, MAIRO 0.05%.

"Average % of top ratings/rankings of the candidate who had the fewest":
Appr 30.5%, ELMDP 24.8%, WV 23.1%, HBH3 20.1%, SC 18.7%, HBH4 17.9%,
MinAvt 17.6%, MAIRO 16.7%, ELLDP 15.1%.

Voters compromising:
ELLDP 7.5%, HBH4 5.6%, MAIRO 4.6%, SC 4.1%, MinAvt 3.7%, HBH3 2.2%,
WV 1.5%, ELMDP 0.3%, Appr 0.0%.

Voters compressing:
Appr 34.3%, ELMDP 19.4%, WV 14.8%, HBH3 6.9%, MinAvt 3.5%, HBH4 3.0%,
ELLDP 0.5%, SC 0.04%, MAIRO 0.0%.

Voters bullet-voting:
Appr 65.7%, HBH3 39.3%, HBH4 29.6%, ELLDP 15.9%, SC 1.2%, MAIRO 0.44%,
ELMDP 0.25%, WV 0.19%, MinAvt 0.10%.

Voters burying:
WV 10.1%, ELLDP 6.3%, ELMDP 5.6%, MinAvt 5.4%, HBH4 5.3%, MAIRO 4.4%,
HBH3 2.9%, SC 0.4%, Appr 0.0%.

Voters ranking worst first:
ELMDP 1.8%, ELLDP 0.3%, SC 0.1%, HBH4 0.05%, HBH3 0.004%, 
WV MinAvt MAIRO Appr = 0.0%.

Overall sincerity:
SC 94.2%, MAIRO 90.5%, MinAvt 87.2%, ELMDP 76.3%, WV 73.4%, ELLDP 70.0%,
HBH4 56.5%, HBH3 48.7%, Appr N/A.

These numbers above are why I am interested in SC and MinAvt...

Plurality failures: detected under ELLDP only.

Sincere Condorcet efficiency:
MAIRO 93.6%, HBH3 92.1%, HBH4 91.0%, SC 89.7%, MinAvt 89.5%, WV 88.8%,
ELLDP 88.7%, ELMDP 88.0%, Appr 87.4%.

Sincere Condorcet *Loser* efficiency (i.e. a bad thing):
ELMDP 1.3%, MinAvt 0.6%, Appr 0.4%, WV 0.4%, HBH3 0.4%, HBH4 0.3%,
ELLDP 0.3%, MAIRO and SC = 0.0%.

Utility maximizer efficiency:
The range was 71.4% to 74.7%. Best to worst: MAIRO, HBH3, HBH4, MinAvt,
ELMDP, Appr, ELLDP, SC, WV.

Hopefully you or others find this interesting to look over.

That's it for now.

Kevin Venzke