[EM] Stats on HBH and a few others

[fsimmons at pcc.edu]

Kevin,

Thanks for running these!  This is valuable information.

> From: 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