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 ---- Election-Methods mailing list - see http://electorama.com/em for list info
