[EM] A Metric for Issue/Candidate Space

[Kevin Venzke]

Hi Forest, this seems rather good. I implemented it such that the pairs are inferred from the top and bottom rankings (fractionalized, but with no equal ranking, just truncation), 3 candidates, 4 blocs. I also made it so that each pair of candidates has a tiny minimum distance, so that some pairwise defeat will always have a greater diameter than a single undefeated candidate. I understood the diameter of S(X) to mean the largest distance between X and some other candidate in S(X).

Interesting aspects: Seems to have little burial incentive. Truncation incentive isn't bad, worse than C//IRV but better than C//A. Compromise is not the best but not bad. I found Mono-raise relatively bad, but that's probably because I built the distance setting into the method itself. Mono-add-top likewise. No Plurality issues yet. If there is only one majority contest, it almost always respects it. I'm a little puzzled why that should work out nicely like that... It tries to avoid electing candidates defeated by "dissimilar" candidates, but that's got no direct tie to the defeat strength.

Let's see if this will post right. Might have to copy to a fixed width text editor. If it looks bad I'll try viewing it in the archive:
http://lists.electorama.com/pipermail/election-methods-electorama.com//2020-December/

But here's a couple of maps placing decloned Copeland and this new "diameter" method:

. . . . . . . . . . . . . . . . . . IFPP. . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . DSC 
. . . . . . . . . . TACC. IRV . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . C/IRV KML BTRIRV. . . . . . . . . . . 
. . . . . . . . .KOTH dcCop . . . .ChainRO. . . . . . . . . 
. . . . . . . . . . SV. . . . . . . . . . . . . . . . . . . 
. . . . . . . . . .C/KOTH . . . . . . . . . . . . . . . . . 
. . . . . . . BPW . . . . . . Marg. . . . . . . . . . . . . 
. . . . . . . **. . . . . . . . . . . . . . . . . . . . . . 
. . . . . . Diam. . . . . C//A. . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . .DMC.WV . . . . VBV . . . . . . . . . . 
. . . . . . . . . . AWP . **. . **. . . . . . . . . . . . . 
. . . . . . . . . . AER CdlA. IBIFA VBV . . . . . . . . . . 
IRVnoelim . . . . . MMPO. . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . MDDA.MAMPO. . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . DAC . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . Bucklin . . . . . . . . . . . . . . 

notes: KML = Kristofer's Linear method fpA-fpC. IBIFA is Chris's method. SV and BPW are Eivind Stensholt methods. AER = aka Approval AV. dcCop = decloned Copeland. IFPP = Craig Carey's Improved FPP. DAC and DSC are Woodall methods. TACC and DMC are other Forest or Jobst methods. AWP is James Green-Armytage's Approval-Weighted Pairwise (using MinMax; all approval methods are using implicit approval). My methods: KOTH, ChainRO, CdlA, VBV (x2), MDDA, MAMPO, ** (unnamed obscure methods).

I will zoom in a bit now:

. . . . . ChainRO . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . IRV . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . BTRIRV. . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . KMLinear. . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
TACC. . C/IRV . . . . . . . . . Marg. . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . VBV . 
. .dcCopeland . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . VBV 
KOTH. SV. . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . C/KOTH. . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . .IBIFA. . 
. . . . . . . . . . . . . . . . .C//A . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . **. . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
. . BPW . . . . . . . . . AER WV. . . . . . . . . . . . . . 
. . **. . . . . . . . . .AWP.DMC. . CdlA. . . . . . . . . . 
. . . . Diam. . . . . . . . . . . . . . . . . . . . . . . . 
. . . . . . . . . . . . . . **. MMPO. . . . . . . . . . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Hope this posts OK.

Kevin
 


Le lundi 7 décembre 2020 à 23:56:20 UTC−6, Forest Simmons <fsimmons at pcc.edu> a écrit : 
>
>How to define such a metric?
>
>How to use it?
>
>Ask the voters which issue they felt to be most important, and which pair of candidates were the 
>farthest apart on that issue. The pair with the most votes is taken to be at unit distance ... the others 
>at distances proportional to their respective mentions.
>
>Use it to in conjunction with the pairwise margins matrix as follows: for each candidste X, let S(X) be 
>the set of candidates that beat or tie X pairwise. In particular X is itself a member of S(X) by virtue of 
>a self tie.
>
>Elect the candidate X that minimizes the diameter of S(X).
>
>Note that if S(X) has only one member then that member is the Condorcet Winner, and the diameter 
>of S(X) is zero, the absolute minimum. 
>
>So the method is Condorcet Compliant.
>
>It seems pretty obvious that it satisfies clone independence.... and mono raise.
>
>Anybody else like this?
>
>How about using it for tournaments? What questions would you ask the fans to estimate the 
>distances between teams?
>----
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