Monroe's voice of reason method is a method that Monroe proposed for its ability to never elect a universally despised candidate in some strategic equilibrium. I.e. it is immune to DH3-type outcomes. The voice of reason method finds the ballot that agrees most often with the pairwise relations (e.g. A is ranked over B on the ballot and A beats B pairwise). It then returns this ballot as its social ordering, so the winner must be someone's first preference, hence avoiding DH3. (It's also possible to devise a Kemeny variant where a ballot's ranking has a score equal to the sum of the number of voters on the winning side for all pairwise relations that the ballot agrees with, e.g. in an election with three candidates in an A>B>C>A cycle, the ballot A>B>C scores the number of voters preferring A>B plus the number of voters preferring B>C. Then the ballot with the highest score is selected as the method's social ordering.) So I thought its strategy resistance might imply DMT or DMT candidate burial resistance that I could perhaps transplant into a Condorcet method (the voice of reason doesn't pass Condorcet). But to my surprise, no! 3: A>B>C>D 3: B>A>C>D 1: C>D>A>B A is the Condorcet winner and DMT candidate. A beats everybody, B beats everybody but A, C beats D, and D is the Condorcet loser, so the Condorcet ordering is A>B>C>D. The A>B>C>D ballot ranked by three voters is in perfect agreement with the Condorcet order, so it is the voice of reason's social order and wins. But now let the B-first faction bury A: 3: A>B>C>D 3: B>C>D>A <-- burial 1: C>D>A>B Then the pairwise victories are: A>B (4) B>C (6), B>D (6) C>A (4) C>D (7) D>A (4) The ballot A>B>C>D agrees with A>B, B>C, B>D, and C>D: 4 of them. The ballot B>C>D>A agrees with B>C, B>D, C>D, C>A, and D>A: 5 of them. and the ballot C>D>A>B agrees with C>D, C>A, D>A, and A>B: 4 of them. So B wins, hence the burial worked, hence there's a DMTCBR failure. (The Kemeny variant scores the three ballot types 23 points, 27 points, and 19 points respectively.) I was surprised, but it's not so strange in retrospect. But it shows that methods that are immune to DH3 don't have to pass DMTCBR. (Do there exist methods that pass DMTCBR but can elect a universally despised candidate with strategic voting? That, I don't know.) -km

Hi Kristofer, Le jeudi 30 juin 2022, 11:44:29 UTC−5, Kristofer Munsterhjelm <km_elmet@t-online.de> a écrit : > Monroe's voice of reason method is a method that Monroe proposed for its > ability to never elect a universally despised candidate in some > strategic equilibrium. I.e. it is immune to DH3-type outcomes.   > So I thought its strategy resistance might imply DMT or DMT candidate > burial resistance that I could perhaps transplant into a Condorcet > method (the voice of reason doesn't pass Condorcet). It's been a while since I read the paper but I had the sense that he intends to avoid the DH3 outcome, but *only* the outcome itself, with no claim of strategy resistance in VOR. His goal seems extremely modest, and I suppose that's what he wants to point out, that few methods can satisfy it. But at the same time VOR can only shine in toy scenarios, ones which might actually have a universally despised candidate. If even one voter top-ranks an otherwise universally despised candidate, VOR can elect that candidate, if that one voter is otherwise the best match to the pairwise matrix. That's not too impressive, particularly considering VOR's lack of other good, expected properties. That said, I do see an appeal of the concept of determining which voter would be the best one to give the decision to. In an ideal world you could identify the median voter (on some spectrum) and let them pick the winner, without constraining the voter to kingmaking between two frontrunners they may not especially like. (But I don't think there will be a burial-resistant method along such lines.) Kevin