[EM] Markus: Re: Beatpath as a proposal in the U.S.

[Juho Laatu]

On 23.11.2011, at 8.11, robert bristow-johnson wrote:

> ...  and, if my understanding is correct, Schulze, ranked-pairs, and minimax all pick the same winner in the case where there are 3 candidates in the Smith set, is that not so?

Minmax may pick the winner also outside the Smith set. (Many consider this to be a problem. I tend to think that sometimes that may make sense.)

Margins and winning votes may give different results also in the case of three candidates. (Schulze is at least by default a winning votes based method. I note that wikipedia and electowiki mix both terms, margins and winning votes in their description of ranked pairs. Minmax can certainly be either. Also other approaches can be used, like the proportion of pairwise defeats.)

>  so, as unlikely as a Condorcet cycle is (and that's the big sale to make to voters and legislators about adopting Condorcet, especially after they rejected IRV as being "too complicated"), it's even more unlikely that, if a cycle ever happens, that more than 3 candidates will be in the cycle.

Those popular Condorcet methods may be more likely to lead to different results because of the margins vs. winning votes difference than because of their differences in handling loops of more than three candidates (or because of electing the winner outside the Smith set).

Loops of four or more are not impossible in real elections. In the wikimedia board 2008 election there was a loop of four (not a top cycle though). See http://meta.wikimedia.org/wiki/Board_elections/2008/Results/en. Maybe in a typical political election cycles are less probable than in wikimedia due to fewer candidates, clearer differences in the level of support, and stronger traditional voting patterns (e.g. left vs. right). And of course having a top cycle of more than three candidates does not yet necessarily mean that these discussed methods would lead to different results.

>  i don't think it will *ever* happen in a governmental election that a larger Smith set occurs and Schulze will be needed to select the correct winner when ranked-pairs fails to do so.

What is the correct winner? Earlier you referred to resistance to voting strategies. Should a method be planned to elect the best possible winner with sincere votes, or should a method be planned so that it is as resistant as possible to strategic voting? A method can thus be optimized to resist strategic voting, or to pick the best/correct winner with sincere votes. The most strategy resistant method does not pick the best winners, and the other way around (unless in some unlikely environment those two happen to be the same method). I guess the choice of the method depends on how strategic you expect the voters to be (and how efficient you expect the voters to be with their strategies). Should we elect the correct winner or be strategy resistant?

Juho






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