Dear Raph Frank, you wrote (31 Aug 2008):
> Btw, is there a simplified explanation of > your PR-STV method somewhere? > > From what I can see, it compares possible > outcomes pairwise like CPO-STV (but only > compares outcomes that differ by 1 member). > > Ideally, the simplified version would just > need to explain the way to perform that > comparison (if each comparison doesn't > depend on any of the others) Suppose that M is the number of seats. Suppose that _A_ and _B_ are two sets of M candidates each. Suppose that sets _A_ and set _B_ differ in exactly one candidate. Suppose that candidate B is that candidate who is in set _B_ but not in set _A_. Suppose that each voter casts a complete ranking of all candidates. Then the strength of the win of set _A_ against set _B_ is the maximum value X such that each candidate in _A_ has a separate quota of X votes against candidate B. In mathematical terms: X is the maximum value such that the voters can be partitioned into M+1 disjoint sets T(1),...,T(M+1) such that: 1. For all i = 1,...,M: |T(i)| >= X. 2. For all i = 1,...,M: Each voter in T(i) prefers candidate A(i) to candidate B. ********* There are mainly two reasons why I define the strength of a win in the manner above. First: The strength of the win of set _A_ against set _B_ should only depend on which candidates of the set _A_ the individual voter prefers to candidate B. But it should not depend on the order in which the individual voter prefers these candidates to candidate B. The reason: Voters, who have understood STV well, will give insincerely low rankings to "strong winners" (i.e. candidates who are elected quite certainly). I call this strategy "Hylland free riding". However, it is also clear that, when a strong winner is one of the favorite candidates of a voter, then this voter will not rank this strong winner below candidates he despises. Therefore, to minimize the vulnerability to Hylland free riding, the order in which the individual voter ranks the strong winners should not have any impact on the result of the elections. Second: The above definition for the strength of a win corresponds to the fact that, in real life, the probability, that a vote management strategy works, depends only on the number of votes for the weakest candidate who participates at this vote management. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info