Re: [EM] ranked pair method that resolves beat path ties.
robert bristow-johnson wrote: because *both* the winning votes is tied and the margins is tied. what else is there? i wonder if it would be better to first rank each pair according to Margins and then, in the case of tie of Margins, Winning Votes are used to break the tie to determine which pair result has priority over the other. for some reason, i like Margins because it is the product of the percent spread (which indicates how decisive a defeat is) times the number of voters participating (which indicates how important the pair election is). that product is a natural measure for how important and decisive a pairwise defeat is. Winning Votes, all by itself, should not be the sole (or primary in the present case) decider. what if there is a lot of voters, but the pair-election is close (say a defeat by 1 vote)? it's not a decisive defeat, but Winning Votes would say it is. i think Margins is more salient than Winning Votes. Note, though, that methods that do Margins first may violate the Plurality criterion. In other words, it may be the case that, in a Margins election, a candidate wins when some other candidate has more first place votes than the winner has any-place votes. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] ranked pair method that resolves beat path ties.
If we are talking about natural measures of defeat strength, then I must say that margins and ratio seem reasonably sensible to me, and winning votes does not. It is hard to justify the idea that defeat 49-48 is as strong as 49-0, and defeat 49-48 is stronger than 48-0. It is also weird that if a strong 49-48 winner loses two votes, it becomes suddenly a strong 47-48 loser. I think winning votes is more a design that is intended to answer to some of the strategic voting concerns, not a tool for natural pairwise preference strength comparison. Election methods can be designed to give best possible winners with sincere votes, or to be as resistant against some chosen set of strategies as possible. I think margins tries to address the first need, and winning votes is more natural as part of the other approach. Juho On 28.11.2011, at 10.12, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: because *both* the winning votes is tied and the margins is tied. what else is there? i wonder if it would be better to first rank each pair according to Margins and then, in the case of tie of Margins, Winning Votes are used to break the tie to determine which pair result has priority over the other. for some reason, i like Margins because it is the product of the percent spread (which indicates how decisive a defeat is) times the number of voters participating (which indicates how important the pair election is). that product is a natural measure for how important and decisive a pairwise defeat is. Winning Votes, all by itself, should not be the sole (or primary in the present case) decider. what if there is a lot of voters, but the pair-election is close (say a defeat by 1 vote)? it's not a decisive defeat, but Winning Votes would say it is. i think Margins is more salient than Winning Votes. Note, though, that methods that do Margins first may violate the Plurality criterion. In other words, it may be the case that, in a Margins election, a candidate wins when some other candidate has more first place votes than the winner has any-place votes. Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] ranked pair method that resolves beat path ties.
so this is interesting. it seems to be an extension of Tideman ranked-pairs that considers first the margins and then the opposing votes (or winning votes for the opponent) to break ties. is that essentially it? On 11/27/11 10:21 PM, Ross Hyman wrote: When beat path produces a tie, this method can produce a single winner unless the tie is genuine. It is the same method I presented earlier except for the addition of the Removing step, which resolves the ties. Candidates are classed in two categories: Winners and Losers. Initially, all candidates are Winners. Every candidate has an associated Set of candidates that includes itself and those candidates that have defeated it. Every candidate initially has a set composed of itself and no other candidates. Winners are those candidates who have no Winners in their set aside from themselves. The pairs are ranked in order.All pairs are ranked in the form AB indicating more voters rank A above B than rank B above A. now this is ranked pairs w.r.t. margins. Pairs with equal votes for A above B and B above A are not ranked. not immediately, but is this not what the procedure below is about? For winning votes ranking, AB is ranked higher than CD if more voters ranked A above B than ranked C above If the same number of voters ranked A above B as ranked C above D then AB is ranked higher than CD if more voters ranked D above C than ranked B above A. so maybe i got it wrong, first it's Winning Votes that determines the order of ranking and then Margins is used to break the tie? If the same number of voters ranked A above B as ranked C above D and the same number ranked D above C as ranked B above A then these pairs are equally ranked. because *both* the winning votes is tied and the margins is tied. what else is there? i wonder if it would be better to first rank each pair according to Margins and then, in the case of tie of Margins, Winning Votes are used to break the tie to determine which pair result has priority over the other. for some reason, i like Margins because it is the product of the percent spread (which indicates how decisive a defeat is) times the number of voters participating (which indicates how important the pair election is). that product is a natural measure for how important and decisive a pairwise defeat is. Winning Votes, all by itself, should not be the sole (or primary in the present case) decider. what if there is a lot of voters, but the pair-election is close (say a defeat by 1 vote)? it's not a decisive defeat, but Winning Votes would say it is. i think Margins is more salient than Winning Votes. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
