[EM] ranked pair method that resolves beat path ties.

[Juho Laatu]

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.
> 
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