----- Original Message ----- From: Kristofer Munsterhjelm Date: Wednesday, June 15, 2011 1:38 pm Subject: Re: [EM] Covering , Ranked Pairs, Beatpath, and River To: [email protected] Cc: [email protected]
> [email protected] wrote: > > If we measure defeat strength of A over B, primarily by > whether or not A covers B, and secondarily by > > the number of winning votes, we get new versions of Ranked > Pairs, River, and Beatpath. These new > > versions retain all of the best properties of their winning > votes versions, while always electing uncovered > > alternatives. > > This trick will work on any method that simply compares > different beat > strengths without taking the score directly into account. You > can define > a greater-than operator as > > "If A covers B, then A is greater than B. > Otherwise, A is greater than B if the wv (margins, whatever) of > A is > greater than B". I would do it this way: If A covers B but X does not cover Y, then the defeat strength of A over B is greater than the defeat strength of X over Y. If both or neither are coverings, then the defeat with the greatest winning votes is the the stronger of the two. The beauty of Ranked Pairs is that all of the covering defeats can be locked in, because covering cycles are impossible. > > So you could in theory do this with Minmax too, but not with > Least > Reversal or Kemeny. > > ---- Election-Methods mailing list - see http://electorama.com/em for list info
