[EM] Covering , Ranked Pairs, Beatpath, and River

[fsimmons at pcc.edu]

----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Wednesday, June 15, 2011 1:38 pm
Subject: Re: [EM] Covering , Ranked Pairs, Beatpath, and River
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu 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.
> 
>