[EM] A distance based method

[fsimmons at pcc.edu]

Here's a simpler version that is basically the same:

Make use of cardinal ratings so that the rating of candidate X on ballot b is given by b(X).

Define the closeness of candidate X to candidate Y as the dot product

 Sum b(X)*b(Y)

where the sum is taken over all b in the set beta of ballots.

While there remain two or more candidates, eliminate the pairwise loser of the two that are least close 
to each other.



----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Wednesday, July 13, 2011 2:35 pm
Subject: Re: [EM] A distance based method
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu wrote:
> > Trying to build a metric from a set of ranked ballots is 
> fraught with
> > difficulties, and your outline of a procedure for doing it is
> > interesting to me.
> > 
> > The simplest, least sophisticated idea I have so far that 
> seems to
> > have some use is to define the distance between two candidates 
> X and
> > Y to be the number of ballots on which at least one of the two 
> is 
> > truncated.
> 
> I'm not sure if that really works. It could give a rough 
> distance 
> between zones of acceptable and unacceptable candidates, but 
> beyond that 
> it gets less reliable. To take a Norwegian example: we have two 
> broad 
> coalitions: one that's left-of-center and one that's right-of-
> center. 
> Say I prefer the left-of-center coalition. I would still rank 
> the 
> right-of-center coalition's individual parties because "if I 
> have to get 
> one of them, I could at least try to pull them as close as 
> possible to 
> my view".
> 
> Popularity could also be a factor. In a Bush-Gore-Nader setting, 
> voters 
> might rank Bush, Gore, and Nader, but skip Browne, Hagelin, and 
> Phillips.
> (Truncation would also pose a problem to the inference idea I 
> gave in my 
> earlier post. In general, noise or variety in the amount of 
> information 
> provided, in any manner, would. But it makes sense to consider 
> perfect 
> situations before going to imperfect ones.)
> 
>