[EM] A distance based method

[Jameson Quinn]

I doubt it's monotonic, though it's probably not a practical problem. That
is, it would probably be totally impractical to try to use the
nonmonotonicity for anything strategic, and it wouldn't even lead to Yee
diagram ugliness.

2011/7/13 <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.)
> >
> >
> ----
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