[EM] A distance based method

[fsimmons at pcc.edu]

Kevin,

Do we agree that working from closest pairs outward solves the Plurality problem (at the expense of 
compromise and less monotonicity)?

> From: Kevin Venzke 
> 
> Hi Forest,
> 
> --- En date de?: Ven 15.7.11, fsimmons at pcc.edu 
> a ?crit?:
> > > I think I will try implementing the "eliminate the
> > pairwise 
> > > loser of
> > > the most distant pair" method. I am curious how well
> > it would 
> > > discourageburial. I wonder also how often it would
> > fail Plurality...
> > 
> > Kevin,? the method fails Plurality, and is vulnerable
> > to burying.? Its strong point should be with regards to
> > compromising.
> 
> I did one test (1D spectrum) with a (too) small number of trials and
> it seemed good there. It was a lot like WV, but a bit better 
> across the
> board. I do wish we could get the compression incentive down.
> 
> (Incidentally, this seems to be an advantage of the MinMax 
> method where
> you count the number of voters who would actually have been able to
> avert a cycle. That is, you have to actually vote C>B>A in order to
> "complain" when B>A gets overridden. And you are not counted as 
> a voice
> for respecting the C>B contest, because you have no way to 
> threaten to
> change your ballot should C>B be overturned.)
> 
> It occurred to me that a very "distant" pair of candidates are, in
> practice, often going to be the frontrunners, registering as "distant"
> because voters don't want to vote for them both. In that case we are
> probably cutting out the "wrong" one early in the process. But after
> that point we get the Plurality failures, as nothing stops the "right"
> frontrunner from being cut down by a noise candidate not generally
> viable.
> 
> I was trying to think of how we could just stop after one comparison.
> I tried a few versions of something like the following: Find the pair
> of Schwartz candidates, if there is more than one (i.e. let's 
> not fail
> Majority Favorite), with the greatest "approval distance," which is
> basically the sum of the "approval opposition" in each 
> direction. Just
> elect the winner of that contest. (Break ties probably by 
> approval of
> the pairwise winner.)
> 
> I think the non-monotonicity of "approval distance" wouldn't be 
> a huge
> practical problem. I might be wrong but it seems like an unintuitive
> strategy to remove the approval distinction between your 
> candidate and
> the frontrunner who beats him pairwise. Even if you do it I 
> wonder in
> how many situations you would have reason to expect it to work?
> 
> Unfortunately, so far my methods (SCAD - "Single Contest Approval
> Distance") don't seem to be very good.
> 
> Kevin Venzke
> 
> 
> 
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> End of Election-Methods Digest, Vol 85, Issue 54
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