[EM] A distance based method

[Kevin Venzke]

Hi Forest,

--- En date de : Ven 15.7.11, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> > 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