[EM] Another three-slot method

[Kevin Venzke]

Forest,

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> Kevin, this looks promising.  Could you expand your explanation of why
> some of the first slot candidates are not to be counted in the contest
> between the AW and the FPW?
> 
> Perhaps an example with two candidates in the first slot would help.
> 
> Forest

Sure:

8 AB>C>?
2 B>C>A
4 C>A>B
14

FPW is B (10); AW is C (14).  If those who placed B first simply truncate, the
scores would be A 12, B 10, C 4, with A winning.  Since B can't win this way,
nobody truncates, and C, the AW, wins.  So to ensure that the majority favorites
don't "sink each other," the 8 voters don't vote for A in the tentative contest.
B wins the election.  (A is the CW, unfortunately, but it's better than C winning.)

I have been calling this method "AWP" for "Approval with Privilege," but I'm sure
there's a better name for it.

This method seems to do well with your manipulability test, but it made me notice
a limitation of it, and of AWP: They seem to be designed for the benefit of
"third front-runner" candidates who expect to win with first preferences, or not
at all.  Note that candidate A (in your test) doesn't expect to receive any 
compromise votes from anyone else.  Only because of that is it safe for A to list 
B as a compromise.

What about a candidate who expects to win with others' compromise votes?  AWP
doesn't offer anything that Approval doesn't.  AWP can actually do worse:

6 B>A>C
2 A>B>C
5 C>A>B
13

This is a "weak centrist" scenario of sorts.  AWP elects B.  The CW is obviously A.
What goes wrong?  The A and C factions both erred strategically.  Because A has few
first preferences, their support for B is counted.  The C faction should have
considered up-ranking A, to turn A into the FPW.

I can see two ways of approaching this problem, based on which of A and C you wish
to protect from their mistakes.  A's problem is a later-no-harm one.  This suggests
to me that you allow the AW to cancel compromise support for the FPW, defensively.
But since the FPW's voters' can (and do, above) contribute to making a candidate the
AW, we're still failing later-no-harm.  (Specifically: If the B voters hadn't listed
A, B would've been the AW.)

C's problem, as I see it, is that C is a spoiler, a hopeless candidate.  You could
apply a filter, such as repeatedly eliminating all candidates who have fewer votes
in total than some other candidate (presently) has first-place votes.  (Call that
a "Plurality filter," as in the Plurality criterion.)  Such a filter would eliminate
C, and uprank A to Favorite status on those ballots.

I thought of applying this filter to IRV.  It appears like it could be useful.  For
the scenario 49 A, 24 B, 27 C>B, C can be eliminated immediately.  However, the A
voters could vote instead A>C, which would prevent C from being filtered out, and
give the win back to A.  That's a later-no-help failure.

That convinced me that the method used after the filter should fail later-no-harm
pretty obviously, so that you cannot safely give lower preferences to the other
side's expected spoilers.  Perhaps MCA is a good, simple choice.

I'm still hesitant about the filter, though, because replacing some candidates with
a set of clones will most likely prevent the filter from working at all, as no one
receives many first preference votes.  This makes the filter seem arbitrary.

Hope I've said something of interest.


Kevin Venzke
stepjak at yahoo.fr


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