[EM] three-slot methods

[Kevin Venzke]

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> However, among three slot methods MCA might be easier to sell.
> 
> I will gladly go with the one that is most acceptable to the public.
> 
> Forest

Here's an idea for a three-slot method which increases somewhat the "strategic
distance" (if that's a term) between the first two slots.  It's not summable,
but doesn't require a pairwise matrix:

The voter places each candidate in one of three slots.
The ballots are counted such that each voter gives a vote to every candidate
placed in either the first or second slot.
If no more than one candidate has votes from a majority, the candidate with the
most votes wins.
Otherwise, eliminate the candidates who don't have votes from a majority, and
recount the votes in the same way as before, except ballots which place none of
the remaining candidates in the third slot, only give a vote to candidates placed
in the first slot.  The candidate with the most votes wins.

I call this method "MAR" for "Majority Approval Runoff," although it doesn't really
end with a runoff.  In the case where two candidates have a majority, it's the same
as finishing with a pairwise comparison, however.  I don't recommend having more
than two counts, since it's not clear how to count ballots which rank all remaining
candidates equally, and consequently not clear how to eliminate more candidates.

The mentality is that the measure of a candidate's suitability for election is
his approval (or "support," to use a less loaded term), but once candidates
have majority approval, another measure is needed.  We could put a lot of things
here instead, such as electing the finalist with the most first-slot votes.

The "strategic distance" between the first two slots is increased from MCA.  That is,
in MCA, it is a bit strange to use the middle slot: If you put A in first and B in
the middle, it means you think A and B might be contenders for Majority Favorite,
but if A doesn't win that way, you think, to some extent, that A isn't a contender
anymore, even by having greatest approval.  Put differently, why would you try to
break an A-B tie for majority favorite, but not for greatest approval?  (Maybe if
one suspects that Worst is a contender by greatest approval, but not by majority
favorite?)

I suspect if, in deciding on MCA strategy, we take it as granted that the odds of
a candidate winning by majority favorite are proportional (or somehow tied) to 
his odds of winning by greatest approval, we might find that the middle slot is
pretty useless.  Worth thinking about.

In MAR, the "distance" between the first two slots is the chance that some candidate
in each slot will have majority approval; the distinction is useful if you want
to approve two very viable candidates.  In MCA that distance is the chance that
such candidates will tie for majority *favorite*, which is much less likely, I
think.

I thought that perhaps MAR would meet Participation, but it doesn't: It's possible
for you to give the election to a middle-slot candidate when a first-slot candidate
would have won, in the case where, without your vote, only Favorite has majority
approval, but with your vote, Compromise also has a majority, and beats Favorite
pairwise (i.e. in the fake runoff).  However, unlike MCA, I can't come up with
any scenario where your vote causes Worst (a third-slot candidate) to win.

I'm not so pleased with the arbitrary nature of a majority cutoff...  It would be
nice if an Approval-type method could be devised which satisfies later-no-harm;
that is, the voter would be able to "withdraw" approval from Compromise if it
would make Favorite win, and not just if some majority rule can be invoked.


Kevin Venzke
stepjak at yahoo.fr


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