[EM] A summable Approval variant for solid majorities

[Kevin Venzke]

Hello.

I don't really believe that under Approval, there would be sincere majority-strength
solid coalitions.  But if there were, and if we have decided that it is crucial
to select a candidate of that coalition if it exists, then I agree that Approval
runs the risk of performing badly.

Some months ago I suggested a method called MAFP (Majority Approval//First 
Preferences).  MAFP is equivalent to MCA except for when multiple candidates have
a median rating of "approved."  In this case MCA elects the one of those 
candidates with the fewest "disapproved" ratings.  MAFP elects the one with the 
most "preferred" rankings.  Then I realized how similar the two methods were, and 
dismissed MAFP for the same reason I criticize MCA.

But now I think MAFP could be very useful if one wants an Approval variant that
meets something similar to Mutual Majority.  Here is the method definition:

1. The voter rates all candidates either Preferred, Approved, or Disapproved.
2. If one or no candidates are preferred or approved by a majority of the voters,
then the candidate preferred or approved by the most voters is elected.
3. Else elect the most preferred candidate among those preferred or approved by
a majority.

This method is summable, meets weak FBC, and fails Participation, just like MCA.

Here is a scenario to demonstrate the intended use:

49 B> >K,D
24 K>D>B
27 D>K>B

All voters are able to assume that if Bush has majority approval, then neither
Dean nor Kerry does.  And if Dean or Kerry do, they likely both do, and Bush won't
have a majority.  (We believe *somebody* will have a majority, though, because
that is my assumption when suggesting that this method is useful.)

So it is safe for Kerry and Dean supporters to downrank their second-favorite,
since the downranking won't be felt unless Kerry and Dean have a majority, in
which case Kerry and Dean should be the only candidates left.  If neither Kerry
nor Dean has a majority, then they can assume the election is lost to Bush,
and it doesn't matter that their "preferred" and "approved" ratings were counted
identically.

Incidentally, Dean wins this election.  He still wins even if the Bush voters feel
like voting Bush>Kerry>Dean, because the Bush voters would not participate in
the contest between Kerry and Dean.  So MAFP is not really designed to pick up
a CW.  Anyway, it is questionable strategy to vote Bush>Kerry>Dean, since 1. it
can make Bush lose to Kerry (if Kerry is more preferred than Bush), and 2. it has 
very limited ability to help Kerry beat Dean (probably only if Dean doesn't have
majority approval).

I'd thought that MAFP was silly because there would not be reason to believe that
you should help a candidate get majority approval, but not then support him
against other majority-approved candidates.  But I assumed that one would not be
able to guess who those other candidates would be.

If voters *don't* feel able to guess who the majority-approved candidates might
be, then the middle rank becomes useless, and the method is just Approval.  So
it seems to me little is lost by using MAFP instead of Approval.  In particular
Participation is lost, but if you avoid using the middle slot, your vote can
only change the winner from one of approved candidates to another that you also
approved, or from a disapproved candidate to another disapproved candidate.  I'm
not able to come up with any way that your vote could e.g. change the winner
from your favorite to your most hated candidate.

Any thoughts?

Kevin Venzke
stepjak at yahoo.fr



	

	
		
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