[EM] MinMax(AWP)

[fsimmons at pcc.edu]

Chris,

thanks for the helpful comments,  Your point is well taken on the first two examples, it's hard to argue 
against the Approval winner in the top cycle.  That's one reason I like UncAAO: it always picks from the 
Smith set, and will always pick the highest approval member of the Smith set or someone that covers 
the highest approval member of the Smith set.

Remember DMC?  DMC elects the lowest approval cdandidate that pairwise beats all of the candidates 
with more approval.  Consider that the highest approval Smith member covers all of the candidates with 
higher approval, so in general it will have more approval than the DMC winner if it is not the DMC winner 
itself.  It is possible that the UncAAO winner will have less approval than the DMC winner, but only when 
the highest approval Smith candidate is covered by some other candidate, and even then it is unlikely 
that it will drop below the DMC winner.  If the Smith set is a cycle of three, then the UncAAO winner will 
be the Smith approval winner, which is often not the case for the DMC winner.

The only reason I can give for electing outside of Smith is that I believe most cycles are artificial, and 
that always electing from the top cycle gives more incentive for creating these artificial cycles through 
burial, for example.

One might say that if one believes in always electing the unique uncovered candidate (i.e. the CW) when 
there is one, then it seems kind of philosophically weird that it is sometimes ok to elect outside the 
uncovered set.

So far UncAAO seems like the best deterministic method on those grounds.

In your last example it seems to me that reversing the four  A>>C preferences to C>>A makes C into a 
Condorcet Winner.

My Best,

Forest



----- Original Message -----
From: "C.Benham" 
Date: Monday, May 3, 2010 8:17 pm
Subject: MinMax(AWP)
To: em , fsimmons at pcc.edu

> 
> Forest,
> 
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
> 
> I don't like any method that fails to elect C here, unless like 
> IRV it 
> has the property
> that a Mutual Dominant Third (MDT) winner can't be successfully 
> buried 
> to elect a
> non-MDT winner.
> 
> If these rankings are from sincere 3-slot ratings ballots, then 
> C is the 
> big SU winner.
> Also the truncating C supporters don't have to do much burying 
> to elect C.
> 
> In common with Winning Votes, your suggested method of using 
> MinMax and 
> weighing
> the defeats by the winner's approval (ranking) opposition to the 
> loser 
> elects B:
> A>B 23, B>C 25, C>A 52.
> 
> 34: A>B
> 17: C>A
> 49: B
> 
> Here A is a MDT winner, but if the B truncators change to B>C 
> then 
> AWP(ranking)
> elects B:
> A>B 17, B>C 34, C>A 49.
> 
> I think the idea that the CW should always be elected but it is 
> sometimes ok to elect
> from outside the Smith set is a bit philosophically weird, and 
> not easy 
> to sell.
> 
> AWP(ranking) needs a lot of information that isn't just in the 
> gross 
> pairwise matrix, which
> could count as a practical disadvantage compared to some other 
> pairwise 
> methods.
> But AWP(ranking) may have sufficient strategy-resistant 
> qualities to 
> justify it as not a bad
> method, but I'm not a fan.
> 
> The Approval-Weighted Pairwise method that James Green-Armytage 
> originally envisaged
> allowed voters to rank among unapproved candidates. That version 
> fails 
> mono-raise.
> 
> 31: A>>B
> 04: A>>C
> 32: B>>C
> 33: C>>A
> 
> B>C 32, C>A 33, A>B 35. C's defeat is the weakest so C wins.
> 
> Now say the 4 A>>C ballots change to C>>A.
> 
> 31: A>>C
> 32: B>>C
> 37: C>>A
> 
> A>B 31, B>C 32, C>A 37. Now B wins.
> 
> Chris Benham
> 
>