[EM] MinMax(AWP)

[Chris Benham]

Forest,


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

Before the reversed ballots:

31: A>>B
04: A>>C
32: B>>C
33: C>>A

A>B  68-32 = 34,   B>C  63-37 = 26,   C>A 65-35 = 30.

After the reversed ballots:

31: A>>B
32: B>>C
37: C>>A  (boosted from 33 by the 4 reversed ballots)

A>B  68-32 = 34,   B>C  63-37 = 26,   C>A 65-35 = 38.


Remember
> DMC?  DMC elects the lowest approval candidate that pairwise beats all
> of the candidates 
>>with more approval. 
Yes. The example of mon-raise failure also applies to it.


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.
>

Can you please remind me: what is the precise definition of  "UncAAO" ?


Chris Benham




Forest Simmons wrote (5 May 2010):


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 candidate 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
> 
>