[EM] UncAAO, DMC, ASM, and TACC

[Forest W Simmons]

Chris,

I'm sure that you are aware that in your example,

31: a|b
32: b|c
37: c|a ,

the UncAAO winner is c, so that DMC is not uniformly better than UnCAAO 
in the three candidate case, assuming that c "should" win.

But I'm not so sure that c should win.  In fact, I believe that more 
likely than not, a ballot set like this reflects a burial of b by the 
37 c faction, anticipating a victory for c from a method like ASM or 
Smith Approval.  So I believe that a ballot set like this would occur 
much more rarely under DMC than under ASM.

I believe that for the most part cyclic preferences among three 
candidates are artificial, especially in a culture where most of the 
issues are highly correlated, as Mike has pointed out.

In other words, I believe that this ballot set is more likely to arrise 
when the burial is rewarded with success.  So in this case, I'm not so 
sure that the ASM (and UncAAO) winner c is better than the DMC winner b.

Another nice method, Jobst's TACC (Total Approval Chain Climbing), also 
gives b as winner. 

Recall that Jobst initializes a "chain" with the lowest approval 
candidate, and (moving up the approval list) adds only those candidates 
to the chain that pairwise defeat each of the other candidates 
currently in the chain.

How does TACC compare with ASM and DMC in other three candidate cases?

Forest


Chris Benham wrote:


>
>Forest W Simmons wrote:
>
>> Here's the question to focus on: is there one method (that uses 
>> approval information) that is uniformly best in the three candidate 
case?
>>
>The answer to that I think is affected by whether the balloting rules 
>allow voters to rank among
>unapproved candidates or not. If not I think ASM is the best. If yes, 
>then DMC is a bit more
>resistant to Burial than ASM, having the property that if there are 
>three candidates X,Y,Z and  X
>is exclusively approved on more than a third of the ballots and wins 
>then altering some ballots from
>Y>X  (and I hope Y=X) to Y>Z  can't change the winner to Y.
>
>But this IRV-like virtue definitely comes at some expense of 
>monotonicity. DMC technically scrapes
>in to compliance with mono-raise and doubtless fails some other 
>monotonicity property that ASM meets.
>
>31: a|b
>32: b|c
>37: c|a
>
>I am a bit perturbed  by  anything  that doesn't elect C here.  C has 
>the most approval, the most FPs,
>the highest Bucklin score and the highest Borda score. ASM elects C but 
>DMC and  James Green-Armytage's
>Approval-Weighted Pairwise elect B.
>
>Chris Benham
>
>http://wiki.electorama.com/wiki/Approval_Sorted_Margins
>