[EM] UncAAO

[Chris Benham]

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


http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-April/008013.html 




> Chris,
>
> I'll have to ponder Adam's critique of three candidate Smith Approval 
> before I can fully respond.
>
> The main advantage of UncAAO over Smith Approval, ASM, DMC, etc. is 
> that it always picks from the uncovered set (no matter how many 
> candidates there are).  And esthetically, the geometry of Unc(whatever 
> starting point)AO is very appealing to me.
>
> If I end up agreeing with you that ASM and DMC are uniformly better 
> than Smith Approval in the three candidate case, then I will explore 
> Unc(ASM)AO and Unc(DMC)AO.  But I'm not sure that the loss of 
> simplicity would be worth it.
>
> Here's the question to focus on: is there one method (that uses 
> approval information) that is uniformly best in the three candidate case?
>
> If so, then that's the method that I would like to try to generalize 
> to an "Unc" method for any number of candidates.
>
> Forest
>
>
>
>  
>

>