[EM] Uncovered set methods (Re: How close can we get to the IIAC)

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:

> Here's a method I proposed a while back that is monotone, clone free,
> always elects a candidate from the uncovered set, and is independent
> from candidates that beat the winner, i.e. if a candidate that 
> pairwise beats the winner is removed, the winner still wins:
> 
> 1. List the candidates in order of decreasing approval.
> 
> 2.  If the approval winner A is uncovered, then A wins.
> 
> 3.  Otherwise, let C1 be the first candidate is the list that covers
> A.  If C1 is uncovered, then C1 wins.
> 
> 4.  Else let C2 be the first candidate in the list that covers C1.
> If C2 is uncovered, then C2 wins.
> 
> etc.
> 
> There are variations on this method that preserve all of the
> mentioned properties, including methods that do not require approval
> information, but I think it is nicer to take into account approval
> information.  If this is done via an approval cutoff on ranked
> ballots, the approval cutoff, AC, itself can be considered a 
> candidate with 50% approval.  No candidate with less than 50%
> approval can cover the AC, and the AC beats pairwise every candidate
> with less than 50% approval, so no candidate at all can cover the AC
>  unless it pairwise beats all of the candidates with less than 50%
> approval.
> 
> What do we do if AC wins the election?   If we want a deterministic
> answer, I suggest that we elect the candidate C that has the least
> pairwise opposition from the AC.

That's UncAAO, right? I've considered adding it to my simulator, but I'm 
unsure of where the simulated voters should put the approval cutoff. 
Should they do so based on "frontrunner plus" strategy, on an objective 
internal condition (above mean utility or similar), or on a contingent 
condition (better than what we have already)? I'm not sure.

Perhaps one could use AC as a none-of-the-above. As it is, it seems a 
bit too strong for that, but if it could be modified to work as NOTA, 
then the simple answer for "AC wins" is "redo the election with other 
candidates". It would make sense if people put the cutoff at the value 
of just proceeding as usual (with no change of the office in question).

I've also been wondering if my variant of second order Copeland always 
elects an uncovered candidate. The method goes: first run a sports type 
of Copeland, where a win is worth 2 points, a tie 1, and a loss zero. 
Then each candidate gets two times the sum of points of the candidates 
he beats, plus the sum of points of the candidates he ties. Greatest 
score wins.
I think this would be the case if the initial points allocation had the 
property that Smith set members have a greater score than non-Smith 
members, but the 2/1/0 Copeland set (those who win in Copeland with 2 
pts for win and 1 for tie) is a subset of the Smith set, not the entire 
Smith set, which might complicate matters.