[EM] Favorability Sorted Ranked Pairs

[Kristofer Munsterhjelm]

On 10/28/23 01:21, Forest Simmons wrote:
> For each pair P of candidates, let Strength(P)=cov(P)+epsilon*wv(P), 
> where cov(P)=One If one member of P covers the other one, Else zero 
> EndIf, and wv(P) is the number of ballots on which the member of P that 
> pairbeats the other outranks the other.

A related thought:

Let a certain sequence S of pairwise victories' score be the sorted 
vector of their magnitudes, from greatest to least, and let S_1 > S_2 if 
leximax, the sorted vector for S_1 is greater than that for S_2.

Then Ranked Pairs consists of finding the sequence corresponding to the 
maximal such vector subject to that the induced ordering of the sequence 
is transitive.

How about finding the maximum sequence subject to that the winner should 
come from some desirable set? Your method is a way to do this for the 
uncovered set... I think (I'd have to prove that the sequence is maximal 
subject to the winner being uncovered). Is there a natural extension for 
other sets like Banks?

If we just brute-forced it, would the Banks-restricted method be 
monotone? It's probably very hard to say.

Or say we brute-forced it with the winner being part of the resistant 
set. This would be burial resistant and shouldn't have the high other 
strats effect of CTE or beat chain methods. Perhaps it would be 
monotone? Maybe there is some more natural way to phrase it than just 
"try every possible ordering and see which maximizes the leximax 
measure, and has a winner in the resistant set".

In a way, election method questions are like number theory ones: so easy 
to ask, sometimes incredibly hard to answer.

-km