[EM] A possible equal-rank/truncation extension of the resistant set

[Kristofer Munsterhjelm]

Here is a possible extension of the resistant set to handle equal-rank 
and truncation:

"A sub-election of an election is the resulting election after some 
candidates have been eliminated and preferences transferred.

A candidate X disqualifies another candidate Y if: in every sub-election 
where X and Y are both present, X has more than 1/k of the first 
preferences *that distinguish between X and Y*, where k is the number of 
non-eliminated candidates in that sub-election.

The resistant set consists of every candidate who is not disqualified by 
someone else."

I'm not yet completely sure that this will preserve the resistant set's 
acyclic nature. Would it be possible to use equal rank to set up a 
situation where, say, in the three candidate Condorcet cycle case, A 
disqualifies B by having more than 1/3 of the voters who don't rank A 
and B equal, B disqualifies C likewise, and C disqualifies A?

Perhaps a way to find that out is to consider the pairwise reduction. 
The pairwise (k=2) component says: A beats B pairwise iff the number of 
voters who strictly prefer A to B exceeds the number of voters who 
strictly prefer B to A.

What Condorcet type is this? wv?

I guess the simpler fractional first preference counting would be margins.

-km