[EM] Sorted Approval Margins (plus two other Condorcet methods)

[C.Benham]

I think Condorcet methods that don't allow voters to enter an approval 
threshold have to choose between trying to
minimise Compromise incentive or trying to reduce Defection incentive.

The methods I like in this category allow voters to rank however many 
candidates they like and also approve all but
one or only one or any number in between of the candidates (consistent 
with their rankings). Equal-ranking is allowed.

Default approval goes only to candidates ranked below no other candidate.

I suggest that voters can just mark one of the candidates as the lowest 
ranked one they approve (i.e. only that candidate
and those ranked higher or equal to it are approved).

But other ways of doing it could be fine.

Regarding which algorithm, I very much like Forest's  Sorted Approval 
Margins.

I also like another method of his, the exact name of which I've 
forgotten (something about "Chain" building or climbing):

*Begin the chain with the most approved candidate.  Then add the most 
approved candidate that covers that candidate.
Then add the most approved candidate that covers all the candidates 
already in the chain.

Keep doing that as many times as possible, and then elect the last added 
candidate*.

I think nearly always this will elect the same candidate as 
Smith//Approval, but is more elegant and ensures that the
winner is Uncovered.

For a practicable Condorcet method that uses plain ranked ballots 
(equal-ranking and truncation allowed), I like
Smith//Ranked below none minus ranked above none.

*Eliminate all the candidates not in the Smith set. Give each remaining 
candidate a score equal to the number of ballots
on which it is ranked (among remaining candidates) below no other 
candidate minus the number of ballots on which it
is ranked (among remaining candidates) above no other candidate.

Elect the candidate with the highest score."

Given how rare top cycles will likely be, I think this is probably good 
enough.

Obviously it meets Plurality.  It fails both Minimal Defense and Chicken 
Dilemma, but never both at once :)

It looks fair and gives a pretty-enough winner.  I'll be back later with 
some examples.

Chris Benham