[EM] "Dominant Solid Coalition" suggested criterion (and strong standard)

[C.Benham]

The "solid coalition score" of a subset S of candidates is the number of 
ballots on which those candidates are voted together
(in any order amongst themselves) above all the candidates not in S.

The  "maximum pairwise opposition score" of subset S of candidates is 
the greatest number of ballots on which a candidate outside
of S is voted above a member of S.

*If there is a subset S of one or more candidates which has a Solid 
Coalition Sore that is higher than its  Maximum Pairwise Opposition Score
then the winner must come from the smallest such S.*

I think this is met by anything that meets Smith or Plurality, and 
anything that meets both of Majority for Solid Coalitions and Irrelevant 
Ballot
Independence.

I think it should mostly supplant Majority for Solid Coalitions as an 
essential standard for single-winner election methods.

The only theoretical point of keeping Majority for Solid Coalitions that 
I am aware of is that it is something that a method can comply with 
while meeting
Later-no-Help and FBC at the cost of lots of Later-Harm failing 
Irrelevant Ballots.

I have in mind Average Ratings systems like Bucklin and MJ. No-one seems 
to promote or care about Later-no-Help and that is the only 
criterion-compliance
advantage those methods have over IBIFA.

In addition I propose a slightly weaker version:  "Pairwise Dominant 
Coalition":

*If the smallest number of ballots on which a member of candidate subset 
S is voted above a candidate not in S is greater than the largest
number of ballots on which a candidate not in S is voted above a member 
of S, then the winner must come from the smallest such S with
at least one member.*

These could probably have been worded more succinctly and elegantly.

Chris Benham