[EM] "Dominant Solid Coalition" suggested criterion (and strong standard)
cbenham at adam.com.au
Sun May 7 21:45:53 PDT 2023
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
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
Later-no-Help and FBC at the cost of lots of Later-Harm failing
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
advantage those methods have over IBIFA.
In addition I propose a slightly weaker version: "Pairwise Dominant
*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.
More information about the Election-Methods