[EM] "Mutual Plurality" criterion suggestion

[Chris Benham]

The Majority for Solid Coalitions (aka Mutual Majority) criterion 
reflects a strong standard of mine, but I'm not happy
that the concept is vulnerable to irrelevant ballots. In other words in 
some election the criterion might insist that A must
win but then if we add a handful of ballots that vote for no-one the 
criterion says that it's now ok for A to not win.

To address this I've come up with a somewhat stronger and more generally 
useful criterion that implies compliance
with Majority for Solid Coalitions.

*If there exists one or more sets S of at least one candidate that is 
voted above (together in any order) above all other
candidates on a greater number of ballots than any outside-S candidate 
is voted above any member of S (in any positions)
then the winner must come from the smallest S.*

In other words if a candidate or set S of candidates need only the 
ballots on which they are voted above all others to win
all their pairwise contests versus all the other (outside-S) candidates, 
then that is good enough.

The brief and I hope adequate name I suggest is the "Mutual Plurality" 
criterion.

As I earlier implied, everything that meets this also meets Majority for 
Solid Coalitions but vice versa isn't the case.

49: A>B
41: B
10: C

Here my suggested criterion says A must win, but Majority for Solid 
Coalitions says nothing but will agree if we remove
two or more of the C ballots.

Bucklin (and some similar methods) meet Majority for Solid Coalitions 
but elect B.

Chris Benham



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