2018-04-25 04:11:27 UTC
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"
As I earlier implied, everything that meets this also meets Majority for
Solid Coalitions but vice versa isn't the case.
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.
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