[EM] "Mutual Plurality" criterion suggestion

[Greg Dennis]

Chris, I think this is an excellent improvement over mutual majority. My
only suggestions are around how it's phrased and named.

I'd probably drop the "smallest S"  when describing it, since it's implied,
i.e. just "If there exists a set S ... then the winner must come from S."
Mutual majority has the same "smallest" implication but I think is usually
omitted from descriptions.

I'm concerned that the name "mutual plurality" makes it sound like a weaker
condition than "mutual majority." Maybe something like "Undefeated
coalition," not sure.

It's clear to me that the Smith set is always a subset of every "mutual
plurality" set, right?


On Tue, Apr 24, 2018 at 9:11 PM, Chris Benham <cbenhamau at yahoo.com.au>
wrote:

> 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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*Greg Dennis, Ph.D. :: Policy Director*
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