[EM] "Mutual Plurality" criterion suggestion

[Chris Benham]

Greg,

I'm glad you like my idea.

I'm sure the definition could be polished and/or made more succinct. At 
the moment I don't have a strong view on your suggestion
on how that should be done. In general I don't mind the odd redundancy 
if it makes it more likely that more people will understand it.

I won't be dying in a ditch for the "Mutual Plurality" name, but I think 
your "Undefeated coalition" suggestion is a bit misleading
and vague.

It was conceived as an irrelevant-ballot independent version of Mutual 
Majority, so I suppose it could be called "Irrelevant-Ballot
Independent Mutual Majority".  Another possible clumsy name: "Mutual 
Dominant Relative Majority"?

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

Yes, but of course there isn't always a "Mutual Plurality" set (or 
subset) while there is always a Smith set.

Chris Benham


On 6/05/2018 6:52 AM, Greg Dennis wrote:
> 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 
> <mailto: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*
> Voter Choice Massachusetts
>
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