# [EM] "Mutual Plurality" criterion suggestion

Greg Dennis greg.dennis at voterchoicema.org
Fri Jul 6 08:40:38 PDT 2018

```I've been thinking about this property more recently, and I'd like to offer
what I believe is an equivalent formulation of it. I'm not saying this is
_the_ way it should be expressed, but this formulation helps me see the
importance of the property:

Consider a set S of candidates such that the following is true. For every
candidate C outside of S, exclude all the ballots that express indifference
between C and all the candidates in S (i.e. C+S all equally ranked, perhaps
left off the ballot altogether), more than half of the remaining ballots
(aka the "relevant ballots"), prefer every member of S to C. If there
exists an S, the winner must come from S.

Do you agree this is equivalent or have I missed something? If so, I like
how this formulation reveals the "majority" threshold lurking inside the
original formulation, and to me makes the name Mutual Relevant Majority
tempting.

On Sat, May 12, 2018 at 1:17 PM, Chris Benham <cbenhamau at yahoo.com.au>
wrote:

> Greg,
>
> I did have, but that wasn't it.  For the purpose of applying the test to
> methods, I think I defined it thus:
>
> *If there is some losing candidate X  with fewer above-bottom votes than
> any other candidate, and all the ballots either
> vote X below all other candidates (or ignore/truncate X) or vote X above
> all other candidates and all the other candidates equal bottom
> (or ignored/truncated), then removing any number of the X-supporting
> ballots can't change the result.*
>
> Maybe a better version is possible. My idea is that those ballots
> contain no information about any of the remotely competitive
> candidates, but would normally (in jurisdictions that allow truncation or
> voting candidates equal-bottom)) be counted as valid, which
> might not be the case if the criterion just talked about "blank" ballots.
>
> Chris Benham
>
>
> On 11/05/2018 7:44 PM, Greg Dennis wrote:
>
>> Chris, do you have a precise definition of "irrelevant ballot"? Just a
>> ballot that expresses indifference between the smallest mutual majority set?
>>
>
>
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--
*Greg Dennis, Ph.D. :: Policy Director*
Voter Choice Massachusetts

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