[EM] "Mutual Plurality" criterion suggestion

Chris Benham cbenhamau at yahoo.com.au
Mon Jul 30 09:55:58 PDT 2018


Sorry to be so tardy in replying.

Your idea seems fine to me.

Chris Benham

On 7/07/2018 1:10 AM, Greg Dennis wrote:
> 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 
> <mailto: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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