[EM] "Mutual Plurality" criterion suggestion

[Chris Benham]

> *If there exists one or more sets S of at least one candidate that is 
> voted above (together in any order) 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.*
>
On 7/05/2018 12:21 AM, Kristofer Munsterhjelm wrote:
> Isn't the set of all candidates always a Mutual Plurality set, in a 
> vacuously true sense? 

I meant to imply that if there aren't any "other candidates" then the 
"set" doesn't exist.  Maybe:

*If there exists one or more subsets S of at least one candidate that is 
voted above (together in any order)  all of the (one or more) outside-S
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.*

But as I initially defined it, then I suppose yes. But that doesn't much 
matter. All methods might then elect from at least one Mutual Plurality
set, but only those who elect from the smallest one meet the criterion.

Chris Benham





On 7/05/2018 12:21 AM, Kristofer Munsterhjelm wrote:
> On 05/06/2018 04:38 PM, Chris Benham wrote:
>> 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.
>
> Isn't the set of all candidates always a Mutual Plurality set, in a 
> vacuously true sense?



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