[EM] "Mutual Plurality" criterion suggestion

[Kristofer Munsterhjelm]

On 05/06/2018 05:58 PM, Chris Benham wrote:
>> *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.

I think the original definition works, as the same thing happens for 
mutual majority. Every method elects from some solid coalition that has 
greater than majority support (namely, the coalition of all candidates), 
but the method only passes the mutual majority criterion if it elects 
from the smallest such set. In some situations, that smallest set *is* 
the set of all candidates, which means there's no special case logic 
needed for such a case; a method that passes mutual majority in the 
"proper" cases is then free to choose any candidate to be elected 
without violating the criterion.

I agree, though. It doesn't much matter, beyond in an elegance of 
definition sense.