[EM] Is there a PR voting method obeying "participation" criterion?

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 01:08 PM 11/17/2009, Warren Smith wrote:
>> It is "fair" if symmetric under permuting the candidates and voters.
>>
>> Conjecture: there does not exist a fair multiwinner proportional 
>> representation
>> voting method obeying participation.
> 
> I don't know how to apply "fair." Can you give an example of a system 
> which is not fair by this definition? That would help.

Choose the first n candidates who registered (not invariant under 
permutation of the candidates). Turn the first n voters who voted into 
dictators (not invariant under permutation of the voters).