[EM] Brian Olson's multiwinner IRNR idea seems busted

[Kristofer Munsterhjelm]

Warren Smith wrote:
> I sent Brian what I believe is a counterexample to proportionality for both
> his suggested method, and a wide class of ways to try to generalize it.
> 
> I won't give the details here, since mixed in with a lot of other crud
> I emailed him.  But quickie crude sketch is:
> 
> Consider 2 winners and N candidates and
> all votes of form (1,1,1,...,1,0) or (0,0,0,...,0,1);
> pick N and the proportions of the 2 kinds of voters, to make the voting method
> mess up.

That actually raises another question. Since Range doesn't meet Majority 
("pizza voting" example), how exactly is proportionality defined for a 
multiwinner version of Range?

The multiwinner analog of Majority, for other methods, would be 
something like "assume the population are divided into N camps, each of 
which vote in a particular order - then the method should reproduce the 
camps' proportions in the assembly, as far as such is possible". The 
mulitiwnner analog of Mutual Majority would be Droop Proportionality or 
proportionality for solid coalitions. But both of these are based on the 
single-winner idea that "a majority wins" (in the former case, a single 
candidate supported by a majority, and in the latter, a set of 
candidates supported by a majority), neither of which is true for Range. 
So what is it that we "want" to see in a "proportional" Range method?