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?
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