Jameson Quinn wrote:
What if you have to elect two with the following voters:
99: A>B>C
1: C>B>A
The two winning orders are A>B>C and C>B>A - sum of distances is 0. So A
and C win. Yet I think most of us would agree that the correct
proportional winners are A and B.
I see your point. The problem is that the A>B>C order is closest to more
than a Droop quota. A brute force hack would be to say "assign the first
n positions of the ordering if it's closest to more than n Droop
quotas", but that seems ugly and would make the constraints a lot more
complex, and might make them unsolvable too.
So, valid objection. Now to figure out how to solve it in an elegant
manner! Any ideas?
(Actually, that particular problem is similar to minimax Approval:
minimize the maximum distance to the most distant. It ends up being
"consensus-like" at the expense of proportionality.)
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