Warren Smith wrote:
Kristofer Munsterhjelm's "monotonic proportional multiwinner method"
-- a few comments
(1) wow, very complicated. Interesting, but I certainly do not feel
at present that I fully understand it.
Alright. If you have any questions, feel free to ask.
(2) RRV obeys a monotonicity property and a proportionality property
http://rangevoting.org/RRV.html
My experiments with multiwinner methods seem to indicate that you need
proportionality not just of single candidates but also of groups of
them, like satisfied by the DPC or by this.
(3) assuming we're willing to spend exponential(C) computer time to handle
elections with C candidates, then KM's constraints form a "linear program" which
in fact would be an "01 integer program" if candidates get elected or
not (cannot be 37% elected). Program has exponential(C) number of
constraints.
So do methods like Schulze STV. In any case, I wonder if it's possible
to make some sort of polytime algorithm for my method, but it would
probably be quite difficult. One would have to understand the nature of
the shifting of constraints as the divisor changes to find the
best-margin council that doesn't contradict, implicitly.
If it's possible, a comparison would be that a method like STV satisfies
the Droop proportionality criterion even though this is also,
mathematically speaking, an integer program ("every coalition supported
by more than k Droop quotas should have at least k members in the
outcome, unless the size of the coalition is less than that").
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