[EM] A monotonic proportional multiwinner method

[Kristofer Munsterhjelm]

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").