[EM] Addendum on hare-clustered MAM

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Feb 11 08:07:34 PST 2022


I think it should be possible to make the clustering method at least
somewhat nicer complexity wise by replacing MAM/Ranked Pairs with
minmax. We would then only have to run one linear program per
constituency, at the expense of losing most of the nice properties of
MAM (like clone independence).

The linear program for minmax would be something like:

- choose the vector w to maximize min X>Y
- subject to:
	- for all X,Y: X>Y = sum over voters v who prefer X to Y: w_v
	- for all v, 0 <= w_v <= 1
	- (sum v over all voters: w_v) = voters/seats (Hare quota)

(Lexicographic max would be a better objective function, but I'm not
aware of any common LP optimizers that support it.)

Since minmax fails mutual majority, the Droop magnification version
wouldn't work.

-km


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