[EM] Semiproportional Bucklin method

[Dan Bishop]

Kristofer Munsterhjelm wrote:
> I think this can be used to make a proof that a summable multiwinner 
> method can't let you actually discover all the Droop sets. The idea 
> would be something like this: say that the method does, and it's 
> summable. Then you can, by a combination of padding with irrelevant 
> votes (for candidates that appear nowhere else), and altering the 
> number of seats, determine the solid coalition set for any number of 
> voters. If you can use the method to determine all the Droop sets, 
> then this in effect lets you reconstruct the DAC/DSC information. But 
> that information takes superpolynomial space, so by pigeonhole, you 
> can't get it from a method that only relies on a polynomial amount of 
> data.
I've long conjectured there is no multi-winner ranked-ballot method that 
is both proportional and summable.

However, you haven't ruled out the possibility that there could exist a 
Droop-proportional method that doesn't require explicitly finding all 
the Droop sets.  Such methods DO exist in the single-winner case, where 
Droop proportionality = Mutual Majority, which can be met by a 
quadratically summable method.