[EM] Another interesting property of the unfortunates class of method

[Kristofer Munsterhjelm]

On 2/23/23 11:13, Kristofer Munsterhjelm wrote:
> What I mean by the "unfortunates class" is a Droop-proportional method 
> like this:
>      1. Use an appropriate method to elect n-1 of n
>      2. Eliminate the loser and repeat until n-1 is equal to the number 
> of seats you want.
> 
> I just realized that this class of method is house-monotone! Because 
> we're eliminating down to a given size set, the result for a smaller 
> election must be a subset of the result for a larger election.
> 
> In other words: nobody gets kicked out when going from a smaller seat 
> outcome to a larger seat outcome. So for all its flaws, this does show 
> that house monotonicity and Droop proportionality are compatible! I 
> wouldn't have thought that's possible.

I probably should show that an unfortunates-class (Droop-proportional) 
method actually exists, since I said I think the Bucklin-derived one is 
only partly/pseudoproportional.

This is relatively simple. For step one, let "an appropriate method" be 
STV. Since it passes the DPC, so should the unfortunates method based on it.

-km