[EM] Did someone say monotonicity? Or: Droop proportionality and monotonicity

[Kristofer Munsterhjelm]

On 04/02/2020 11.25, Toby Pereira wrote:
> I feel compelled to point out that proportionality is not the same as
> Droop proportionality. Something can fail one particular "brand" of
> proportionality and still be proportional.

Yes, you're right :-)

What I like about Droop proportionality is that it implies that
proportional groups of voters (to some degree) don't have to coordinate
to get someone they prefer elected. That is also why something like
Warren's "racist"/"color proportionality" doesn't impress me as much,
because those proportionality criteria basically say that if everybody
who supports a certain party vote all the party members at max and
everybody else at min, then the party gets its share. That criterion
only tells you what happens if all the voters either coordinate or
compromise (give up their chance at deciding who gets to win within the
party in order to get the party as a whole to get its share of the seats).

Of course, methods that pass DPC might still have a serious coordination
or compromising incentive. (The criterion is stronger the more seats
there are.) But at least it reduces the need to employ such strategies.

Ideally I'd like to have a kind of proportionality that reduces to
Webster in the party list case, rather than reducing to LR-Droop, since
Webster is much better behaved as a party list method. The only such
criteria I've found so far are extraordinarily complex to state, though.

Perhaps also something that's to the Smith set what the DPC is to mutual
majority.

(And obviously, a method passing such a "Webster criterion" would
automatically fail the DPC, which is yet another indication of what you
say: proportionality isn't the same thing as Droop.)