Raph Frank wrote:
On Mon, Nov 2, 2009 at 8:56 PM, Juho <[email protected]> wrote:
I agree that DPC is a nice criterion. In practice I'm not that strict since
I believe also methods that are close to DPC work quite well. For example
basic d'Hondt with party lists may be close enough to PR although that
method slightly favours large parties (when allocating the fractional
seats).
d'Hondt is the same as Droop (assuming that all parties vote as a single block).
If there are 5 seats and you have 20%+ of the votes, you are
guaranteed to get 1 seat under both d'Hondt and Droop.
How about Sainte-Lague/Webster's? Since it's a divisor method, it would
(seldomly) violate quota, and so a ballot-based version of it couldn't
meet the DPC. Yet, I would say that such a version would (absent other
flaws) be proportional - I just don't know how to actually construct it.
If the limitations of apportionment methods are true for party-neutral
multiwinner methods as well, then it's impossible to have both
population pair monotonicity (what we usually call "monotonicity") and
to always obey quota. Although I haven't checked this in detail, it does
seem like the limitations would hold, because: otherwise, assume some
party-neutral multiwinner method X passes both - then you could just
have everybody vote party list style in X, and so use X as an
apportionment method, but that would cause a contradiction.
So if that reasoning is correct, then in order to have a monotone
multiwinner method (I don't know of any), we must accept that it some
times fails the DPC. Of course, if the DPC is the only acceptable
criterion of proportionality, then no "proportional" multiwinner method
can be monotone.
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