[EM] STV - the transferrable part is OK (fair), the sequential round elimination is not

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Mon, Nov 2, 2009 at 8:56 PM, Juho <juho4880 at yahoo.co.uk> 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.