Raph Frank wrote:
If you mean the Droop proportionality criterion: no, it doesn't. Since no
reweighting is done in the first round, it elects the Condorcet winner then,
and that's incompatible with the DPC.
What about running the process for double the number of steps as there
are seats.
If there are 5 seats, then the first 4 rounds would be 'setup' rounds.
Assuming the winners in each round is A, B, C ..., then the election
would proceed as
Setup stage
Round 1: A
Round 2: AB
Round 3: ABC
Round 4: ABCD
Election stage
Round 5:
E elected: ABCDE
Round 6:
A eliminated and then F elected:
Winners: BCDEF
Round 7:
B eliminated and then G elected
Winners: CDEFG
Round 8:
C eliminated and then H elected
Winners: DEFGH
Round 9:
D eliminated and then I elected
Winners: EFGHI
Note: a candidate may be referred to by more than 1 letter. A
candidate might be eliminated in round 6 but then re-elected in round
8, so that candidate is both A and H.
I wonder if it can be shown that if there is at least one solid
coalition with a) a Droop quota and b) none of them elected, then
they one of them is guaranteed to get elected for the final. If that
was true, then each of the winners in rounds 5-9 would meet the
criteron. Effectively, if a candidate who is part of a solid
coalition is eliminated, he would be reelected immediately, or
replaced by another candidate who also meets the criteron.
I don't think so. Though I haven't investigated this method, I'm
thinking that since it uses a divisor method (Sainte-Laguë), there would
be instances where it breaks quota, just like ordinary Sainte-Laguë
breaks quota, since quota (no candidate or party should need more than a
quota worth of votes to get a seat, or get a seat with less than a
quota's worth) is incompatible with the two criteria Sainte-Laguë meets
(population pair and house monotonicity).
On the other hand, quota violations are very rare in ordinary
Sainte-Laguë/Webster, so it might not matter. Yet it does seem to matter
when we port divisor methods directly to single-winner methods (e.g
RRV), as quota methods outperform them in my simulations.
Perhaps there's a multiwinner analog of the Condorcet criterion. If so,
we would have a base on which to construct a method instead of having to
guess blindly. Perhaps something like "if the method, when electing k
winners, returns the set X, and there is a way of partitioning the
ballots into k piles so that each pile has a CW, and each CW is in X,
then the method passes this criterion".
Or, is there something that is to the Droop proportionality criterion as
the Smith criterion is to mutual majority?
None of this is really applicable to the runoff (since we don't want DPC
there), but since we were discussing methods that do meet the DPC, my
mind wanders :-)
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