Raph Frank wrote:
On Sat, Nov 15, 2008 at 3:45 PM, Kristofer Munsterhjelm
<[EMAIL PROTECTED]> wrote:
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).
Well, I was thinking if the proposal was used with d'Hondt.
D'Hondt is also a divisor method, and since divisor methods meet the two
monotonicity criteria, they are all incompatible with quota. To my
knowledge, only divisor methods meet both monotonicity criteria. I'm
unsure as to whether that is true for divisor methods on sets, like
Ossipoff's Cycle Webster method, but it doesn't seem to be the case for
Cycle Webster, at least.
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?
In the single winner case, Droop proportionality says that if a
majority ranks a group of candidates above all other candidates, then
one of those candidates will win. All methods that meet the condorcet
criterion would also meet the Droop proportionality criteron.
However, all single winner methods that meet the Droop proportionality
criterion don't necessarily meet the condorcet criterion. IRV being
an example that meets the Droop proportionality criterion but not meet
the condorcet criterion.
The single-winner criterion corresponding to the DPC is the mutual
majority criterion. Any method that's Smith also passes mutual majority,
and since Condorcet is just the case of the Smith set being a singleton,
any Condorcet method passes the criterion when there's a CW. When
there's not, a method may pass or fail; it passes if it's Smith, and it
may either if it's not. Minmax and Black both fail mutual majority, to
my knowledge. While I'm not familiar with which well known Condorcet
methods, if any, that pass mutual majority while not being Smith, it's
easy to make one: "CW if there is one, else IRV", for instance.
In that context, a multi-winner condorcet criterion would have to a
stricter requirement than merely meeting the Droop criterion and any
method that fails the Droop proportionality criterion would have to
fail it.
It may pass it yet fail DPC if the multi-winner Condorcet "winner"
(winner set?) is not present in all elections. If it elects the
multiwinner Condorcet candidates (and in that case passes the DPC) when
they exist, but fails DPC in all other cases, then it would fail DPC in
general. But if it's like the Smith set, in that it's a subset of the
Droop Proportionality set (mutual majority set in the case of
single-winner), then what you say is true.
If it's a subset of the DP set, then we know that it can't always be a
proper subset. Otherwise, there would be cases where there are no
eliminations in STV, so that any method that passes DPC must elect the
entire set; if the subset was a proper subset, it would the fail the
DPC, which is not desirable. But that's not so surprising, since it's
also the case with Smith (regarding the mutual majority set); just
produce ballots that all vote A > B > C and then a cycle among the other
candidates.
But what would this multi-winner Condorcet criterion be? That's the
question. One may also ask whether it's a desirable criterion (like
Condorcet), or if it's too strict (like Participation).
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