Would this work as an analog of Droop proportionality, but for voting
methods based on divisor list methods?
With a given divisor p, if X voters vote Y candidates above all others,
then at least min(Y, f(X/p)) of the candidates in this set should be
elected, where f is a rounding function (simple rounding off in Webster).
Then, when electing v seats, set p to the lowest possible value so that
there is at least one set of cardinality v that can be elected. All sets
that can be elected without contradicting the first paragraph in that
instance (there may be one, or there may be more) are considered "eligible".
To pass the criterion, the method must elect one of the eligible sets.
//
If everyone votes party line, this should reduce the method to an
ordinary divisor method. For instance,
100 voters: A1 A2 A3 A4
100 voters: A1 A2 A3
100 voters: A1 A2
100 voters: A1
50 voters: B1 B2 B3 B4
50 voters: B1 B2 B3
50 voters: B1 B2
50 voters: B1
3 to elect, then the lowest p for Webster satisfies round(100/p) +
round(50/p) = 3, i.e. p = 40.1 (actually, ever so slightly more than 40,
but this doesn't matter at this point because the constraints don't
change until p = 40 on one hand and p slightly lower than 200/3 on the
other).
p = 40.1 gives A 2 seats and B 1, as expected. For this example, there
is only one eligible set. If voters had been indifferent as to the
ordering of their own party's candidates, there would have been more,
such as {A1, A3, B1}, {A2, A4, B2}, etc.
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