Raph Frank wrote:
Proportional Approval voting uses a different satisfaction metric.
Each voter is consider to have satisfaction of
1 + 1/2 + 1/3 + .... + 1/N
where N is the number of approved candidates who are elected.
Proportional approval voting also uses raw Approval scores instead of a
cumulative ballot. However, it is hard to calculate the optimum outcome
(i.e. the winner set that maximizes satisfaction), and it's not summable.
SAV does approximate PAV in a sense: if a voter votes for two
candidates, those candidates are given power 1/2 each. If a voter votes
for three candidates, those candidates are given power 1/3 each, and so
on. However, the approximation ends there, because the candidates may or
may not be elected.
One could also make a Sainte-Lague version by having the satisfaction as:
1 + 1/3 + 1/5 + ... + 1/N
and I think there was an earlier message on this list (somewhere...)
with the idea of generalizing this to ratings by using logarithms to
construct a function that, for f(maxrating) = 1, f(2*maxrating) = 1 +
1/2, f(3 * maxrating) = 1 + 1/2 + 1/3, etc., while being defined on
positive reals in general.
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