Raph Frank wrote:
No that isn't what I was suggesting (unless there is a
miscommunication)
It was
1) Use d'Hondt to split seats between all root candidates
Sainte-Laguë would be better, I think. Or Warren's "dynamic divisor"
scheme, although the problem of how to generalize it to party-neutral
methods reappear.
2) Each candidate, who receives seats, takes one.
3) Algorithm is applied recursively, with each candidate assigning
any spare seats to his clients proportionally.
This doesn't handle loops well/at all. It basically requires a tree
structure.
How about using a Markov weighting process to assign weights to each
candidate? The Markov process would be like an extremely large number of
voters moving randomly through the (looped) network, depositing
"strength" at each vote they visit, and selecting links so that those
with more power gets picked more often - like the "random surfer" model
in PageRank.
After having done this, each candidate now has a fraction assigned to
him. Pick the n highest score candidates.
One possible problem with this idea is that in a tree, if A is connected
to enough candidates below him, the "random voters" may not stick with A
long enough to give him a seat, whereas they may give those below him a
seat. This problem follows from that a loop has no real "root".
It may also not be entirely proportional. It would avoid the long chain
problem (since linking to others diminish your own power), but may have
other ones. A reweighted variant could be employed by first electing
someone (according to the Markov process), then reweighting that
person's power, then running it again and so on. However, if my
simulation is to be believed and the result can be generalized, then
using a good majoritarian yet party-neutral method as the base of a
reweighted multiwinner method produces inferior proportionality to other
dedicated multiwinner methods (partly because of the left-right-center
problem where center should win the single-winner election, but left and
right should win the two-winner election).
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