Raph Frank wrote:
On Wed, Oct 29, 2008 at 7:12 PM, Kristofer Munsterhjelm
<[EMAIL PROTECTED]> wrote:
A multiwinner analog of random
candidate would be vulnerable to cloning, and I don't think random ballot
(pick n ballots) would be proportional either.
Actually, pick n ballots would be proportional. If there are N seats
and you have 1/N support, then on average you will get one seat.
Ofc, there would be variation from the average. An extremist faction
could win all N seats, but that is not likely.
However, that is also true for single seat random ballot, a candidate
with 1% support could win.
There's another problem. If you pick n ballots, with some probability
more than one ballot is going to have the same first place candidate.
This might be solvable by picking the first place candidate of the first
of the n ballots, then eliminating it, and so on. Would that be cloneproof?
I think Woodall wrote that Clone-Winner is incompatible with Droop
proportionality; but what of Clone-Loser? It should pass Clone loser,
since adding a clone never splits the vote, since the worst thing that
could happen is that one of the clones are eliminated, after which
another clone may be in first place on the other ballots.
Has anyone considered PR-STV with random ballot elimination? It would
work exactly like PR-STV except one ballot would be picked and the
lowest ranked candidate on the ballot uneliminated candidate would be
eliminated (excluding elected candidates). Also, ballots that are
being 'held' by elected candidates would not be included for
selection.
It might be nonmonotonic. The monotonicity criterion for
nondeterministic methods would be "raising A on a ballot shouldn't
decrease A's probability of winning". The single-winner equivalent would
be "IRV with random ballot elimination".
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