fsimm...@pcc.edu wrote:
The Rivest lottery is non-monotone, but here is a monotone, clone
independent lottery that always selects from the uncovered set:
1. Let C1 be a candidate chosen by random ballot. If C1 is uncovered,
then C1 wins.
2. Else use random ballot to find a candidte C2 that covers C1. If C2
is uncovered, then C2 wins.
3. Else use random ballot to find a candidte C3 that covers C2. If C3
is uncovered, then C3 wins.
4. Else use random ballot to find a candidte C4 that covers C3. If C4
is uncovered, then C4 wins.
etc.
Note that the clone independence has the nice character of the
"Condorcet Lottery" and the Rivest method: the conditional probability
that a member C of the clone set S is chosen given that the winner is in
the clone set is equal to the probability that C would be chosen from S
if the method were applied soley to S.
I suppose this method can be used to "enhance" any base method so it
elects from the uncovered set. Just let C1 be the winner of the base method.
Whether or not that introduces more criteria failures is another question.
One could also run the above lottery a billion times and elect the
candidate that wins most often.
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