On Tue, 28 Dec 2004, Forest Simmons wrote:
Here are two analogous questions concerning a cycle in which A beats C beats B beats A:
3000 A 3000 A=B 4000 B>C
(1) Suppose that A, B, and C represent parties, and that based on these ballots, we are supposed to allocate 100 seats in congress to the parties A, B, and C. How many seats should each party get?
(2) Suppose that A, B, and C represent individual candidates, and that based on these ballots we are supposed to put 100 marbles in a bag for a drawing to determine the winner. How many marbles should each candidate get?
In other words, we should be able to use ideas from Proportional Representation to get ideas for non-deterministic single winner methods.
I'm not claiming that every non-deterministic method gives rise to a multiwinner system that is "proportional," nor that every PR system gives rise to a suitable distribution of probabilities. But I do believe that this correspondence between seat allocation and non-deterministic methods should be a fertile source of cross pollination, and that the non-deterministic methods should be the main beneficiaries considering all of the work that has gone into PR systems, compared with the little effort that has gone into developing non-deterministic single winner methods.
Forest
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