[EM] Re: non-determinism and PR.

[Forest Simmons]

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