On Sun, Nov 17, 2002 at 12:01:28PM -0500, Raul Miller wrote: > This is an informal request for discussion about how to handle quorum > and supermajority requirements.
I just got a chance to catch up on the discussion. I will give a suggested solution, but first I would like to make a point that I don't think has been stated directly (though it is at the heart of Clinton's examples): Any method in which an option can be eliminated "early"--ie, without a fully head-to-head with all the other options--has the same fundamental flaw as instant runoff, and should be rejected for the same reason. So for example, the clause, in most drafts, that first eliminated options that were defeated by the default option, was a direct invitation to insincere strategic voting. It would encourage voters to put the default option second, in an attempt to knock out the other candidates early. Exactly what we're trying to avoid with the Condorcet method. This clause is gone in Raul's most recent draft, though I think its treatment of the default option is still flawed (as long as one option defeats the default, any option with a supermajority requirement is effectively relieved of that requirement). I suspect that any method with a special elimination rule involving the default option is broken. My understanding is that the spirit of the quorum and supermajority requirements is that the winner should have the appropriate margin over the default, not over the other candidates. Given this, here is my attempt: 1. Create the matrix of pair-wise counts. P(A, B) is the count of voters prefering option A to option B. 2. If there is a default option Z, a. If there is a quorum Q, for all other options A add Q to P(Z, A). So if the quorum is 10, a preference of 20 to 10 for A over Z "acts like" 20 to 20. b. For every option A that requires a supermajority x (a fraction between 1/2 and 1), multiply P(Z, A) by x/(1-x). So if A requires a 2/3 supermajority, a preference of 200 to 100 for A over Z "acts like" 200 to 200. (Er, ignore the case of both a quorum and a supermajority requirement for the moment.) I increase P(Z, A) instead of decreasing P(A, Z) because a preference for the default ought to be strong in CSSD. 3. Do a "textbook" Condorcet/CSSD algorithm on the modified counts. Yes, you will find some odd outcomes, but I don't see anything too outlandish. For example, in a straight election with no supermajority requirement, the winner might not be prefered to the default. I think you just have to accept this as a corner case (which is definitely is--remember, this sort of thing doesn't often happen in practice). Most importantly, to the extent that Condorcet/CSSD is resistent to strategy, this algorithm should be as well, since any strategy against this would just be a scaled version of a strategy against plain Condorcet/CSSD. Well, I haven't thought this all the way through, but it has a nice feel. Andrew