I recommend AER (Approval-Elimination Runoff, or "Approval AV") for cases where Schulze(wv) is considered impractical (due to the need for a pairwise matrix) or unintuitive (as a decision-making process).
AER is like IRV, except that the elimination order is set in stone at the beginning based on "approval" (non-last rankings, or based on a cutoff). This allows AER to be monotonic (although it is at the expense of Mono-add-top and the LNH properties). It also permits two counts of the ballots to suffice, if N^2 tallies (as in a pairwise matrix) become acceptable. I prefer AER to Approval because of its superior ability to respect pairwise victories. It satisfies Majority (like IRV). It doesn't meet any Condorcet criteria (even the weaker "gross" forms), though. For instance: 5 C>A 4 C>B 6 A 6 B 21 total C is the CW, but in AER's search for a majority, C is eliminated, since C has the lowest approval. A is elected. Note, though, that Approval might not have done any better in this scenario. Here is the mitigating feature I've come up with: When the AER winner wins, he is the majority favorite on the remaining ballots. A majority favorite can't be beaten pairwise by any candidate remaining on the ballots (intuitively). Who remains on the ballots? We know that every candidate with greater approval must still be on the ballots (not eliminated), because if they had been eliminated, the AER winner must have already been eliminated, which is nonsense. That means a few things, all related. I couldn't settle on just one: 1. The CW can only lose to a candidate with greater approval. 2. The AER winner has either a pairwise or approval victory over every other candidate. 3. The AER winner pairwise beats every candidate with greater approval. It's easy to show that if the CW loses in AER, some CW>AERW voters must have approved both candidates. Let "C" represent the number of voters preferring the CW and approving only him. Let "C,A" be the number preferring the CW but approving both. Suppose there are no C,A voters, yet A wins. If C beats A pairwise, then C > A + A,C We know A must have greater approval, so A + A,C > C + A,C; or, A > C But if A > C, C can't exceed A plus some other number, so the scenario isn't possible. I'm not certain if this is too trivial to be called a "guarantee." But in any case I think this kind of reasoning might help convince even Condorcet fans that AER is not an unnecessarily random or senseless method. Kevin Venzke [EMAIL PROTECTED] _________________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français ! Yahoo! Mail : http://fr.mail.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info