Juho, I see from the "Method support poll" that you are "close to supporting" a "Two round system".
I regard the normal version of this, where both rounds are by Plurality and the top two from the first round run off in the second, as pretty awful. The only criterion compliance advantage it has over FPP is Condorcet Loser, and generally the only thing good about it is that its equivalent to IRV when there are three (or fewer) candidates. One attempted improvement I've seen suggested is to use Approval in the first round, and then have the two most approved candidates run off in the second. Unfortunately that would be a strategy farce because rich parties with some hope of coming first in the Approval round will have an incentive to gain an unfair advantage by each running two candidates, plus many voters will have incentive to engage in easy Pushover strategizing by approving both their sincere favourite/s and the candidate that they think their favourite can most easily beat in the second round. With too much of that, it is possible that both of the finalists will be "turkeys". I've recently had an idea on how to fix this without, say, having votes cast in the first round also count in the second. "The first round uses approval ballots. If there is a second round, it is between two candidates. The first candidate to qualify for the second round is the Approval winner (A) Of those candidates B whose approval scores would exceed A's if ballots that approve both or neither of A and B were altered so that they only approve of B, select as the second qualifier the candidate that is most approved on ballots that don't approve A. If there are none such candidates B, then there is no second round and A is elected." Of course it is possible to "automate" this into a single-round method that uses ranked ballots with an approval cutoff, but that would fail the Plurality criterion, the Irrelevant Ballots criterion and probably some (maybe more serious) others. (Here by "round" I mean trip to the polling stations, with the results of any previous "round" in the same election known to the voters.) 49: A 24: B 27: CB (C>B, both approved) Here the two finalists are B and C. In the single-round version, C would win, failing the Plurality criterion. A simpler version which is more often decisive in the first round but has a greater later-harm problem would only consider the candidate that is most approved on ballots that don't approve the approval winner (i.e. has the greatest "approval opposition" to the approval winner) for the position of second qualifier. In the above example that would be A, who would be rejected and so B would be elected in the first round. But then the C supporters could have got C into the second round (with A) by only approving C. One possible problem with this idea of mine is that it may not be widely seen/understood as legitimate that there may be a candidate or candidates that don't make it into the second round but have a higher approval score than the second qualifier. The only way around that is to relax the insistence that only two candidates go into the second round, and say that all candidates with approval scores higher than the second qualifier's also qualify for the second round. (If there are more than two candidates in the second round, then if we want to keep it a binary-input system, Approval should be used instead of FPP.) In the above example that would presumably mean that again B would be elected in the first round, unless perhaps A volunteers to drop out, because otherwise all three candidates qualify. I bring this up for jurisdictions which for some reason want to keep having two election rounds, each with the voters giving simple binary inputs. Do you think the French will like it? Chris Benham ---- election-methods mailing list - see http://electorama.com/em for list info