I've just realized that, regarding the strategy for that method where single votes are free, and large ones are paids for, I spoke too soon. Of course the free & low-price votes are so much a better deal that there'd be some incentive to give them to every candidate with positive strategic value, unless there's a candidate so strategically important that it's justified to spend much more money per vote to give him more. Also, I was talking about if one had a fixed amount to spend n the votes, but really the amount that one would spend would depend on the strategic values. Since that method isn't going to be adopted anyway, and since its strategy is more complicated than I thought, maybe it would be better not to try to figure it out. *** But lest that undermine the credibililty of what I was saying about strategy for Plurality, Approval, & Cardinal-Measure, those statements are all from Robert Weber, Samuel Merrill, & Gary Cox (but I should say that if you notice an error, it's probably mine). The assumption that one or more of them mentioned was just that the probability of two candidates' vote totals being within a certain distance of eachother is linerly related, and I suggested here why that could reasonably be expected to likely be so. It seems to me, however, that only Borda (and probably $0,$1,$10,$100) needs that assumption to calculate its strategy, and that Plurality, Approval & Cardinal Measure don't need that assumption. *** Maybe, with method I described, in which you pay for how much your vote benefitted you, an exception to sincere voting would be that you wouldn't give anything to alternatives with negative strategic value. I'm sure it's premature to concern oneself with strategy details of methods that are unlikely to be adopted for a very long time. Even if you like a method like that, in which pretty much no one really loses, because everyone buys what they get, it isn't something that you can propose for your mayor election any time soon, so you have reason to be interested in more proposable methods. And sorry if I've said too much about all this. Mike Ossipoff