In a recent message to an individual that was inadvertentlyk posted here, due to a problem of the mailer, I admitted that Condorcet(EM) has problems with order-reversal. But it's important to keep that in perspective by pointing out that all the other simple methods, except for Schulze, have considerably worse problems. Simpson-Kramer is almost as good. And if some members of an electorate were sophisticated & devious to use order-reversal, others would be sophisticated & well-informed enough to deter it by defensive strategy, as I've described. Plus, Tom Round, Steve, & I have also discussed enhancements that could be added to simple methods, to gain better strategky protection. That future sophisticated electorate could choose to adopt some of these enhancements. Tese include a candidate withdrawal option, a 2nd balloting (in methods such as BeatsAll//Approval & Smith//Condorcet///Approval), and an option for the voter to indicate his specification of what the believes to be the 1-dimensional ordering (such as a political spectrum) that he believes the candidates or alternatives to have. I've already described that option here, and this letter probably isn't the place to describe in detail this or the other enhancements. In that previous letter, I also said that, if there's a subcycle, then that could cause Condorcet(EM) to require a defensive strategy of ranking a less-liked alternative equal to a more-liked one in order to protect a Condorcet winner. But it must be pointed out that a Condorcet winner would never be in a natural cycle of any kind, so we're talking about a _strategic_ cycle, engineered by impossibly sophisticated offensive strategy, using impossible predictive information. Say it's a Green, a Democrat, & several Republicans. You're a Green. The Democrat is Condorcet winner. You want to steal his win by order-reversal, but you know that defensive truncation is probably being used against the Green, making it impossible for you to make the Republicans as beaten as the Green is. So, if you still want to try the order-reversal, you have to do more than jkust make a fake main cycle--you must also engineer a fake subcycle among the Republicans, making each of them beaten by as big a majority as the Green is. Bigger, actually. For that, you must have very good information about how the Republican & Democrat voters rate the various Republicans with respect to eachother, and make use of that information to make a cycle among the Republican candidates such that everyk Republican has a bigger majority against him than the Green does. What? You wouldn't want to try that? Neither would anyone else. It sounds impossible, to me, due to the predictive information it needs. So I can safely say that Condorcet(EM) doesn't require ranking a lower-ranked alternative equal to a more liked one in order to protect a Condorcet winner. Of course it also never requires ranking a less-liked alternative _over_ a more-liked one either. *** I've been a little unfair to Saari's point systems. What I was arguing was that, by the standards that I've said are important to many people, including us, point assignment systems can't be as good as Condorcet(EM) or Schulze. I stand by that claim, but point assignment methods are better than the _worst_ rank balloting methods such as IRO. I've recently advocated a point-assignment method on ER: Approval. You give each candidate either 1 or 0 points. Though, with a flexible point system like the ones that Saari proposes, one could calculate strategies to optimize one's statistical expectation, it would be a difficult calculation, based on one's utility ratings for the candidates and some probability estimates. Voting an Approval strategy is simpler. Weber, in the Winter 95 issue of _Journal of Economic Perspectives_, describers an Approval strategy calculation. Of course most voters aren't going to do that either, any more than they do a similar calculation with Plurality. What most will do will be to just vote for the candidate they expect to need as a compromise, the Condorcret winner (though they might defect on the CW if they believe that someone they like more will get more votes than all those whom they like less), and for everyone whom they like more. My point, then, is that the added flexibility of the methods that Saari proposes would just confuse people, and only a few mathematicians would actually be qualified to calculate strategies that would make use of that flexibility. But I do agree that, as far as basic merit goes, Saari's methods are as good as Approval--though they're unnecessarily complicated and confusing for voters. The advantage of Approval over Condorcet(EM) & Schulze is its _simplicity_, ;and ease of implementation. Saari's flexible methods would lose that advantage. However, the best of the methods that are already familiar to the public, in my opinion, is the Olympic 0-10 method: Voters may give anywhere from 0 to 10 points to any alternative. Again, the flexibility would be difficult for nonmathematicians to use, but this method has the very big advantage of prior familiarity to the public. Mike