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Because of the great desirability of avoiding the ABE problem, it's worth considering or looking at<br>all sorts of possible solutions. <br><br>MMPO and MDDTR are known to work fine, though they have vulnerability to non-valid criticisms.<br><br>The mutuality-requiring methods work fine too, and, though someone here has made angry noises about them,<br>he isn't saying anything other than personal opinion, and would be unlikely to be able to make a public case<br>against the mutuality-requiring methods.<br><br>Nevertheless, it's always useful to consider other approaches. <br><br>I'd spoken of two approaches to avoiding ABE:<br><br>1. Counting combined support (even if one-sided) against a candidate.<br><br>2. Mutuality-requirement<br><br>And now,<br><br>3. Faction-size (as a ballot option)<br><br>4. Hypothetical cooperation or noncooperation<br><br>How they'd work:<br><br>3. Faction-size (as a ballot option):<br><br>In the kind of ABE situation we've been speaking of, the problem would be solved<br>if the A voters could indicate on their ballot that their middle-rating for B is<br>conditional upon B having at least as many top-ratings as A has.<br><br>Of course sometimes it's necessary to support a compromise with less favoriteness,<br>and so this requirement should be optional.<br><br>4. Hypothetical cooperation or noncooperation:<br><br>This could be automatic or optional.<br><br>There could be a rule that, ballot1's middle rating to a candidate2 who isn't in<br>a mutual approval set in common with any of ballot1's top-rated candidates is counted<br>only if that candidate2 would outpoll each of ballot1's top-rated candidates if, for each<br>candidate1 on ballot 1:<br><br>...no ballot top-rating candidate2 and not candidate1 gives a middle-rating to candidate1<br>and no ballot top-rating candidate1 and not candidate2 gives a middle-rating to candidate2.<br><br>[end of tentative, work-in-progress, maybe-useful definition of the hypothetical noncooperation approach]<br><br>Alternatively, that last paragraph could replace "no ballot" with "every ballot". That would be<br>the hypothetical cooperation approach, which probably amounts to the same thing.<br><br>The above could be applied to all the middle-ratings, based on an initial assumption that<br>all middle ratings are counted. Of course, the application of the above requirements<br>would likely change the conditions that had caused some middle ratings to be given or<br>with-held. It would be simplest to disregard that change. To have the system re-examine the <br>noncounting of middle-ratings, and re-apply its requirement, could result in an unstable<br>outcome that changes with each re-examination.<br><br>Just using an initial assumption that all middle ratings are counted might be adequate for<br>avoiding the ABE problem. It certainly is, in the simple ABE situation that's been discussed<br>here.<br><br>----------------------------<br><br>I'm not saying that these ABE approaches are as workable or desirable as approaches #1 and #2. But,<br>as I said, all possibilities are worth naming, due to the importance of avoiding the co-operation/<br>defection problem. Approach #3 seems simple and workable, and useful for situations like the<br>usual ABE.<br><br>Mike Ossipoff<br><br><br><br><br> <br> </div></body>
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