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Though the options of voting as in AOCBucklin, MTAOC or MCAOC in an Approval election make some sense, when the election is regarded as<br>that kind of election, with some people (the Approval-ballot voters) rating everyone at top-rank, one can't help noticing that some aspects of those<br>vote-management options, in an Approval election, seem suboptimal for the voter.<br><br>Two conclusions suggest themselves:<br><br>1. Maybe MTA, MCA and ABucklin don't often really improve on Approval. Maybe Approval-style voting is often the best strategy<br>in those methods.<br><br>2. Maybe there could be a better vote-management option in an Approval election.<br><br>Regarding #2, how about Stepwise-to-Majority?<br><br>I'd previously proposed Middle-When-Needed, and Stepwise-When-Needed. Stepwise-When-Needed could be called <br>Stepwise-to-Win. The rankings, as in Bucklin, keep simultaneously giving a vote to their next choice, stepwise, by stages,<br>as in ABucklin, each ballot continuing to do so as long as no candidate it's already given to is the current winner. I acknowledged, at that<br>time, that it would often turn out to be no different from an Approval count of all the ranked candidates.<br><br>Then I noticed that the those 2 methods probably fail FBC. I wondered if there's something somewhat similar that meets FBC.<br><br>Maybe, judging candidates by an arbitrary number like majority would avoid the problem, as opposed to judging by whether one of<br>your higher ranked candidates is winning.<br><br>Hence, Stepwise-to-Majority.<br><br>During the Buckliln-like vote-giving stages, each ballot keeps giving to its next choice till someone it has given to has a majority.<br><br>But could this happen?:<br><br>If you rank your favorite, F, in 1st place, s/he gets a majority, even though s/he doesn't win, because someone else has a higher<br>majority. <br><br>A number of people rank F, and, if you help F get a majority, then they won't give a vote to their next choice.<br><br>That's regrettable, because their next choice could win with those votes, while F can't win. And when their next choice doesn't win,<br>someone worse than s/he (as judged by you) wins.<br><br>You got a worse result because you didn't favorite-bury.<br><br>So maybe, even if that scenario is merely possible, I shouldn't propose Stepwise-to-Majority unless it turns out that the FBC-failure scenario<br>can't happen.<br><br>But more worrying is the fact that one could tell that same story about ABucklin (the ER-Bucklin defined at electowiki).<br><br>Of course a vague verbal scenario like the above might not have an actual numerical example that can carry it out. There might<br>be some reason why such an example couldn't work. Still, it's worrying.<br><br>Does anyone know if there's actually a proof that ER-Bucklin meets FBC? <br><br>Can it be shown that the verbal FBC-Failure scenario described above couldn't really happen?<br><br>Might ABucklin fail FBC?<br><br>Mike Ossipoff<br><br> </div></body>
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