<html><body bgcolor="#FFFFFF"><blockquote type="cite"><span class="Apple-style-span" style="color: rgb(0, 0, 0); font-size: 13px; -webkit-tap-highlight-color: rgba(26, 26, 26, 0.296875); -webkit-composition-fill-color: rgba(175, 192, 227, 0.230469); -webkit-composition-frame-color: rgba(77, 128, 180, 0.230469); "><span>On May 16, 2010, at 9:50 AM, Kristofer Munsterhjelm <<a href="mailto:km-elmet@broadpark.no" x-apple-data-detectors="true"><a href="mailto:km-elmet@broadpark.no">km-elmet@broadpark.no</a></a>> wrote:</span><br><span></span><br><blockquote type="cite"><span>Abd ul-Rahman Lomax wrote:</span><br></blockquote><blockquote type="cite"><span></span><br></blockquote><blockquote type="cite"><blockquote type="cite"><span>"Demanding" is an odd word to use for "allowing." "Condorcet" doesn't really refer to ballot form, though it is often assumed to use a full-ranking ballot. In any case, a ballot that allows full ranking, if it allows equal ranking and this causes an empty space to open up for each equal ranking, is a ratings ballot, in fact. It's Borda count converted to Range by having fixed ranks that assume equal preference strength. Then the voter assigns the candidates to the ranks. It is simply set-wise ranking, but the voter may simply rank any way the voter pleases, and full ranking is a reasonable option, just as is bullet voting or intermediate options, as fits the opinion of the voter.</span><br></blockquote></blockquote><blockquote type="cite"><span></span><br></blockquote><blockquote type="cite"><span>If the range is too narrow or too wide, the equivalence fails.</span><br></blockquote><blockquote type="cite"><span></span><br></blockquote><blockquote type="cite"><span>For an example of the former, there's no way to express all possible Range-4 ballots with a ranked ballot with three candidates, even if you permit equal rank.</span><br></blockquote><span></span><br><span>Of course not. The equivalent Range ballot is Range 2, not Range 4.</span><br><span></span><br><blockquote type="cite"><span>To do so, you would have to be able to vote for "Nothing", e.g.</span><br></blockquote><blockquote type="cite"><span>A > B >> C, which is A > B > {} > C, which is A gets 4 pts, B gets 3, C gets 1.</span><br></blockquote><blockquote type="cite"><span></span><br></blockquote><blockquote type="cite"><span>It works the other way as well: if you have five candidates, ranked ballots expressing a full preference ordering cannot be converted to Range-4.</span><br></blockquote><span></span><br><span>Incorrect. To allow full ranking, for N possible candidates, you need Range(N-1). Number of ratings = number of ranks. With 5 candidates, the Range ballot needed for full ranking is indeed Range 4. If the voter does not equal rank, the ballot is a Borda ballot. Borda works as a method to the extent that preference strength between adjacent ranks is equal, or averages to equal. Borda breaks down when this assumption breaks down. True clones with pure Borda cause ratings to fall for all lower-rated (ranked) candidates, whereas with Range (Borda with equal ranking and thus empty ranked allowed) ratings are independent.</span><br><span></span><br><span>Borda is a Range method with a peculiar restriction. That restriction made sense when it was assumed that the only relevant information was rank order. It is really the same error as vote-for-one, which works fine when a majority is required....</span></span></blockquote></body></html>