<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV><BR>><I> CB: Not necessarily, no. I have in mind something like<BR></I>><I> (with sincere ratings):<BR></I>><I> <BR></I>><I> 49: A(99) > C(2) > B(1)<BR></I>><I> 48: B(99) > C(2) > A(1)<BR></I>><I> 03: C(99) > A(98) > B(1)<BR></I>><I> <BR></I>><I> C is the CW, but A is a much more stable, much higher SU,<BR></I>><I> arguably as </I><I>fair or fairer winner.<BR></I>><I> <BR></I><STRONG></STRONG></DIV>
<DIV><STRONG>Aaron Armitage</STRONG> wrote:<BR>Any strategically informed voter will give approval-like ratings, and will<BR>approve the top two frontrunner he likes better, as well as any candidates<BR>he prefers to that frontrunner, which means that the stated ratings will<BR>look like that regardless of the real ones and a range election will tend<BR>to produce that result regardless of how much utility voters attach to<BR>each candidate. And, of course, IRV produces the same result.<BR><BR>What you're suggesting, then, is a case where the sincere ratings just<BR>happen to match the stated ratings that would be produced by strategic<BR>voting, and that in this special case the strategic voting under range or<BR>approval will look legitimate in elected A over C despite the existence of<BR>a majority coalition for C over A. But range and approal must assume that<BR>this is always the case, when it almost never is.</DIV>
<DIV> </DIV>
<DIV>CB: I explicitly specified that the ratings are sincere. You seem to be assuming<BR>that I am promoting Range or Approval as better than all the Condorcet methods<BR>when I am not. I just gave the example to show that the sincere CW isn't necessarily</DIV>
<DIV>the most stable or only justifiable winner. (Maybe I am in the wrong thread.)</DIV>
<DIV> </DIV>
<DIV>Since all Condorcet methods fail Later-no-Harm, in practice in a Condorcet election</DIV>
<DIV>the A and C supporters would most likely truncate making A the voted CW. If only</DIV>
<DIV>the A supporters truncate then the candidates are in a cycle that would most likely</DIV>
<DIV>be resolved in favour of A.</DIV>
<DIV> </DIV>
<DIV>In response to my question "what do you mean by 'Smith/IRV'?" Aaron replied:<BR></DIV>
<DIV>"...we would first check to see who is in the Smith set.<BR>If there's only one, he is the Condorcet winner and is elected. If not, we<BR>eliminate all non-Smith candidates and the lowest Smith set member. Then<BR>repeat until a winner emerges."</DIV>
<DIV> </DIV>
<DIV>I assume that "eliminate" means "eliminate at once and drop from the ballots", so</DIV>
<DIV>the first Smith-set member to be eliminated is the one with the fewest initial first<BR>preferences. I think that is a method suggested by N.Tideman in his book. Is</DIV>
<DIV>that right?</DIV>
<DIV> </DIV>
<DIV>In any case that method and "Smith//IRV" (eliminate and drop from the ballots all</DIV>
<DIV>non-members of the Smith set and then apply IRV) both fail Mono-Append and</DIV>
<DIV>Mono-add-Plump, unlike Smith,IRV.</DIV>
<DIV> </DIV>
<DIV>Chris Benham<BR><BR></DIV></div><br>
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