<HTML><FONT FACE=arial,helvetica><HTML><FONT SIZE=2 PTSIZE=10 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Mike<BR>
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In response to my post you gave the following example of an IRV failure:<BR>
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50: ABCDE<BR>
51: BACDE<BR>
100: CDBEA<BR>
53: DECBA<BR>
49: EDCBA<BR>
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This type of example is not unfamiliar to me ( it or something very like it ) turned up several times in a series of posts called " The Turkey Problem " and "Is Condorcet The Turkey?" that ran (in circles) for months during your period of retirement.<BR>
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This first example is countered with a second example which is usually something like:<BR>
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47 A>B>C<BR>
4 B>A>C<BR>
2 B>C>A<BR>
47 C>B>A<BR>
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in which B is the Condorcet winner with a very low percentage of the first preference vote.<BR>
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In the first example IRV will probably elect the wrong candidate.<BR>
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In the second example Condorcet will probably elect the wrong candidate.<BR>
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So why do I think the Condorcet winner is correct in the first example and the IRV winner in the second?<BR>
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It is a question of the utility of the candidates. Ranked ballots show that candidate A is preferred to B but not how much candidate A is preferred to candidate B. A could have a utility of 1.0 and B a utility of 0.9 or A could have a utility of 1.0 and B a utility of 0.4. A low first preference vote Condorcet winner could well be a low utility, non-entity candidate whose only virtue is that he/she offends nobody. Why not use Cardinal Ratings instead? Because Cardinal Rating is very subject to manipulation and there is a strong incentive to rank candidates only at the top and bottom of the scale. Why not use Approval instead then? This solves the strategy problems but makes the method insensitive by only giving the voters only two levels of utility.<BR>
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Basically every single winner method you can think of has both problems of strategy and problems of legitimacy of winner. Some have arguably more problems than others (Borda) and Plurality most of all, but all have problems. Which problems you subjectively consider important decides both which criteria you consider important and which methods you think are good.<BR>
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You wrote:<BR>
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>Let's simplify this by only showing the preferences that IRV actually looks <BR>
>at and counts:<BR>
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>50: AB<BR>
>51: B<BR>
>100: C<BR>
>53: D<BR>
>49: ED<BR>
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>It looks rather sparse, doesn't it, when we leave out people's voted <BR>
>preferences that IRV doesn't count.<BR>
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Yes IRV does ignore information. But there is also a problem with Condorcet in this respect too. Take for example the ballot paper A>B>C>D>E. In the pairwise comparisons the fourth choice D counts 1 against E in the pairwise comparison, A the first choice also counts 1 in any pairwise comparison. Candidates A and D are not of equal utility to the voter that is why A is 1st and D 4th yet their votes both count at a value of 1 in the pairwise comparisons. Condorcet uses all the information but treats it as equal in the pairwise comparisons when it clearly is not.<BR>
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You also wrote:<BR>
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>You make it sound as if IRV's inadequacy were somehow unavoidabale. But it's <BR>
>merely the avoidable result of the fact that the busiest promoters won't <BR>
>take the trouble to educate themselves.<BR>
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Whatever single winner system you choose some sort of inadequacy is unavoidable whether it's the loss of an election under Condorcet WV due to offensive order reversal or a Condorcet winner being eliminated in a 3 candidate IRV count as a result of having just less than 1/3 of the vote. With single method methods the elimination of one problem more often than not leads to the creation of another.<BR>
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You also said:<BR>
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>Anyone claiming that those plausible & ordinary situations won't happen <BR>
>often should explain why they believe that.<BR>
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>Though there aren't recorded and publislhed data that would show how often <BR>
>these failures are happening in existing IRV elections, it's a sure thing <BR>
>that they'll happen regularly<BR>
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You are correct these situations will indeed happen under IRV as surely as low utility winner situations will occur under Condorcet. The kind of situation you had been referring to in your previous posts was that of Favourite Betrayal. Looking at Australian elections I have found little if any evidence of this. In South Australia in 1997 in a number of seats both National/Liberal or Labor could have defeated the other's candidate by voting Australian Democrat ( examination of the transfer patterns in seats where the AD's came second showed that over 80% of Liberal/National voters preferenced the AD's over Labor and vice-versa). This didn't happen. You yourself are not going to betray Nader in order to help a mainstream Democrat beat Bush.<BR>
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David Gamble<BR>
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