<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">In a message dated 9/28/03 6:06:48 AM Central Daylight Time, donald@mich.com writes:<BR>
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>>Donald: Odds are that you are correct, that is, there are good reasons why<BR>
neither of them is any good, but you are not alone, almost all the cycle<BR>
resolutions are no good. Most people who concoct cycle resolutions do not<BR>
understand the context of a circular tie. As a result, their cycle<BR>
resolutions depend on defective data, which inturn makes the solution<BR>
defective, or in other words, garbage in garbage out. I'm talking about<BR>
the lower choices. A circular tie proves that the lower choices are<BR>
flawed. To use the lower choices when they are flawed is the wrong thing<BR>
to do.<<<BR>
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I do not believe the statement "a circular tie proves that the lower choices are flawed." Quite the contrary, circular ties are inevitable. <BR>
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>>First, let me say that a circular tie is not the fault of Condorcet. When<BR>
a circular tie has occurred, it merely means that Condorcet has reveled<BR>
that the voters have voted in a circular pattern. At this point everyone<BR>
should realize that something is wrong and should not use any cycle<BR>
resolution that depends on the lower choices because the lower choices are<BR>
at least suspect.<<<BR>
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No, nothing is wrong. Some set of voters said A>B and another set of voters said C>A and a distinctly different set said B>C. It is only when a method counts the ballots that we get a "paradox" that says as many voted A>B>C as voted C>A>B. <BR>
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>>A circular tie should be regarded as a warning bell to the fact that the<BR>
lower choices in this election are flawed and should not be trusted. Most<BR>
likely this flaw was caused by the voters not being informed well enough to<BR>
make good lower choices.<<<BR>
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No, a circular tie just says that the "lower" choices of some voters are the "higher" choices of other voters. <BR>
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>>Years ago, on this list, I suggested that when Condorcet shows a circular<BR>
tie that the best thing to do was to eliminate one candidate. Most likely<BR>
this will break the cycle. Then you can resume using Condorcet if you<BR>
must.<<<BR>
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Yes, that is obvious. No paradox can occur in a two-way race, so the objective of any method is to reduce the number of candidates to 2. The only real question is which method to use to do that.<BR>
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>>Anyway, in my school of thinking, almost all choices are suspect and the<BR>
policy should be to use as few as possible. This is one of the reasons I<BR>
favor Irving because Irving will use less lower choices than any other<BR>
multi choice method. Consider the following election: 45 Axx 45 Bxx<BR>
10 Cxx<BR>
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Condorcet will use all the lower choices. Irving will only use ten percent<BR>
of the lower choices. Using less is best. A multi choice election that<BR>
has a majority winner in the first choices is ideal because no lower<BR>
choices will be used. Think about that, if that is the ideal, then we<BR>
should stay as close as possible to the ideal as we can when picking an<BR>
election method.<<<BR>
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I'm not sure I understand all of the terms in the preceding two paragraphs, but as a voter my opinion is that any method that doesn't choose a candidate who gets 50%+1 of the first place rankings will result in a rebellion by a majority, and any that discards valid ballots because they lead to a cycle would be declared unconstitutional in the US at first use. <BR>
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The existance of cycles in Condorcet-based methods is a natural consequence of combinatorial mathematics. There is nothing "wrong" with the voters who participated in the election. <BR>
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