>>Donald: Odds are that you are correct, that is, there are good reasons why
neither of them is any good, but you are not alone, almost all the cycle
resolutions are no good. Most people who concoct cycle resolutions do not
understand the context of a circular tie. As a result, their cycle
resolutions depend on defective data, which inturn makes the solution
defective, or in other words, garbage in garbage out. I'm talking about
the lower choices. A circular tie proves that the lower choices are
flawed. To use the lower choices when they are flawed is the wrong thing
to do.<<
I do not believe the statement "a circular tie proves that the lower choices are flawed." Quite the contrary, circular ties are inevitable.
>>First, let me say that a circular tie is not the fault of Condorcet. When
a circular tie has occurred, it merely means that Condorcet has reveled
that the voters have voted in a circular pattern. At this point everyone
should realize that something is wrong and should not use any cycle
resolution that depends on the lower choices because the lower choices are
at least suspect.<<
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.
>>A circular tie should be regarded as a warning bell to the fact that the
lower choices in this election are flawed and should not be trusted. Most
likely this flaw was caused by the voters not being informed well enough to
make good lower choices.<<
No, a circular tie just says that the "lower" choices of some voters are the "higher" choices of other voters.
>>Years ago, on this list, I suggested that when Condorcet shows a circular
tie that the best thing to do was to eliminate one candidate. Most likely
this will break the cycle. Then you can resume using Condorcet if you
must.<<
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.
>>Anyway, in my school of thinking, almost all choices are suspect and the
policy should be to use as few as possible. This is one of the reasons I
favor Irving because Irving will use less lower choices than any other
multi choice method. Consider the following election: 45 Axx 45 Bxx
10 Cxx
Condorcet will use all the lower choices. Irving will only use ten percent
of the lower choices. Using less is best. A multi choice election that
has a majority winner in the first choices is ideal because no lower
choices will be used. Think about that, if that is the ideal, then we
should stay as close as possible to the ideal as we can when picking an
election method.<<
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.
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.
--- Begin Message ---Greetings Diana and list members, Diana, you wrote: Date: Tue, 23 Sep 2003 10:54:45 +0100 "I know there are already far too many methods out there..."Donald here: `When you're right, you're right', but go ahead and spoil our day anyway, give us a few more cycle resolutions. Diana: "...but here's another (two) that I'm vaguely partial to. I'm sure there are good reasons why neither of them is any good, but since I can't see them (and neither can my work colleagues) I thought I'd toss them out to this list for the eagle-eyed to pick over." Donald: Odds are that you are correct, that is, there are good reasons why neither of them is any good, but you are not alone, almost all the cycle resolutions are no good. Most people who concoct cycle resolutions do not understand the context of a circular tie. As a result, their cycle resolutions depend on defective data, which inturn makes the solution defective, or in other words, garbage in garbage out. I'm talking about the lower choices. A circular tie proves that the lower choices are flawed. To use the lower choices when they are flawed is the wrong thing to do. First, let me say that a circular tie is not the fault of Condorcet. When a circular tie has occurred, it merely means that Condorcet has reveled that the voters have voted in a circular pattern. At this point everyone should realize that something is wrong and should not use any cycle resolution that depends on the lower choices because the lower choices are at least suspect. A circular tie should be regarded as a warning bell to the fact that the lower choices in this election are flawed and should not be trusted. Most likely this flaw was caused by the voters not being informed well enough to make good lower choices. Years ago, on this list, I suggested that when Condorcet shows a circular tie that the best thing to do was to eliminate one candidate. Most likely this will break the cycle. Then you can resume using Condorcet if you must. Anyway, in my school of thinking, almost all choices are suspect and the policy should be to use as few as possible. This is one of the reasons I favor Irving because Irving will use less lower choices than any other multi choice method. Consider the following election: 45 Axx 45 Bxx 10 Cxx Condorcet will use all the lower choices. Irving will only use ten percent of the lower choices. Using less is best. A multi choice election that has a majority winner in the first choices is ideal because no lower choices will be used. Think about that, if that is the ideal, then we should stay as close as possible to the ideal as we can when picking an election method. Donald, ---- Election-methods mailing list - see http://electorama.com/em for list info
--- End Message ---
