On Tue, 15 Jul 2008 14:38:32 -0000
Bruce R. Gilson wrote:
--- In [EMAIL PROTECTED], Dave Ketchum <[EMAIL PROTECTED]> wrote:
On Mon, 14 Jul 2008 20:04:19 -0000 Bruce R. Gilson wrote:
[...]
I wish I could be so sure that cycles are going to be rare. That's the
one thing that scares me about Condorcet methods. A sort
of "Obama beats Clinton, Clinton beats McCain, McCain beats
Obama" cycle could really cause a scandal.
Such should not result in a scandal, assuming valid counts of the
ballots. They simply describe a near tie in power, such as A>B>C>A.
Note that while single voters can vote any two of the three
inequalities, it takes multiple voters in about equal strengths to
vote all three together.
My very point is that last sentence, except for the "about equal strengths." I
am not very sure how equal the 6 numbers have to be: those voting ABC,
ACB, BAC, BCA, CAB, CBA. Certainly not all 6 need be close, though
perhaps some combination does; I have not worked out the arithmetic.
As soon as you put in some cycle-resolving system, you will downgrade the
preferences of some of these 6 groups -- obviously you have to, because
that's the only way to break the cycle. And the people in those groups will
feel that the election mechanism is disregarding their preferences (or at
least weighting them less than others' preferences). And that will be the
scandal.
Saying it more clearly, for A+B+C as the simplest cycle:
Given six equal sized groups of voters:
A>B, B>C, and C>A can do an A>B>C>A cycle with 2/3 of the
strength of each group pushing the cycle forward and 1/3 acting as a
brake.
A>C, C>B, and B>A can do a similar A>C>B>A cycle.
Combine the two cycles and you still have a three member cycle,
again with a tie.
Stray far enough from equality and the weakest candidate has no
effect, leaving a two candidate race,
In between you have a headache for which the rules BETTER be decided
on before the election. This does not require favoring any groups -
vote counts are the proper basis for the decisions.
"at highest a flaw in the laws of nature"? No, but could be a flaw in
our understanding of such.
--
[EMAIL PROTECTED] people.clarityconnect.com/webpages3/davek
Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.
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