Jason, Think of A > B (which is the same as B < A) to mean preferring A to B. And A = B to mean no preference between A and B. You get to pick the preferences between each pair of objects. Some sets of choices will be consistent with a transitive relation, some won't. I'm looking for a choice that results in the maximum amount of inconsistencies with transitivity. For example, with three objects, let's call them rock, paper, scissors, I might have rock < paper < scissors < rock. --ms

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From: Jason <jason@lunkwill.org> Date: 2007/09/04 Tue PM 02:18:18 CDT To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] violating transitivity

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On Tue, 4 Sep 2007, Michael Speciner wrote:

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My daughter asked me a question based on a homework assignment:

Given n objects, and a choice of a comparison (<, =, >) between each of the nChoose2 pairs of them, what is the maximum number of the nChoose3 triples of the objects that can simultaneously violate transitivity (e.g. A > B >= C

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= A)? You must be using a specialized definition of <,=,> if A>B>=C>=A is true. Can you be more specific?

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