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Maximization of a transitive preference

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Consider the statement "if b Belongs to C({b, c}) and a is weakly preferred to b, then a belongs to C({a, b, c})", Is this implied by the maximization of a preference? Is it implied by the maximization of a transitive preference? (Provide a proof or a counterexample). Is the statement a testable implication of either?

Reference no: EM133131946

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