Numerical representation of intransitive preferences on a countable set |
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Authors: | Douglas S Bridges |
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Institution: | Department of Mathematics, University College, Buckingham MK18 1EG, England |
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Abstract: | Let > be a preference relation on a countable set X. We prove that if > is acyclic (that is, has irreflexive transitive closure), then there exists a mapping u of X into such that x > y entails u(x)>u(y). We also give a simple proof of a representation theorem of Fishburn when > is an interval order. |
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