A numerical representation of preferences with intransitive indifference |
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Authors: | Douglas S. Bridges |
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Affiliation: | University College, Buckingham MK18 1EG, UK |
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Abstract: | It is shown that, under certain conditions on a preference relation on a subset X of Rm, there exist real-valued functions u and v on X such that x is preferred to y if and only if u(x)>v(y). This generalises the familiar representation of preferences by a utility function in the case where the preference and indifference relations are transitive. The continuity of the functions u and v is also discussed. |
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