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Ville Axioms and Consumer Theory

Leonid Hurwicz
Marcel K. Richter

Abstract

We show that a "no-cycle" condition, of a continuous type introduced by Ville, is equivalent to the Antonelli (or Slutsky) symmetry conditions, which together with other axioms is known to be a basis for constructing a utility function from expenditure data. The "no-cycle" condition is attractive because--unlike the symmetry condition--it has an evident behavioral interpretation, through which relate it to the strong axiom of revealed preference. We show, nevertheless, that the "no-cycle" condition does not imply even the weak axiom of revealed preference.