This paper shows how revealed preference relations, observed under general budget sets, can be extended using closure operators which impose certain assumptions on preferences. Common extensions are based on the assumption that preferences are convex and/or monotonic, but we also consider...

This paper provides an efficient way to generate a set of random choices on a set of budgets which satisfy the Generalised Axiom of Revealed Preferences (GARP), that is, they are consistent with utility maximisation. The choices are drawn from an approximate uniform distribution on the...

We provide two methods to compute the largest subset of a set of observations that is consistent with the Generalised Axiom of Revealed Preference. The algorithm provided by Houtman and Maks (1985) is not computationally feasible for larger data sets, while our methods are not limited in that...

It is shown that for two dimensional commodity spaces any homothetic utility function that rationalizes each pair of observations in a set of consumption data also rationalizes the entire set. The result is used to provide a simplified nonparametric test for homotheticity of demand and a measure...

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible...

We provide an efficient way to generate random choices which are consistent with utility maximisation. They are drawn from an approximate uniform distribution on the admissible region on each budget based on a Markovian Monte Carlo algorithm due to Smith (Oper Res 32(6):1296–1308, <CitationRef CitationID="CR11">1984</CitationRef>). This...</citationref>

We introduce a nonparametric method to compare risk aversion of different investors based on revealed preference methods. Using Yaari's (1969) [50] definition of “more risk averse than”, we show that it is sufficient to compare the revealed preference relations of two investors. This makes...