A geometric approach to revealed preference via Hamiltonian cycles

Jan Heufer

Theory and Decision, 2014, vol. 76, issue 3, 329-341

Abstract: 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 length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $$(L-1)$$ ( L − 1 ) -polytope into a facet of a convex monotonic hull in $$L$$ L -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles. Copyright Springer Science+Business Media New York 2014

Keywords: Cyclic polytopes; Hamiltonian cycles; Preference cycles; Revealed preference; Strong axiom of revealed reference; Weak axiom of revealed preference (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11238-013-9373-4

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