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Lexicographic decomposition of chains and the concept of a planar chain

2002; Elsevier BV; Volume: 37; Issue: 2 Linguagem: Inglês

10.1016/s0304-4068(02)00010-1

1873-1538

Alan F. Beardon, Juan C. Candeal, Gerhard Herden, Esteban Induráin, Ghanshyam B. Mehta,

Game Theory and Voting Systems

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17–38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R2,<l).