Affiliation:
1. Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche, Università di Trieste, 34127 Trieste, Italy
2. Dipartimento di Economia e Management, DEM, Università di Brescia, 25122 Brescia, Italy
Abstract
Chipman contended, in stark contrast to the conventional view, that, utility is not a real number but a vector, and that it is inherently lexicographic in nature. On the other hand, in recent years continuous multi-utility representations of a preorder on a topological space, which proved to be the best kind of continuous representation, have been deeply studied. In this paper, we first state a general result, which guarantees, for every preordered topological space, the existence of a lexicographic order-embedding of the Chipman type. Then, we combine the Chipman approach and the continuous multi-utility approach, by stating a theorem that guarantees, under certain general conditions, the coexistence of these two kinds of continuous representations.
Reference19 articles.
1. The Debreu Gap Lemma and some generalizations;Herden;J. Math. Econom.,2004
2. The foundations of utility;Chipman;Econometrica,1960
3. Chipman, J.S., Hurwicz, L., Richter, M., and Sonnenschein, H.F. (1971). Preference, Utility and Demand, Harcourt Brace and Jovano-vich.
4. Debreu’s Gap Theorem;Beardon;Econ. Theory,1992
5. A continuous utility theorem for closed preorders on a σ-compact metrizable space;Levin;Sov. Math. Dokl.,1983