In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance.
On the Arrow-Hahn utility representation method / M.Gori; G.Pianigiani. - In: MATHEMATICAL SOCIAL SCIENCES. - ISSN 0165-4896. - STAMPA. - 59:(2010), pp. 282-287. [10.1016/j.mathsocsci.2009.11.004]
On the Arrow-Hahn utility representation method
GORI, MICHELE;PIANIGIANI, GIULIO
2010
Abstract
In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance.
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