The constructive theory of preference relations on a locally compact space

AbstractThis paper, which is written within a rigorously constructive framework, deals with preference relations (strict weak orders) on a locally compact space X, and with the representation of such relations by continuous utility functions (order isomorphisms) from X into ℝ. Necessary conditions are given for finding the values of a utility function algorithmically in terms of the parameters when X is a locally compact, convex subset of RN. These conditions single out the class of admissible preference relations, which are investigated in some detail. The paper concludes with some results on the algorithmic continuity of the process which assigns utility functions to admissible preference relations.The work of this paper can be regarded as a recursive development of preference and utility theory