THE CONSTRUCTIVE THEORY OF PREFERENCE RELATIONS ON A LOCALLY COMPACT SPACE .2.

The constructive development of the theory of preference relations and their representation by utility functions provides many problems that , because of their algorithmic nature, do not arise naturally in a tra ditional, non-constructive approach: for example, there is the problem of calculating the distance from points in the consumption set to the upper contour set of a given consumption bundle. We began to address such problems in Bridges (1982, 1989, 1991). This paper continues thos e investigations and includes substantial improvements on several resu lts in Bridges (1989), such as a version of the Arrow-Hahn theorem on the existence of continuous utility functions representing certain pre ference relations on locally compact, convex subsets of R(n)