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 traditional, 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 those investigations and includes substantial improvements on several results in Bridges (1989), such as a version of the Arrow-Hahn theorem on the existence of continuous utility functions representing certain preference relations on locally compact, convex subsets of R(n)