The Possibility of Anonymous Social Orderings Using Curvature of Indifference Hypersurfaces

This paper concerns the aggregation of individual preferences into a social ordering. Working in a higher-dimensional economic environment where an indifference hypersurface is the level set of a utility function representing a preference relation, we give axiomatic conditions under which a function on the indifference hypersurfaces can be used to define a rational anonymous social ordering function. We show that the curvature of the indifference hypersurfaces can potentially be used as such a function, and discuss a possible economic interpretation of the curvature. The minmax-like definition of our social ordering function coincides with the Rawlsian difference principle under certain circumstances.