An Additive Group Utility for a Fund Manager

The additive utility formula developed by Harsanyi specifies how a rational ethical individual acting on behalf of other people ought to behave. Unfortunately the formula is not invariant to arbitrary utility transformations and hence requires interpersonal comparisons of utility. Many economists have also attacked the formula on ethical grounds.

This paper transplants the Harsanyi paradigm to a new context: that of fund management. We add three further axioms to the Harsanyi argument and deduce the weighted group utility formula with each individual's weight equal to the inverse of the marginal utility of his investment in the fund. These weights make our formula invariant to arbitrary utility transformations which eliminates the problem of interpersonal comparisons of utility. We also explore a number of other properties of this group utility function.