Mark J. Machina CARDINAL PROPERTIES OF "LOCAL UTILITY FUNCTIONS" This paper outlines the cardinal properties of "local utility

Consider the set D[a,b] of all cumulative distribution functions F(·) over some interval [a,b], and an individual whose preference ranking over this set can be represented by a real-valued preference functional V(F), in the sense that the distribution F*(·) is weakly preferred to F(·) if and only if V(F*) ≥ V(F). Note that V(·) is ordinal in the sense that some other functional V*(·) will represent the same preference ranking if and only if V*(·) = φ(V(·)) for some increasing function φ(·). If the individual is an expected utility maximizer, we know that V(·), or some increasing transformation of it, will take the linear form V(F) ≡ U(x)dF(x), where U(·) is known as the individual's von Neumann-Morgenstern utility function. In such a case we know that the individual will rank the distributions F*(·) and Fo(·) according to the sign of V(F*) V(Fo) = U(x)·[dF*(x)-dFo(x)] (1)