Polynomial utility

Summary We characterize continuous representability of preference relations by multiplicative functions and by certain polynomial functions, on connected topological spaces. Our methods show that the same Continuity Principle that yielded additive utility representations in earlier work applies much more generally.     

From ability to pay to concepts of equal sacrifice

The ability-to-pay approach to taxation in Mill's tradition is given a rigorous treatment in a social choice theoretic framework. Generalized concepts of equal sacrifice are axiomatized making explicit use of the ability-to-pay principle. Extensive statements on progressivity are derived. However, there is no such axiomatized concept that implies non-excessive progressitivity irrespective of taxpayers' utility function.     

Additive utility

Summary We put the theory of cardinal and additive utilities on the same kind of simple foundation as the theory of ordinal utility. We give necessary and sufficient conditions for preferences to have continuous cardinal or additive utility functions, on connected topological spaces. Basing our proofs on fundamental algebraic theorems yields new techniques that allow us to give simple proofs of earlier results (cf. [4, 14] and to provide a basis for new results [10].The assistance of the National Science Foundation, Grant SES-8510620, is gratefully acknowledged.     

Preference densities and social choices

We discuss a ranking method that allows social pairwise rankings of alternatives to depend on more than just individuals’ pairwise rankings. This violates Arrow’s Independence of Irrelevant Alternatives, but allows Borda’s rank-order counting, which provides a limited accounting for individual preference intensities. We capture Arrow’s rules (i.e., with IIA) and Borda’s method as two polar cases, and allow cases in between. Our main result provides the critical line dividing those degrees of intensity, or preference density, that yield positive results from those that yield negative results. We thank two referees for helpful comments.     

Revelations of a gambler

Knowing that a decision maker maximizes expected utility with respect to some (unknown) utility U and some (unknown) probability P, what can one tell about P by observing his decisions? We discuss this revealed preference question primarily in the simple case of a two-element (H and T) state space, and show that the possible revelations of P_T/P_H are precisely those of the form P_T/P_Hε∪^K_k=1 (γ_k,δ_k), for some algebraic numbers γ_k,δ_k.     

Internalizing intergenerational externalities by regionalization

The emission of long-lived pollutants and public debt policies are related by the joint problem of intergenerational externalities. This paper examines both phenomena from the local perspective, in a model with interregional household mobility. We conclude that local environmental agencies have incentives to internalize all intergenerational pollution externalities, provided all rents of immobile production factors, including waste emissions, are appropriated by the regions. Contrary to widespread belief, however, neutrality of local public debt is not guaranteed in general. Shifts in the intertemporal pattern of local taxes change the net wealth of local property owners if distortionary residence-based taxes are imposed to service the local debt.