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We identify general domain properties that induce the non-existence of efficient, strategy-proof, and non-dictatorial rules in the 2-agent exchange economy. Applying these properties, we establish impossibility results in several restricted domains; for example, the intertemporal exchange problem (without saving technology) with preferences represented by the discounted sum of a temporal utility function, the "risk sharing problem" with risk averse expected utility preferences, the CES-preference domain, etc. None of the earlier studies applies to these examples. Keywords:Strategy-proofness; efficiency; dictatorship; exchange economy; domain. * Department of Economics, University of Kansas, Lawrence, KS66045, USA. E-mail:bgju@ku.edu. I am grateful to Professor William Thomson for helpful comments and suggestions. I also thank seminar participants in University of Rochester, John Duggan, and François Maniquet. I thank two anonymous referees for their detailed comments, which were very helpful in revising the earlier version. All remaining errors are mine.

We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barberà, Sonnenschein, and Zhou (1991). Here we assume that agents' preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, "goods", "bads", and "nulls". We focus on "voting rules", which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the "separable domain" is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof.

In claims problems, we study coalitional manipulations via claims merging and splitting. We characterize (division) rules that are non-manipulable via (pairwise) splitting and that also satisfy standard axioms of equal treatment of equals, consistency, and continuity. And we obtain a similar result for non-manipulability via (pairwise) merging. Copyright Springer-Verlag Berlin/Heidelberg 2003Claims problem, non-manipulability via pairwise splitting , non-manipulability via pairwise merging ,

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