This paper contains a generalization of the General Possibility Theorem to situations where choice over two-element (more generally, “small”) sets is not possible. The analysis is developed in terms of the social choice function formulation rather than the social welfare function approach. In this formulation, assumptions concerning the size of sets of feasible alternatives are explicit, allowing the role of these assumptions in inducing impossibility results to be explored.

The paper reports on an experimental investigation of four methods of allocating public goods. The two basic processes studied are direct contribution and a public goods auction process. Both of these processes are studied with and without an additional unanimity feature. The results suggest that the auction process outperforms direct contribution. The effect of unanimity is to decrease the efficiency of both processes. Much of the paper is focused on an analysis of these results.

We have attempted here to trace the implications, in terms of operational procedures, of some postulates about the "physical" nature of objects on one hand and individual choice behaviour on the other. We summarize the major result in very loose terms by asserting that if when choosing from among several objects which are characterized by "qualitative" or "ordinal" properties, an individual's choice obeys a transitivity law, then the choice is necessarily" dictated" by one characteristic a lone; that is, the underlying preference must be lexicographic in one of these ordinal properties. The reader must consult the text below for an elaboration on the meaning of the terms emphasized by quotation marks before the proper context of the result can be established.