We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a...

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1900 a, b)....

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology. The purpose is expository: no attempt is made to provide complete proofs, for which references are given, nor to...

The theory of social choice introduced in [5,6] is robust; it is completely independent of the choice of topology on spaces of preference. This theory has been fruitful in linking diverse forms of resource allocation; it has been shown [17] that contractibility is necessary and sufficient for...

90 Classical problems in economics are concerned with the solutions of several simultaneous nonlinear optimization problems, one for each consumer or producer, all facing constraints posed by the scarcity of resources. Often their interests conflict, and it is generally impossible to find a...

Social choice theory is concerned with providing a rationale for social decisions when individuals have diverse opinions. Voting is an obvious way in which societies aggregate individual preferences to obtain social ones. The procedure of voting registers individual comparisons between...