In international circles, the concern of the day is the state of the world economy. There is a general appreciation of the severity of the problem, but no widespread agreement about either diagnosis or solutions. We shall focus here on a particular set of topics that have emerged as major issues...

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...

An important problem in environmental economics arises from te irreversibility of consuming or destroying certain resources. Extractive resources like oil are a clear example. Even for environmental resources the same seems to be true in a number of environmental cases, for example biodiversity,...

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)....

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...

We study the aggregation of preferences when intensities are taken into account: the aggregation of cardinal preferences, and also of von Neumann-Morgenstern utilities for choices under uncertainty. We show that with a finite number of choices there exist no continuous anonymous aggregation...

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...

The problem of endowing preferences with manifold structures emerged from discussions with Gerard Debreu in 1975 . Time has shown that such structures can be useful in understanding the behavior of economic systems . In Chichilnisky (1976) spaces of smooth preferences were endowed with a Hilbert...