Topological Social Choice

The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets": additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ omists and mathematicians, yet there is no authoritative collection of papers in the area. Nor is there any surveyor book to give a perspective and act as a guide to the issues in and contributions to this new area. One of the two aims of this volume is in some measure to play this role: the other aim is of course to present interesting and surprising new results.

The use of new mathematical techniques leads to powerful new results and shows social choice theory to be linked to resources allocation theory

Klappentext

Topological social choice has evolved from a district area of social choice to a field which is integrated into the mainstreams of both social choice and general equilibrium theory. It has come to integrate and bridge these previously disparate areas, revealing deep and unexpected connections between them. In the process it has clarified the topological and geometric basis of social choice theory. This volume contains wide-ranging reviews of the economic and technical issues in this area, together with important new contributions.

Inhalt
Social choice and resource allocation: a topological perspective.- Market arbitrage, social choice and the core.- Topological and discrete social choice: in a search of a theory.- Informational geometry of social choice.- Topological methods in social choice: an overview.- A note on continuous social choice.- Strategy-proofness of continuous aggregation maps.- The geometry of implementation: a necessary and sufficient condition for straightforward games.- Homotopy properties of Pareto aggregation rules.- Social choice with infinite populations: construction of a rule and impossibility results.- Topological aggregation, the case of an infinite population.- Topological aggregation of preferences: the case of a continuum of agents.- Continuity and equity with infinite horizons.- A note on weak ?-Chichilnisky rules.