Some paradoxes of preference aggregation

Introduction The purpose of this paper is to provide a brief review of some of the major paradoxes or impossibility theorems in social choice theory and the important issues highlighted by these theorems. The first and most famous of these theorems is, of course, Arrow's (1950, 1951, 1967), but, over the four decades or so since Arrow proved his impossibility result, numerous other impossibility theorems have been proved in social choice theory, giving a very distinctive flavour to this particular area where economics, politics, and ethics overlap in a significant fashion. These results, which often differ much in their formal structures, have one basic similarity. Essentially, a paradox or an impossibility theorem in social choice theory shows that there does not exist a social decision procedure satisfying certain plausible properties: the more plausible or appealing these properties, the more dramatic is the impossibility result under consideration. At first sight, the impossibility results in the literature on social choice may seem to be purely intellectual exercises without much practical interest. If the objective of studying the theory of social choice is to provide a solution to the normative problem of how the society should choose one of the possibly many different options available to it (or, alternatively, how the society should rank these different options), then why should anyone be interested in a proposition that shows that certain appealing properties of a social decision procedure are logically incompatible in the sense that no social decision procedure can simultaneously satisfy all these properties? This rhetorical question does have a point.