A long time choosing

Reasonable rules for aggregating votes generate choice inconsistencies or fail to satisfy other desirable properties. This has been known and intelligently discussed since at least the 18th century, as illuminated by the informative historical piece by Iain MacLean which begins this volume. The prescience of these early writers on the subject is impressive as is their engagement with practical issues. None the less this early recognition of current concerns had little influence, apparently through failure to communicate effectively either with colleagues or with a wider audience.

The resurgence of interest in the past half-century arises from the famous demonstration by Kenneth Arrow that no social choice rule could satisfy apparently inoffensive assumptions without generating choice inconsistencies for certain configurations of opinion. The resilience of negative results of this nature is shown by several papers in this collection from the proceedings of a 1992 conference. The breadth of their relevance is shown by Bruno Leclerc and Bernard Monjardet, who outline a general framework integrating social choice results with, for instance, related problems from statistics.

Besides papers focusing on refinement of familiar Arrow-type results, other papers explore problems with ethical requirements less often discussed by economists. Marc Fleurbaey, for instance, shows the difficulties in making precise notions of equal opportunity with examples of insightful simplicity. Peter Hammond discusses the formalisation of respect for rights, exploring well-known problems where rights conflict and offering more speculative comments on the possibility for more promising formulations.

After a section on game theoretical results of relevance to social choice questions, the collection ends with two pieces having more applied concerns separated from those of the main body of the book. William Barnett writes on the existence of monetary aggregates and Thierry Karcher, Patrick Moyes and Alain Trannoy present a "preliminary incursion" into the extension of inequality comparisons to an intertemporal context. Their results so far are, however, by their own admission, limited by assumptions which render income mobility ethically uninteresting by seemingly ruling out any sort of life-cycle smoothing of utility streams through saving or borrowing. It is difficult to see the possibility of satisfactorily addressing this issue without incorporating a model of intertemporal consumer behaviour.

This is a volume which will be valuable for technically minded readers with an interest in social choice questions, either to update them on recent work or to serve as a compendium of results in the fields of several contributing authors. It shows how unlikely is the current talk of loss of interest in social choice questions among academics even if the lack of wider practical influence that MacLean regrets in the historical context seems to have improved little in 200 years.

Ian Preston is a lecturer in economics at University College London and a research fellow, Institute for Fiscal Studies.