ABSTRACT
Introduction The modern theory of social choice is the culmination of two traditions – utilitarianism and the mathematical theory of elections and committee decisions (Sen 1986). From the former comes the idea that the effects of decisions, including public policy decisions, are to be judged in terms of the personal welfare of individuals. In its simplest form, utilitarianism compares two social states by comparing the sum of individual utilities in these states. The second tradition was concerned with the design of elections, and focused heavily on the comparison of alternative voting mechanisms. From here comes the idea that the information base for social welfare decisions is to be the ordinal rankings of alternatives by individuals. As Sen (1986) describes it: ‘The union produced modern social choice theory. The big bang that characterized the beginning took the form of an impossibility theorem.’ Arrow (1951) showed that, when aggregating individual preference rankings into a social ordering, a small list of mild desirable conditions cannot be fulfilled by any ranking whatsoever. The ensuing literature built upon this, and provided a whole array of negative results. In the face of these results, it is perhaps understandable that the question of the computational feasibility of implementing different social choice rules took back stage. Upon reading Arrow, one takes away the feeling (not entirely justified) that there is not much room for improvement over the rules, such as majority voting, in use today. Since majority voting is computationally simple to implement, and if major improvements are beyond our reach, perhaps there is not much left to say on the subject. There are both theoretical and practical reasons why impossibility reasons are not a cause for giving up on thinking about computational issues in social choice. For one, as Mas-Colell et al. (1995: 799) conclude in their text:
The result of Arrow’s impossibility theorem is somewhat disturbing, but it would be facile to conclude from it that ‘democracy is impossible’. What it shows is something else – that we should not expect a collectivity of individuals to behave with the kind of coherence that we may hope from an individual . . . In practice collective judgments are made and decisions are taken. What Arrow’s theorem tells us, in essence is that the institutional detail and procedures of the political process cannot be neglected
Indeed, the very fact that we cannot devise ideal voting systems explains a large portion of political activity (e.g. conflict over the order in which alternatives are considered by a committee). Even within the realm of what is possible, different rules governing the political process matter, and there is scope for weighing in on the computational properties of alternatives. On the normative side, it may be possible here to make a principled distinction between what is, and what is not, practically feasible. If we want an improvement upon existing procedures, we ought not to neglect the computational dimensions of the problem. On the positive side, it is probably a fair conjecture that prominent rules and procedures have their place in society because of their computational properties. This is to say more than just that ‘majority voting is computationally efficient’. The way in which social decisions are made, the way in which rules and institutions evolve, the effect that new technologies such as mass media and the Internet have on political process, are all affected by the complexity inherent in aggregating a large and diverse set of opinions about alternatives before a group. To understand how individuals and groups cope with complexity is to develop a better understanding of the political process. An appreciation of this point goes back right to the beginning of the discipline. Recall the claim of utilitarians such as Bentham (1789) that social decisions can be made on the basis of calculations involving individual utilities. Objections to this view arose soon after. In his essay ‘Bentham’, Mill expressed doubts about the form of utilitarianism preached by Bentham, as well as by his father James Mill, and writes:
We think utility, or happiness, much too complex and indefinite an end to be sought, except through the medium of various secondary ends, concerning which there may be, and often is, agreement among persons who differ in their ultimate standard.
