Pareto Bentham and Rawls the dilemma of preference aggregation

The need to make comparative evaluations between different rules motivates much of law and economics. Consequently, the second methodological problem in law and economics concerns the choice of criteria for carrying out such comparative analysis. In practical terms, this problem concerns the method of aggregation of individual preferences into social preferences. This problem is not unique to law and economics. It is part of a much larger methodological debate in economic philosophy and welfare economics.

Already in the late nineteenth century, F.Y. Edgeworth (1881: 7-8) stated the moral dilemma of social welfare analysis, observing that a moral calculus should proceed with a comparative evaluation of 'the happiness of one person with the happiness of another. ... Such comparison can no longer be shirked, if there is to be any systematic morality at all'. The problem obviously arises from the fact that economists do not have any reliable method for measuring individuals' utility, let alone make interpersonal comparisons of utility.

Economic analysis generally utilizes one of the three fundamental criteria of preference aggregation.

Positive, normative and functional schools in law and economics 67 Ordinal preferences and the Pareto criterion

The first criterion of social welfare is largely attributable to Italian economist and sociologist Vilfredo Pareto. The Pareto criterion limits the inquiry to ordinal preferences of the relevant individuals. According to Pareto, an optimal allocation is one that maximizes the well-being of one individual relative to the well-being of other individuals being constant.5 In normal situations, there are several possible solutions that would qualify for such a criterion of social optimality. For example, if the social problem is that of distributing a benefit between two parties, any hypothetical distribution would be Pareto optimal, since there is no possible alternative redistribution that would make one party better off without harming another one.

The Pareto criterion has been criticized for two main reasons: (a) it is status quo dependent, in that different results are achieved depending on the choice of the initial allocation; and (b) it only allows ordinal evaluation of preferences, since it does not contain any mechanism to induce parties or decision makers to reveal or evaluate cardinal preferences (that is, the intensity of preferences). As a result of these shortcomings scholars (for example, Calabresi, 1991), have questioned the usefulness of the Pareto criterion in its applications to law and economics.

Utilitarian tests: Bentham and Kaldor-Hicks

In the nineteenth and early twentieth centuries, economists and philosophers developed welfare paradigms according to which the degree of all affected individuals had to be taken into account in any comparative evaluation of different states of the world. This methodological trend, related to utilitarian philosophy, is best represented by philosophers and jurists such as Bentham (1839) and later economists such as Kaldor (1939) and Hicks (1939), who in different ways formulated criteria of social welfare that accounted for the cardinal preferences of individuals.

In Principles of Morals and Legislation, Bentham (1789) presents his theory of value and motivation. He suggests that mankind is governed by two masters: 'pain' and 'pleasure'. The two provide the fundamental motivation for human action. Bentham notes that not all individuals derive pleasure from the same objects or activities, and not all human sensibilities are the same.6 Bentham's moral imperative, which has greatly influenced the methodological debate in law and economics, is that policy makers have an obligation to select rules that give 'the greatest happiness to the greatest number'. As pointed out by Kelly (1998: 158) this formulation is quite problematic, since it identifies two maximands (that is, degree of pleasure and number of individuals) without specifying the tradeoff between one and the other. Bentham's utilitarian approach is thus, at best, merely inspirational for policy purposes.

Later economists, including Kaldor (1939), Hicks (1939) and Scitovsky (1941), formulated more rigorous welfare paradigms which avoided the theoretical ambiguities of Bentham's proposition. However, these formulations presented a different set of difficulties in their implementation. The core idea of their approach is that state A is to be preferred to state B if those who gain from the move to A gain enough to compensate those who lose. This is generally known as the Kaldor-Hicks test of potential compensation. It is one of 'potential' compensation because the compensation of the losers is only hypothetical and does not actually need to take place.7 In practical terms, the Kaldor-Hicks criterion requires a comparison of the gains of one group and the losses of the other group. As long as the gainers gain more than the losers lose, the move is deemed efficient. Mathematically, both the Bentham and the Kaldor-Hicks versions of efficiency are carried out by comparing the aggregate payoffs of the various alternatives and selecting the option that maximizes such summation.

Non-linear social preferences: Nash and Rawls

Other paradigms of social welfare depart from the straight utilitarian approach, suggesting that social welfare maximization requires something more than the maximization of total payoffs for the various members of society. Societies are formed by a network of individual relations and there are some important interpersonal effects that are part of individual utility functions. Additionally, human nature is characterized by diminishing marginal utility, which gives relevance to the distribution of benefits across members of the group.

Imagine two hypothetical regimes: (a) in which all members of society eat a meal a day; and (b) in which only a random one-half of the population eat a double meal while the other unlucky half remains starving. From a Kaldor-Hicks perspective, the two alternatives are not distinguishable from the point of view of efficiency because the total amount of food available remains unchanged. In a Kaldor-Hicks test, those who get a double meal have just enough to compensate the others and thus society should remain indifferent between the two allocational systems. Obviously, this indifference proposition would leave most observers unsatisfied. In the absence of actual compensation, the criterion fails to consider the diminishing marginal benefit of a second meal and the increasing marginal pain of starvation. Likewise, the randomized distribution of meals fails to consider the interpersonal effects of unfair allocations. Fortunate individuals suffer a utility loss by knowing that other individuals are starving while they enjoy a double meal. Because of the diminishing marginal utility of wealth and interpersonal utility effects, from an ex ante point of view, no individual would choose allocation system (b), even though the expected return from (b) is equal to the return from (a).

Scholars who try to evaluate the welfare implications of distributional inequalities generally do so by invoking Rawls's (1971)8 theories ofjustice or by utilizing Nash's (1950)9 framework of welfare.

The intuition underlying these criteria of welfare is relatively straightforward: the well-being of a society is judged according to the well-being of its weakest members. The use of an algebraic product to aggregate individual preferences captures that intuition. Like the strength of a chain is determined by the strength of its weakest link, so the chain of products in an algebraic multiplication is heavily affected by the smallest multipliers. Indeed, at the limit, if there is a zero in the chain of products, the entire grand total will collapse to zero. This means that the entire social welfare of a group approaches zero as the utility of one of its members goes to zero.

In the law and economics tradition, these models of social welfare have not enjoyed great popularity. This is not so much for an ideological preconception but rather for a combination of several practical reasons. These include the general tendency to undertake a two-step optimization in the design of policies, and the difficulties of identifying an objective criterion for assessing interpersonal utility and diminishing marginal utility effects. From a methodological point of view, distributional concerns are generally kept separate from the pursuit of efficiency in policy making. Such separation has been rationalized on the basis that the legal system is too costly an instrument for distribution, given the advantage of the tax system for wholesale reallocation of wealth (for example, Kaplow and Shavell, 1994).

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