7 Distributive Justice: Rawlsian and Utilitarian Rules

7 Distributive justice: Rawlsian and utilitarian rules 7.1. The philosophical background Over more than two centuries, utilitarianism had been the uncontested school of thought for issues of welfare and redistribution. In Hutcheson’s (1725) An Inquiry into the Original of Our Ideas of Beauty and Virtue, one can find the utilitarian postulate of ‘the greatest happiness of the greatest number’ which became famous through Bentham’s work (1776) who admitted to have been heavily influenced by Helvétius’s writings (1758). In order to decide whether state x is at least as good for society as state y (the reader will hopefully excuse our more prosaic language), utilitarianism prescribes that the utilities that accrue to the individual members of society under the two states be summed or aggregated. So x will be chosen for society if the utility sum under x is at least as large as the utility sum under y. Utilitarianism is outcome-oriented and consequentialist in nature. While it focuses on maximizing the sum of individual utilities,it is largely unconcerned with the interpersonal distribution of this sum. Rawls (1971) developed his concept of justice as fairness, proposing two principles of justice which are meant to be guidelines for how the basic structure of society is to realize the values of liberty and equality. It is probably fair to say that Rawls’s work has become a powerful contestant of utilitarianism over the last few decades. In his first principle, Rawls requires each person to have an equal right to the most extensive basic liberty compatible with a similar liberty for others. Basic liberties are political liberty, freedom of speech and assembly, liberty of conscience and freedom of thought, the right to hold personal property, and others. Rawls’s second principle, the difference principle, on which economists have focused in particular, requires that social and economic inequalities are to be arranged so that they are both to the greatest benefit of the least advantaged members of society and attached to offices and positions open to all under conditions of fair equality of opportun- ity. Rawls argued that benefits should be judged not in terms of utilities but through an index of so-called primary goods which comprise the basic liberties, 122 DISTRIBUTIVE JUSTICE opportunities and powers, self-respect, and income and wealth. Several of these items are clearly non-welfaristic in character. Rawls’s concept of primary goods is chiefly means-oriented. Individuals have rational plans with different final ends. They all require these primary goods for the execution of their plans. In the following sections, we shall axiomatically describe and compare both utilitarianism and the first half of Rawls’s second principle, often called the maximin rule; more precisely, we shall characterize the lexicographic version of this rule. In order to make this comparison as coherent as possible, we shall reformulate Rawls’s maximin principle in terms of utilities. We frankly admit that this is a heavy truncation of Rawls’s philosophical edifice, but, as just said, it allows us to make comparisons with utilitarianism; without such a reformulation a comparison would become much harder. As has become clear from the discussion above, the informational basis of utilitarianism is different from the basis of Rawlsianism. Utilitarianism con- siders gains and losses across individuals and uses summation. In other words, it is required that utility differences be measurable and comparable interpersonally. Rawls’s maximin principle requires that levels of utility be comparable interpersonally but there is no need for measuring utility differences. The following section will make these concepts more precise. 7.2. The informational structure Remember that in the third proof of Arrow’s theorem in section 2.4, we were exploiting the fact that in a world of ordinal utility with no trace of interpersonal comparability, every individual is perfectly free to map his or her utility scale into another one by a strictly monotone transformation. Inform- ationally speaking, the ‘original’ utility index and the ‘new’ one generated by a strictly increasing transformation cannot be distinguished. They belong to the same information set which is very large in this case, since any strictly increasing transformation is as good, informationally wise, as any other. We shall see in due course that with the introduction of various types of comparisons, the size of the class of admissible transformations will shrink. In other words, there is an inverse relationship between the size of the set of transformations that keep information invariant and the amount of usable information. In the following, we shall largely follow the analysis of D’Aspremont and Gevers (1977). With N being a finite set of individuals and with X being a finite set of conceivable social states, let, for all i ∈ N and for all x, y ∈ X, u(x, i), u(y, i) be individual i’s utility values defined on X × N . The cartesian THE INFORMATIONAL STRUCTURE 123 product X × N allows us to link individuals i, j, k, let’s say, to social alternat- ives x, y, z, ... so that the individuals’ positions under different social states can be considered (how does individual i in state x, for example, fare in comparison to person j under alternative y?). The values u(x, i), u(y, i) of individual i’s utility are seen either through the eyes of an ethical observer (Harsanyi) or are unanimous evaluations ‘under a veil of ignorance’ (Rawls). Let U = (u(·,1), ..., u(·, n)) be an n-tuple of utility functions for the n members of society, a profile for short. The set of all possible profiles will be denoted by U. A social evaluation functional or social welfare functional (see section 2.4 above) is a mapping F from U to E, the set of all orderings of X. This defin- ition implies that the domain of F is assumed to be unrestricted. For every 1 2 ∈ U = ( 1) = ( 2) U , U ,wewriteRU 1 F U and RU 2 F U . Let us now come back to the informational structure. The Arrovian world of ordinally measurable, non-comparable utilities (OMN) can be described formally as follows. 1 2 ∈ U = ∈ ϕ OMN. For every U , U , RU 1 RU 2 if for every i N , i is a strictly 2 1 increasing transformation such that, for all x ∈ X, u (x, i) = ϕi(u (x, i)) where u1(·, ·) and u2(·, ·) are the utility components of profiles U 1, U 2 respectively. This is the informational set-up of section 2.4. We next wish to introduce interpersonal comparisons of utility levels while preserving ordinal measurability (OMCL). Note that this requirement reduces the set of permissible transformations. 1 2 ∈ U = ϕ OMCL. For every U , U , RU 1 RU 2 if is a strictly increasing transformation such that for all i ∈ N and for all x ∈ X, u2(x, i) = ϕ(u1(x, i)). If individual utilities are transformed, they are subjected to a common transformation. Note that level comparisons of individual utilities are possible within this informational requirement since u1(x, i) ≥ u1(x, j) iff ϕ(u1(x, i)) ≥ ϕ(u1(x, j)) for all i, j ∈ N and all x ∈ X. Interpersonal comparisons of utility gains and losses are, of course, not possible. We now introduce cardinal individual utility functions without any interpersonal comparability (CMN). 1 2 ∈ U = CMN. For every U , U , RU 1 RU 2 if there exist 2n numbers α1, ..., αn, β1 > 0, ..., βn > 0 such that, for all i ∈ N and for all 2 1 x ∈ X, u (x, i) = αi + βi · u (x, i). Note that the values for αi can be positive, negative or zero, whereas the values for βi must be strictly positive (i ∈{1, ..., n}). Each individual can choose his or her origin and utility scale independently. This means that neither level comparability nor a comparison of utility gains and losses is possible across individuals. This informational structure will be used in the following chapter on bargaining solutions. 124 DISTRIBUTIVE JUSTICE Comparability of both levels and gains and losses would be possible if we required that αi = αj and βi = βj for all i, j ∈ N ,meaning that both origin and scale unit are the same for everyone. This would be a very severe limitation of admissible transformations but would, of course, render the amount of usable information much richer. However, for our purposes in the sequel, we do not need this restriction of admissible transforms. What we need is the possibility of comparing gains and losses across individuals. This can be achieved by introducing cardinally measurable and unit-comparable utilities (CMCU). 1 2 ∈ U = + CMCU. For every U , U , RU 1 RU 2 if there exist n 1 numbers 2 α1, ..., αn and β>0 such that, for all i ∈ N and for all x ∈ X, u (x, i) = 1 αi + βu (x, i). The interpersonal comparison of utility differences is now possible; utility levels cannot be compared across individuals. We have seen above that assumptions of measurability specify which types of transformations may be applied to an individual’s utility function without altering the individually usable information. Comparability assumptions such as a common scale unit for all i ∈ N specify how much of this information can be used across persons. Let us recapitulate the different forms of informational set-up in the following scheme: OMN no interpersonal comparisons possible, ordinal Arrovian neither of utility levels nor of gains approach and losses OMCL interpersonal comparisons of utility ordinal Rawlsian levels possible, but not of gains approach and losses CMN no interpersonal comparisons possible, cardinal bargaining neither of utility levels nor of gains approach and losses CMCU an interpersonal comparison of gains cardinal utilitarian and losses possible, not of utility levels approach 7.3.

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