Impartiality: Definition and Representation

IMPARTIALITY IS THE MORAL IMPERATIVE requiring that conflicting claims be evaluated without prejudice. In this paper I propose an axiomatic definition of impartiality and examine its implications for the theory of social welfare functions. Following the seminal work of Harsanyi (1953, 1977) I take as given the set of individuals that constitute the society and the set of social alternatives, representing the constitutions, income distributions, institutions, or policies among which the society must choose. Moreover, the moral value judgment that should govern this choice is modeled as a preference relation of an ethical observer. However, unlike Harsanyi, who defines the observer's preference relation on the set of all extended lotteries (i.e., joint probability distributions on social alternatives and individuals) I define the observer's preference relation on a set of allocations whose elements are assignments of social-alternative lotteries (i.e., probability distributions on the set of social alternatives) to individuals. As in Harsanyi's theory, the observer's preference relation is supposed to govern the choice among social alternatives of individuals placed behind a "veil of ignorance" regarding their social position and preferences. Harsanyi assumes that the observer's preference relation on the set of extended lotteries and the individual preference relations on the set of social-alternative lotteries satisfy the axioms of expected utility theory and jointly satisfy the principle of acceptance.2 He shows that the observer's preference relation may be represented as a weighted sum of individual von Neumann-Morgenstern utilities and defines impartiality as the restriction that the individual utilities are assigned equal weights. This representation may be interpreted as assigning equal probabilities to the events of being each individual in society. Note, however, that given any preference relation that is representable as a weighted sum of individual utilities with strictly positive weights, a new set of individual utilities may be defined (by multiplying each utility function by its weight and dividing through by the inverse of the number of individuals) to obtain a new representation of the preference relation with uniform weights. In other words, the same observer's preference relation is represented as a weighted sum of individual utilities with equal weights. Since this manipulation does not change the underlying observer's preference relation, it does not make it impartial except in a tautological sense.