2. Ordinalist Views of the Social Welfare Function.
Pareto's rejection of cardinal utility rendered mean-
ingless a sum-of-utilities criterion. If utility for an
individual was not even measurable, one could hardly
proceed to adding utilities for different individuals.
Pareto recognized this problem.
First of all, he introduced a necessary condition for
social optimality, which has come to be known as
Pareto-optimality: a social decision is Pareto-optimal
if there is no alternative decision which could have
made everybody at least as well off and at least one
person better off. In this definition, each individual is
expressing a preference for one social alternative
against another, but no measurement of preference
intensity is required. Pareto-optimality is thus a purely
ordinal concept.
It is, however, a weak condition. It is possible to
compare two alternative social decisions only if there
is essential unanimity. To put the matter another way,
among any given set of alternatives there will usually
be many which would satisfy the definition. A mani-
festly unjust allocation, with vast wealth for a few and
poverty for many, will nevertheless be Pareto-optimal
if there is no way of improving the lot of the many
without injuring the few in some measure. Pareto
himself was very clear on this point.
Pareto-optimality is nevertheless a very useful con-
cept in clearing away a whole realm of possible deci-
sions which are not compatible with any reasonable
definition of social welfare. It might be argued that
every application of utilitarianism in practice, as to
law, has in fact used only the concept of Pareto-
optimality. In welfare economics, similarly, it has
turned also to be useful in characterizing sharply the
types of institutional arrangements which lead to
efficient solutions, making it possible to isolate the
debate on distributive problems which it cannot solve.
Pareto later (1913) went further. He suggested that
each individual in his judgments about social decisions
considers the effects on others as well as on himself.
The exposition is a bit obscure, but it appears to coin-
cide with that developed later and independently by
the economist, Abram Bergson (1938). Each individual
has his own evaluation of a social state, which is a
function of the utilities of all individuals: Wi(U1,...,
Un). Since the evaluation is done by a single individual,
this function has only ordinal significance. The Ui's
themselves may be thought of as an arbitrary numerical
scaling of the individuals' preferences; they also have
only ordinal significance, but this creates no conceptual
problem, since the choice of the social welfare func-
tion, Wi, for the ith individual, already takes account
of the particular numerical representation of individ-
uals' ordinal utilities.
Interpersonal comparisons of utility are indeed
made, but they are ethical judgments by an observer,
not factual judgments.
Pareto (but not Bergson) went one step further. The
“government” will form the social welfare function
which will guide it in its choices by a parallel
amalgamation of the social welfare functions of the
individuals, i.e., a function, V(W1,..., Wn). Pareto's
concept of a social welfare function remained un-
known, though the concept of Pareto-optimality be-
came widely known and influential beginning with the
1930's, as is clear in Bergson's work. The latter became
very influential and is accepted as a major landmark;
but in fact it has had little application.
Bergson accepted fully the ordinalist viewpoint, so
that the ethical judgments are always those of a single
individual. This approach loses, however, an important
feature of most thinking about social welfare, namely,
its impartiality among individuals, as stressed by
Bentham and given classic, if insufficiently precise,
expression in the categorical imperative of Kant. In
Bergson's theory, any individual's social welfare func-
tion may be what he wishes, and it is in no way
excluded that his own utility plays a disproportionate
role. Pareto, by his second-level social welfare function
for the government implicitly recognized the need for
social welfare judgments not tied to particular individ-
uals. But the ordinalist position seems to imply that
all preferences are acts of individuals, so that in fact
Pareto had no basis for the second level of judgment.
