1. Bentham's Utilitarianism. To Bentham, the util-
ity of each individual was an objectively meaningful
magnitude; from the point of view of the community,
one man's utility is the same as another's, and therefore
it is the sum of the utilities of all individuals which
ought to determine social policy. Bentham is indeed
concerned strongly to argue that the actual measure-
ment of another's utility is apt to be very difficult, and
therefore it is best to let each individual decide as much
as possible for himself. In symbols, if U1,..., Un are
the utilities of the n individuals in the society, each
being affected by a social decision, the decision should
be made so as to make the sum, U1 + U2 +... + Un,
as large as possible. An expression of this form, which
defines a utility for social choices as a function of the
utilities of individuals, is usually termed a social welfare
function. Bentham's conclusion is really clearly enough
stated, but there are considerable gaps in the underly-
ing argument. The addition of utilities assumes an
objective or at least interpersonally valid common unit;
but no argument is given for the existence of one and
no procedure for determining it, except possibly the
view that the just noticeable difference is such a unit.
Even if the existence and meaningfulness of such a unit
is established, it is logically arbitrary to add the util-
ities instead of combining them in some other way.
The argument that all individuals should appear
alike in a social judgment leads only to the conclusion
that the social welfare function should be a symmetric
function of individual utilities, not that it should be
a sum.
The Bentham criterion was defended later by John
Stuart Mill, but his arguments bear mostly on the
propriety and meaning of basing social welfare judg-
ments on individual preferences and not at all on the
commensurability of different individuals' utilities or
on the form of social welfare function. Mill, like Henry
Sidgwick and others, considered the primary use of
Bentham's doctrines to be applicability to the legal
system of criminal justice; since the conclusions arrived
at were qualitative, not quantitative, in nature, vague-
ness on questions of measurability was not noticed.
After the spread of marginal utility theory, the
economist F. Y. Edgeworth expounded the notion of
utility much more systematically than Bentham had
done, with little originality in the foundations, though
with a great deal of depth in applications. In particular,
he applied the sum-of-utilities criterion to the choice
of taxation schemes. The implication is one of radical
egalitarianism, as indeed Bentham had already per-
ceived. If, as is usually assumed, the marginal utility
of money is decreasing, if all individuals have the same
utility function for money, and if a fixed sum of money
is to be distributed, then the sum of utilities is
maximized when money income is distributed equally.
(Here, “money” may be thought of as standing for all
types of desired goods.) Then the only argument against
complete equality of income is that any procedure to
accomplish it would also reduce total income, which
is the amount to be divided. The argument can be also
put this way; resources should be taken from the rich
and given to the poor, not because they are poorer
per se but because they place a higher value on a given
quantity of goods. If it were possible to differentiate
between equally wealthy individuals on the basis of
their sensitivities to income increments, it would be
proper to give more to the more sensitive.
Apart from Edgeworth, there was little interest in
applying the sum-of-utilities criterion to economic or
any other policy. Very possibly, the radically egali-
tarian implications were too unpalatable, as they
clearly were to Edgeworth. Subsequent work on “wel-
fare economics,” as the theory of economic policy is
usually known, tended to be very obscure on funda-
mentals (although very clarifying in other ways).
