A theory of Justice: Revised Edition

The Political Element in the Development of
Economic Theory,
trans. Paul Streeten (London, Routledge and Kegan Paul, Ltd., 1953), pp. 38f.
J. J. C. Smart in 
An Outline of a System of Utilitarian Ethics
(Cambridge, The University Press,
1961), p. 18, leaves the matter unsettled, but affirms the classical principle in the case where it is
necessary to break ties. As unambiguous proponents of the average doctrine, see J. C. Harsanyi,
“Cardinal Utility in Welfare Economics and the Theory of Risk Taking,” 
Journal of Political Econ-
omy,
vol. 61 (1953), and “Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of
Utility,” 
Journal of Political Economy,
vol. 63 (1955); and R. B. Brandt, “Some Merits of One Form
of Rule Utilitarianism,” in 
University of Colorado Studies
(Boulder, Colo., 1967), pp. 39–65. But
note the qualification regarding Brandt’s view in §29 below, note 31. For a discussion of Harsanyi,
see P. K. Pattanaik, “Risk, Impersonality, and the Social Welfare Function,” 
Journal of Political
Economy,
vol. 76 (1968), and Sen, 
Collective Choice and Social Welfare,
pp. 141–146.
140
The Original Position

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INDEFINITE INCREASE OF POPULATION
Formally the condition for increasing population size indefinitely is that
the curve y 
F(x), where y is average per capita utility and x is popula-
tion size, should be flatter than the rectangular hyperbola xy 
c. For xy
equals the total utility, and the area of the rectangle representing this
total increases as x increases whenever the curve y 
F(x) is flatter than
xy 
c.
Now this consequence of the classical principle seems to show that it
would be rejected by the parties in favor of the average principle. The two
principles would be equivalent only if it is supposed that average well-be-
ing always falls sufficiently fast (beyond a certain point anyway) so that
there is no serious conflict between them. But this assumption seems
questionable. From the standpoint of the persons in the original position,
it would appear more rational to agree to some sort of floor to hold up
average welfare. Since the parties aim to advance their own interests, they
have no desire in any event to maximize the sum total of satisfaction. I
assume, therefore, that the more plausible utilitarian alternative to the two
principles of justice is the average and not the classical principle.
I now wish to consider how the parties might arrive at the average
principle. The reasoning I shall sketch is perfectly general and if it were
sound it would sidestep entirely the problem of how to present the alter-
natives. The average principle would be recognized as the only reason-
able candidate. Imagine a situation in which a single rational individual
can choose which of several societies to enter.
23
To fix ideas, assume first
that the members of these societies all have the same preferences. And
assume also that these preferences satisfy conditions that enable one to
23. Here I follow the first stages of W. S. Vickrey’s presentation in “Utility, Strategy, and Social
Decision Rules,” 
Quarterly Journal of Economics,
vol. 74 (1960), pp. 523f.
141
27. The Reasoning for Average Utility

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define a cardinal utility. Further, each society has the same resources and
the same distribution of natural talents. Nevertheless, individuals with
different talents have different incomes; and each society has a redistribu-
tion policy which if pushed beyond a certain point weakens incentives
and thereby lowers production. Supposing that different policies are fol-
lowed in these societies, how will a single individual decide which soci-
ety to join? If he knows his own abilities and interests precisely, and if he
has detailed information about these societies, he may be able to foresee
the well-being that he will almost certainly enjoy in each one. He can
then decide on this basis. There is no need for him to make any prob-
abilistic calculations.
But this case is rather special. Let us alter it step by step so that it
increasingly resembles that of someone in the original position. Thus,
suppose first that the hypothetical joiner is unsure about the role his
talents will enable him to fill in these various societies. If he assumes that
his preferences are the same as everyone else, he may decide by trying to
maximize his expected well-being. He computes his prospect for a given
society by taking as the alternative utilities those of the representative
members of that society and as the likelihoods for each position his
estimates of his chances of attaining it. His expectation is defined, then,
by a weighted sum of utilities of representative individuals, that is, by the
expression 
p
1
u
1
, where p
1
is the likelihood of his achieving the ith
position, and u
i
the utility of the corresponding representative man. He
then chooses the society offering the highest prospect.
Several further modifications bring the situation closer to that of the
original position. Assume that the hypothetical joiner knows nothing
about either his abilities or the place he is likely to hold in each society. It
is still assumed, though, that his preferences are the same as the people in
these societies. Now suppose that he continues to reason along prob-
abilistic lines by holding that he has an equal chance of being any individ-
ual (that is, that his chance of falling under any representative man is the
fraction of society that this man represents). In this case his prospects are
still identical with the average utility for each society. These modifica-
tions have at last brought his expected gains for each society in line with
its average welfare.
So far we have assumed that all individuals have similar preferences
whether or not they belong to the same society. Their conceptions of the
good are roughly the same. Once this highly restrictive assumption is
dropped, we take the final step and arrive at a variation of the initial
situation. Nothing is known, let us say, about the particular preferences of
142
The Original Position

---

the members of these societies or of the person deciding. These facts as
well as a knowledge of the structure of these societies are ruled out. The
veil of ignorance is now complete. But one can still imagine that the
hypothetical newcomer reasons much as before. He assumes that there is
an equal likelihood of his turning out to be anyone, fully endowed with
that person’s preferences, abilities, and social position. Once again his
prospect is highest for that society with the greatest average utility. We
can see this in the following way. Let n be the number of persons in a
society. Let their levels of well-being be u
1
, u
2
, . . . , u
n
. Then the total
utility is 
u
i 
and the average is
u
i
/n. Assuming that one has an equal
chance of being any person, one’s prospect is: 1/n u
1
1/n u
2
. . .
1 /n u
n
or 
u
i
/n. The value of the prospect is identical with the average
utility.
Thus if we waive the problem of interpersonal comparisons of utility,
and if the parties are viewed as rational individuals who have no aversion
to risk and who follow the principle of insufficient reason in computing
likelihoods (the principle that underlies the preceding probabilistic calcu-
lations), then the idea of the initial situation leads naturally to the average
principle. By choosing it the parties maximize their expected well-being
as seen from this point of view. Some form of contract theory provides,
then, a way of arguing for the average over the classical view. In fact, how
else is the average principle to be accounted for? After all, it is not a
teleological doctrine, strictly speaking, as the classical view is, and there-
fore it lacks some of the intuitive appeal of the idea of maximizing the
good. Presumably one who held the average principle would want to
invoke the contract theory at least to this extent.
In the preceding discussion I have assumed that utility is understood in
the traditional sense as the satisfaction of desire and cardinal interper-
sonal comparisons are regarded as possible. But this notion of utility
has been largely abandoned by economic theory in recent decades; it is
thought to be too vague and to play no essential role in explaining eco-
nomic behavior. Utility is now understood as a way of representing the
choices of economic agents and not as a measure of satisfaction. The
main kind of cardinal utility presently recognized derives from the Neu-
man-Morgenstern construction, which is based on choices between pros-
pects involving risks (§49). Unlike the traditional notion, this measure
takes attitudes to uncertainty into account and it does not seek to provide
a basis for interpersonal comparisons. Nevertheless, it is still possible to
formulate the principle of average utility using this kind of measure: one
supposes the parties in the original position, or some variant thereof, to
143
27. The Reasoning for Average Utility

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have Neuman-Morgenstern utility function and to assess their prospects
accordingly.
24
Of course, certain precautions must be taken; for example,
these utility functions cannot take into account all kinds of considera-
tions but must reflect the parties’ estimate of what furthers their good. If
they were influenced by other reasons, we would not have a teleological
theory.
When these restrictions are observed, however, an average utilitarian
view can be stated that takes into account the high level of risk aversion
that it seems any normal person would have in the original position; and
the greater this risk aversion the more this form of utility principle would
resemble the difference principle, at least when the evaluation of eco-
nomic benefits is in question. Of course, these two principles are not the
same, since there are many important differences between them. But
there is this similarity: risk and uncertainty from a suitably general per-
spective leads both views to weight more heavily the advantages of those
whose situation is less fortunate. In fact, reasonable risk aversion may be
so great, once the enormous hazards of the decision in the original posi-
tion are fully appreciated, that the utilitarian weighting may be, for prac-
tical purposes, so close to the difference principle as to make the simplic-
ity of the latter (§49) decisive in its favor.
28. SOME DIFFICULTIES WITH THE
AVERAGE PRINCIPLE
28. Difficulties with the Average Principle
Before taking up the arguments for the two principles of justice I wish to
mention several difficulties with the average principle of utility. First,
though, we should note an objection which turns out to be only apparent.
As we have seen, this principle may be viewed as the ethics of a single
rational individual prepared to take whatever chances necessary to maxi-
mize his prospects from the standpoint of the initial situation. (If there is
no objective basis for probabilities, they are computed by the principle of
insufficient reason.) Now it is tempting to argue against this principle that
24. How this might be done was shown by J. C. Harsanyi. See his “Cardinal Utility in Welfare
Economics and the Theory of Risk Taking,”