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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas

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The historical development of the notion of social
welfare cannot be easily understood without reference
to the gradual evolution of a formal analysis of individ-
ual choice, which we briefly summarize. Three charac-


teristics of this history, which are shared with the
history of the concept of social welfare, are striking:
(1) the form of the basic problems were established
during the eighteenth century and display the charac-
teristic rationalism and optimism of the Enlightenment;
(2) the analysis retained its general form but underwent
systematic transformation under the impact of twen-
tieth-century epistemological currents; and (3) there
are strong historical links with the development of the
theory of probability and its applications, links which
are not easy to explain on purely logical grounds.

The first work to discuss individual choice system-
atically is that of Daniel Bernoulli in 1738. He was
concerned to explain phenomena of which insurance
was typical—that individuals would engage in bets
whose actuarial value was negative. Bernoulli's solution
was that what guided the individual's decisions to
accept or reject bets was not the money outcomes
themselves but their “moral values” as he judged them.
In later terminology, the individual attached utilities
to different amounts of money and accepted an un-
certainty if and only if it increased the expected value
of the utility. He also postulated that in general utility
increased by lesser and lesser amounts as the quantity
of money increased, an assumption now known as
diminishing marginal utility. Then the individual
would shy away from bets which were actuarially
favorable if they increased uncertainty in money terms
(in particular, if they involved a very small probability
of very high returns) and would accept insurance
policies if they reduced monetary uncertainty, for the
high returns offered in the one case had relatively little
additional utility, while the low returns avoided in the
second case imply large losses of utility. Bernoulli thus
required a cardinal utility (in this case, an interval
scale) for his explanation of human behavior under

The idea that the drive of an individual to increase
some measure of satisfaction explained his behavior was
widespread, though rather vague, in the eighteenth
century; Galiani, Condillac, and Turgot argued that in
some measure the prices of commodities reflected the
utilities they presented to individuals, for individuals
were willing to pay more for those objects which
provided them more satisfaction. This particular doc-
trine, indeed ran into a difficulty that Adam Smith
noted, that water was surely more useful than diamonds
but commanded a much lower price. But the doctrine
that the increase of utility or happiness is the complete
explanation of individual behavior is most emphasized
by Jeremy Bentham in writings extending from 1776
to his death in 1832. Further, and even more impor-
tantly, Bentham introduced the doctrine of the paral-
lelism between the descriptive and the normative in
terpretations of utility; not only does an individual seek
happiness but he ought to do so, and society ought
to help him to this end. “Nature has placed mankind
under the governance of two sovereign masters, pain
and pleasure. It is for them alone to point out what
we ought to do, as well as to determine what we shall
do.... By the principle of utility is meant that princi-
ple which approves or disapproves of every action
whatsoever, according to the tendency which it ap-
pears to have to augment or diminish the happiness
of the party whose interest is in question” (Bentham,
1780; 1961). Bentham took it for granted that utility
was a measurable magnitude; he further elaborated in
various ways the factors which determine utility, such
as nearness in time and certainty, but at no point is
there a clearly defined procedure for measuring utility,
such as would be demanded by modern scientific phi-
losophy. The one suggestion he made was that suffi-
ciently small increments in wealth were not percep-
tible; therefore, a natural unit for measuring utility is
the minimum sensible, or just noticeable difference, as
psychophysicists were later to term it.

Although Bentham's notions were widely influential,
especially among English economists (as well as being
violently repudiated by the romantic thinkers of the
early nineteenth century), a further elaboration was not
achieved until about 1870 when Bentham's simple
hedonistic psychology proved to be of surprising use
in economic analysis. Smith's water-diamond paradox
was at last resolved; while water as a whole was more
valuable than diamonds, the relevant comparison was
between an additional increment of water and an
additional increment of diamonds, and since water was
so much more abundant, it was not surprising that the
incremental or marginal utility of water was much
lower. (Actually, Bentham had already shown Smith's
error but did not directly relate utilities to prices in
any form; in any case, Bentham's contribution was not
recognized.) This basic point was grasped simulta-
neously by Stanley Jevons in England, Léon Walras
in France, and Carl Menger in Austria, between 1871
and 1874; they had in fact been anticipated by Gossen
in Germany in 1854.

The further technical developments of the theory
of individual choice in economic contexts are not of
interest here, but the power of the utility concept led
among other things to an analysis of its meaning.
Already in his doctoral dissertation in 1892, Mathe-
matical Investigations in the Theory of Value and
the American economist Irving Fisher observed
that the assumption of the measurability of utility in
fact was inessential to economic theory. This point was
developed independently and taken up much further
by Vilfredo Pareto, from 1896 on. At any moment,


given the prices of various goods and his income, an
individual has available to him all bundles of goods
whose cost does not exceed his income. The “marginal
utility” theory stated that he chose among those bun-
dles the one with the highest utility. But all that was
necessary for the theoretical explanation was that the
individual have an ordering of different bundles; then
the individual is presumed to select that bundle among
those available which is highest on his ordering. Thus
only ordinal preferences matter; two utility functions
which implied the same ordinal preference compari-
sons would predict the same choice of commodity
bundles at given prices and income. But this meant
in turn that no set of observations on the individual's
purchasing behavior could distinguish one of these
utility functions from another. In fact, more generally,
no observation of the individual's choices from any set
of bundles could make this distinction. But then the
neo-positivist and operational epistemology, so char-
acteristic of this century, would insist that there was
no meaning to distinguishing one utility function from
another. It was the ordering itself that was meaningful,
and all utility functions which implied it were equally
valid or invalid.

The ordinalist position, defined above, only began
to spread widely in the 1930's and became orthodox,
ironically enough at a moment when the foundations
for a more sophisticated theory of cardinal utility had
already been laid. The general approach is to make
some additional hypotheses about the kind of choices
which an individual will or ought to make. Then it
is demonstrated that there is a way of assigning numer-
ical utilities to different possible bundles of goods or
other alternative decisions such that the utilities
assigned reflect the ordering (higher utility to preferred
alternatives) and that the function assigning utilities
to alternatives has some especially simple form. More
particularly, it is assumed that the different commodi-
ties can be divided into classes in such a way that the
preferences for commodities in one class are inde-
pendent of the amounts of the commodities in the other
classes. Then there is a way of assigning utilities to
bundles of commodities within each class and defining
the utility of the entire bundle as the sum of the utilities
over classes. Such a definition of utility can easily be
shown to be an interval scale. This process by which
utilities are simultaneously assigned within classes and
in total so as to satisfy an additivity property has
become known as conjoint measurement.

A particular case of conjoint measurement is of
special significance. An ordinalist position undermined
Bernoulli's theory of choice (described above) in risky
situations; if cardinal utility had no meaning, there was
no way of taking its mathematical expectation. But in
the case of risk-bearing, it is very natural to make an
appropriate independence assumption, and it is possi-
ble so to choose a utility function that an individual's
behavior in accepting or rejecting risks can be
described by saying that he is choosing the higher
expected utility. The philosopher Frank Ramsey made
this observation in a paper published posthumously in
1931, in the collection called The Foundations of
Mathematics and Other Essays
(p. 156), but it made
no impact; the point was rediscovered by John von
Neumann and Oskar Morgenstern, as part of their great
work on the theory of games, in 1944. The cardinalist
position in this case is rehabilitated, but it has changed
its meaning. It is no longer a measure inherently asso-
ciated with an outcome; instead, the utility function
is precisely that which measures the individual's will-
ingness to take risks.