Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

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Dictionary of the History of Ideas | ||

*3. Utility.* Before discussing games of strategy

proper and developing the essence of the theory, a

clarification of the medium in which the payoff is made

is needed. When a game is played for money then the

winnings in money can be taken as the criterion for

the outcome, be it a game of chance or of strategy.

But when the score is not set in ready-made numerical

terms, or even by a simple “win” or “lose” declaration,

the matter is more difficult. While it would be possible

merely to postulate the existence of a number, it is

desirable to show how a numerical criterion of a speci-

fiable character can be established. This was accom-

plished (von Neumann and Morgenstern, 1944) by

showing that “utility” can be defined as a number up

to a positive linear transformation without fixing a unit

or a zero. In these terms payoffs will be expressed. The

utility concept takes prior rank even over money units,

though they be available. Utility thus defined is what

the individual will fundamentally aim for when select-

ing his strategy. The above-mentioned numerical ex-

pression is obtained from a small set of plausible axioms

by combining probability and an individual's com-

pletely ordered set of preferences (fulfilling the

Archimedean order property), showing that the indi-

vidual will think in terms of expected utility. It is

proved that these axioms define “utility” and make it

numerical in the desired manner. It is an additional

step to assume that the individual will endeavor to

maximize this utility.

The new utility theory also has given rise to a large

literature. Though modifications of the original version

have been proposed (e.g., the use of subjective,

Bayesian probabilities instead of the frequency con-

cept, etc.) the theory has entered virtually all writings

on decision-making and the more modern treatments

of economics. The theory has its antecedents in D.

Bernoulli's famous treatment of the “St. Petersburg

Paradox” (1738; Menger, 1934 and 1967) in which he

introduced the notion of moral expectation, i.e., a value

concept, in order to account for the fact that in spite

of an infinitely large mathematical expectation in that

game a person will not risk his entire possessions as

a stake in order to be allowed to play this game, even

if it could be offered. The second step in the direction

of von Neumann-Morgenstern utility theory was taken

by F. P. Ramsey in his “Truth and Probability” (1926;

1931); but this paper was only rediscovered after the

expected utility theory in the von Neumann-

Morgenstern formulation was developed and had be-

come dominant. The use of subjective probability does

not invalidate the theory (Pfanzagl, 1962; 1967) as was

already noted on the occasion of the original formula-

tion in 1944. The new theory of numerical utility is

not identical with theories of “cardinal” or “ordinal”

utility of the older and neo-classical economists, nor

has it a basis in philosophical or political utilitarianism.

In order to establish further the empirical validity

and power of the new theory a great number of exper-

iments have been made—a *novum* in this field. These

experiments attempt to test the validity of the under-

lying axioms, and to clarify the question of how indi-

viduals behave typically in situations involving risk.

This behavior is clearly a phenomenon that any theory

of decision-making has to take into account, given the

glaring fact of the prevalence of chance in human

affairs.

The development of the new theory of utility defi-

nitely advances our ability to analyze decisions (Fish-

(Martin, 1963).

Dictionary of the History of Ideas | ||