BIBLIOGRAPHY
For histories of the theory of individual choice in eco-
nomics, see E. Kauder, A History of Marginal Utility Theory
(Princeton, 1965), and G. J. Stigler, “The Development of
Utility Theory,” Journal of Political Economy, 58 (1950),
307-27, 373-96. Bernoulli's paper originally appeared in
Comentarii Academiae Scientiarum Imperiales Petropoli-
tanae, 5 (1738), 175-92. It has been translated into English
in Econometrica, 12 (1954), 23-36. The quotation from J.
Bentham appears in his An Introduction to the Principles
of Morals and Legislation, reprinted in The Utilitarians
(Garden City, N.Y., 1961), p. 17. For a survey of the theory
of conjoint measurement, see P. C. Fishburn, “A Note on
Recent Developments in Additive Utility Theories for
Multiple-Factor Situations,” Operations Research, 14 (1966),
1143-48.
No adequate secondary sources exist for most of Part II.
See Bentham's work just cited; W. Stark, ed. Jeremy
Bentham's Economic Writings (London, 1954); M. P. Mack,
Jeremy Bentham: An Odyssey of Ideas, 1748-1792 (New
York, 1963); F. Y. Edgeworth, Mathematical Psychics
(London, 1881), and idem, “The Pure Theory of Taxation,”
in Papers Relating to Political Economy (London, 1925), II,
102; V. Pareto, The Mind and Society (New York, 1935),
4, 1459-74; A. Bergson, Essays in Normative Economics
(Cambridge, Mass., 1966), Part I; W. S. Vickrey, “Measuring
Marginal Utility by Reaction to Risk,” Econometrica, 13
(1945), 319-33, and idem, “Utility, Strategy, and Decision
Rules,” Quarterly Journal of Economics, 74 (1960), 507-35;
J. M. Fleming, “A Cardinal Concept of Welfare,” Quarterly
Journal of Economics, 64 (1952), 366-84; J. Harsanyi, “Car-
dinal Welfare, Individualistic Ethics, and Interpersonal
Comparisons of Utility,” Journal of Political Economy, 56
(1953), 309-21; W. E. Armstrong, “Utility and the Theory
of Welfare,” Oxford Economic Papers, New Series, 3 (1951),
259-71; L. Goodman and H. Markowitz, “Social Welfare
Functions Based on Individual Rankings,” American Journal
of Sociology, 58 (1952), 257-62; J. Rothenberg, The Meas
urement of Social Welfare (Englewood Cliffs, N.J., 1961);
and J. Rawls, “Distributive Justice,” in P. Laslett and
W. G. Runciman, eds. Philosophy, Politics, and Society,
Third Series (Oxford, 1967), pp. 58-82.
For the work discussed in Part III, see C. G. Hoag and
G. Hallett, Proportional Representation (New York, 1926),
for the work of Hallett, Hare, and others on proportional
representation and preferential voting. See also: J. Rothen-
berg, op. cit.; K. J. Arrow, Social Choice and Individual
Values, 2nd ed. (New York, 1963); D. Black, The Theory
of Committees and Elections (Cambridge, 1958); I.
Todhunter, A History of the Mathematical Theory of Proba-
bility from the Time of Pascal to that of Laplace (Cambridge
and London, 1865); A. K. Sen, “A Possibility Theorem on
Majority Decisions,” Econometrica, 34 (1966), 491-99;
G. Tullock, Toward a Mathematics of Politics (Ann Arbor,
1967), Ch. III; and Y. Murakami, Logic and Social Choice
(London and New York, 1968). The work of Condorcet is
discussed by Black, pp. 159-80; see also G. G. Granger, La
mathématique sociale du Marquis de Condorcet (Paris, 1956),
esp. pp. 94-129. Condorcet's study was entitled Essai sur
l'application de l'analyse à la probabilité des décisions
rendues à la pluralité des voix (Paris, 1785). For Laplace's
work on elections, see Black, pp. 180-83.
KENNETH J. ARROW
[See also Democracy;
Economic History; Economic Theory
of Natural Liberty; Equality;
Game Theory; Probability;
Rationality; Utilitarianism;
Utility.]
