A deviant development in choice theory: the contributions byArmstrong, Luce, and Fishburn
DOI:
https://doi.org/10.1590/1980-53575543gaKeywords:
Intransitivity, Ordinalist revolution, Semiorder, PreferencesAbstract
Recent research in the history of economic thought has shown the diversity of themes and positions concerning economic behavior in the so-called Ordinalist Revolution. This paper aims to recover the developments of a research line that began by critically examining the developments of that theoretical movement. The investigation departs from W. E. Armstrong’s insistent defense of the intransitivity of indifference based on evidence from experimental psychology, pointing out the impossibility of discernment between close alternatives. The study verifies how R. D. Luce, an influential mathematician in psychology, formalized Armstrong’s idea with a semiorder concept, a generalization of a weak order, the standard representation of preferences in microeconomics. Lastly, the investigation is on the role of P. C. Fishburn in this episode, considering that he was a remarkable author in mathematical economics, with several contributions in choice, uncertainty, and collective choice theories, including related work with the indifference intransitivity assumption in these topics.
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References
Algom, D. 2021. “The Weber–Fechner Law: A Misnomer That Persists but That Should Go Away”. Psychological Review 128 (4): 757–765.
Allais, M. 1953. “Le Comportement de l’Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l’Ecole Americaine”. Econometrica 21 (4) : 503–546.
Anônimo. 1980. “W. E. Armstrong”. The Times 26 de março:19.
Armstrong, W. E. 1924. “Rossel Island Money: A Unique Monetary System”. The Economic Journal 34 (135):
–429.
Armstrong, W. E. 1939a. “Primitive Polynesian Economy. By Raymond Firth”. The Economic Journal 49 (196): 729–731.
Armstrong, W. E. 1939b. “The Determinateness of the Utility Function”. The Economic Journal 49 (195): 453–467.
Armstrong, W. E. 1940a. “Principles of Economic Sociology. By D. M. Goodfellow; Land, Labour and Diet in
Northern Rhodesia. By Audrey I. Richards”. The Economic Journal 50 (198-199): 315–317.
Armstrong, W. E. 1940b. “The Economic Life of Primitive Peoples. By Melville J. Herskovits”. The Economic
Journal 50 (200): 515–516.
Armstrong, W. E. 1946. “Malay Fishermen: Their Peasant Economy. By Raymond Firth. The Economic Journal 56 (224): 653–654.
Armstrong, W. E. 1948. “Uncertainty and the Utility Function”. The Economic Journal 58 (229): 1–10.
Armstrong, W. E. 1949. “Primitive Money in its Ethnological, Historical and Economic Aspects. By Paul Einzig”. The Economic Journal 59 (235): 439–440.
Armstrong, W. E. 1950. “A Note on the Theory of Consumer’s Behaviour”. Oxford Economic Papers 2 (1):
–122.
Armstrong, W. E. 1951. “Utility and the Theory of Welfare”. Oxford Economic Papers 3 (3): 259–271.
Armstrong, W. E. 1953. “[Marginal Preference and the Theory of Welfare]: A Reply”. Oxford Economic Papers 5 (3): 264–270.
Armstrong, W. E. 1955. “Concerning Marginal Utility”. Oxford Economic Papers 7 (2): 170–176.
Armstrong, W. E. 1958a. “The Measuremente of Utility. By Tapas Majumdar”. Economica 25 (100): 351-352.
Armstrong, W. E. 1958b. “Utility and the” Ordinalist Fallacy””. The Review of Economic Studies 25 (3): 172–181.
Boianovsky, M. 2014. “Robertson and the Cambridge Approach to Utility and Welfare”. Cambridge Journal of Economics 38 (4): 961–985.
Bowley, M. 1938. “Saving and Investment. By W. E. Armstrong”. Economica 5 (18): 251–252.
Brams, S. J., W. V. Gehrlein e F. S. Roberts. 2009. “Preface”. In The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn, edited by S. J. Brams, W. V. Gehrlein and F. S. Roberts, v–ix. Berlin: Springer.
Brams, S. J., W. V. Gehrlein e F. S. Roberts. 2021. “Peter C. Fishburn (1936-2021)”. Social Choice and Welfare
:1–3.
Breathnach, C. S. 1993. “W H R Rivers and the Hazards of Interpretation”. Journal of the Royal Society of
Medicine 86 (7): 413–416.
Edgeworth, F. Y. 1881. Mathematical Psychics. London: C. Kegan Paul & CO.
Edwards, W. 1954. “The Theory of Decision Making”. Psychological Bulletin 51 (4): 380–417.
Fernandez-Grela, M. 2006. “Disaggregating the Components of the Hicks-Allen Composite Commodity”. History of Political Economy 38:32–47.
Fiévet, A. 2022. “On the Shoulders of Giants: from Lange (1934) to Samuelson (1938) on the “unique” measure of utility”. The European Journal of the History of Economic Thought 29 (6): 1125–1145.
Fishburn, P. C. 1964. Decision and Value Theory. New York: John Wiley & Sons.
Fishburn, P. C. 1968. “Utility Theory”. Management Science 14 (5): 335–378.
Fishburn, P. C. 1970a. “Conditions for Simple Majority Decision Functions with Intransitive Individual Indifference”. Journal of Economic Theory 2 (4): 354–367.
Fishburn, P. C. 1970b. “Intransitive Indifference in Preference Theory: a Survey”. Operations Research 18 (2): 207–228.
Fishburn, P. C. 1970c. “Intransitive Individual Indifference and Transitive Majorities”. Econometrica 38 (3):
–489.
Fishburn, P. C. 1970d. “Suborders on Commodity Spaces”. Journal of Economic Theory 2 (4): 321–328.
Fishburn, P. C. 1970e. “The Irrationality of Transitivity in Social Choice”. Behavioral Science 15 (2): 119–123.
Fishburn, P. C. 1970f. Utility Theory for Decision Making. New York: John Wiley & Sons.
Fishburn, P. C. 1970g. “Utility Theory with Inexact Preferences and Degrees of Preference”. Synthese 21: 204–221.
Fishburn, P. C. 1971. “Should Social Choice Be Based on Binary Comparisons?” The Journal of Mathematical Sociology 1 (1):133–142.
Fishburn, P. C. 1972. “Minimal Preferences on Lotteries”. Journal of Mathematical Psychology 9 (3):294–305.
Fishburn, P. C. 1973a. “Summation Social Choice Functions”. Econometrica 41 (6): 1183–1196.
Fishburn, P. C. 1973b. The Theory of Social Choice. Princeton: Princeton University Press.
Fishburn, P. C. 1974. “Lexicographic Orders, Utilities and Decision Rules: a Survey”. Management Science 20(11): 1442–1471.
Fishburn, P. C. 1975. “A Theory of Subjective Expected Utility with Vague Preferences”. Theory and Decision
:287–310.
Fishburn, P. C. 1977. “Models of individual Preference and Choice”. Synthese 36:287–314.
Forrester, J. 2008. “1919: Psychology and Psychoanalysis, Cambridge and London - Myers, Jones and MacCurdy”. Psychoanalysis and History 10 (1): 37–94.
Friedman, M. e L. J. Savage. 1948. “The Utility Analysis of Choice Involving Risk”. The Journal of Political
Economy LVI (4): 279–304.
Gallistel, C. R. e D. H. Krantz. 2013. “R. Duncan Luce (1925-2012)”. The American Journal of Psychology
(4): 493–498.
Georgescu-Roegen, N. 1936. “The Pure Theory of Consumer’s Behavior”. The Quarterly Journal of Economics 50 (4): 545–593.
Georgescu-Roegen, N. 1954. “Choice, Expectations and Measurability”. The Quarterly Journal of Economics
(4): 503–534.
Green, H. A. J. 1958. “Mr. Armstrong and the Theory OD Demand”. Metroeconomica 10 (2): 74–80.
Gregory, C. A. 2004. “Armstrong, Wallace Edwin (1896–1980), anthropologist and economist”. Oxford Dictionary of National Biography, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb9780198614128e66809, Acessado em 30/12/2024.
Gregory, C. A. e J. Urry. 1987. “Armstrong, Wallace Edwin”. Em The New Palgrave: a Dictionary of Economics, editado por J. Eatwell, M. Milgate e P. Newman, 1:114–115. London: Macmillan.
Hands, D. W. 2010. “Economics, Psychology and the History of Consumer Choice Theory”. Cambridge Journal of Economics 34:633–648.
Hands, D. W. 2011. “Back to the Ordinalist Revolution: Behavioral Economic Concerns in Early Modern Consumer Choice Theory”. Metroeconomica 62 (2): 386–410.
Hayek, F. A. 1941. The Pure Theory of Capital. Auburn: The Ludwig von Mises Institute, 2009.
Hicks, J. R. 1956. A Revision of Demand Theory. Oxford: Clarendon Press.
Hicks, J. R. e R. G. D. Allen. 1934a. “A Reconsideration of the Theory of Value. Part I”. Economica 1 (1): 52–76.
Hicks, J. R. e R. G. D. Allen. 1934b. “A Reconsideration of the Theory of Value. Part II. A Mathematical Theory
of Individual Demand Functions”. Economica 1 (2): 196–219.
Hudík, M. 2014. “Reference-Dependence and Marginal Utility: Alt, Samuelson, and Bernardelli”. History of
Political Economy 46 (4): 677–693.
Hupman, A. C. e J. Simon. 2022. “The Legacy of Peter Fishburn: Foundational Work and Lasting Impact”.
Decision Analysis 20 (1): 1–15. INFORMS. Peter C. Fishburn. https://www.informs.org/Explore/HistoryofO.R.-Excellence/Biographical-Profiles/Fishburn-Peter-C. Acessado em 30/12/2024.
Knight, K. L. 2018. A.C. Pigou and the ’Marshallian’ Thought Style: A Study in the Philosophy and Mathematics Underlying Cambridge Economics. Cham: Palgrave Macmillan.
Lenfant, J. S. 2018. “Probabilising the Consumer: Georgescu-Roegen, Marschak and Quandt on the Modelling of the Consumer in the 1950s”. The European Journal of the History of Economic Thought 25(1):36–72.
Lerner, A. P. 1937. “Saving and Investment. By W. E. Armstrong”. The Economic Journal 47 (187): 521–522.
Liep, J. 2015. “Dogomomo Xmas, Kwangwe’s Races, and a Murder: W.E. Armstrong and the Rossel Island
Money”. Oceania 85 (2): 183–198.
Luce, R. D. 1956. “Semiorders and a Theory of Utility Discrimination”. Econometrica 24 (2): 178–191.
Luce, R. D. 1988. This Week Citations Classic: “Games and Decision - introduction and critical survey”. Current Contents (15): 16.
Luce, R. D. 1989. “R. Duncan Luce”. In A History of Psychology in Autobiography, edited by G. Lindzey, vol.
:244–289. Stanford: Stanford University Press.
Luce, R. D. e W. Edwards. 1958. “The Derivation of Subjective Scales from Just Noticeable Differences”.
Psychological Review 65 (4): 222-237.
Luce, R. D., A. J. Marley e C. T. Ng. 2009. “Entropy-Related Measures of the Utility of Gambling”. In The
Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn, edited by S. J. Brams, W. V. Gehrlein e F. S. Roberts, 5–25. Berlin: Springer.
Luce, R. D. e H. Raiffa. 1957. Games and Decision - introduction and critical survey. New York: John Wiley & Sons.
Majumdar, T. 1957. “Armstrong and the Utility Measurement Controversy”. Oxford Economic Papers 9 (1): 30–40.
Majumdar, T. 1958. The Measurement of Utility. London: Macmillan & Co LTD.
Masin, S. C, V. Zudini e M. Antonelli. 2009. “Early Alternative Derivations of Fechner’s Law”. Journal of the
History of the Behavioral Sciences 45 (1): 56–65.
McClelland, J. L. 2012. “R. Duncan Luce (1925–2012)”. Science 337 (6102): 1619–1619.
Moscati, I. 2007. “Early Experiments in Consumer Demand Theory: 1930 –1970”. History of Political Economy 39 (3): 359–401.
Moscati, I. 2013. “How Cardinal Utility Entered Economic Analysis: 1909–1944”. The European Journal of the
History of Economic Thought 20 (6): 906–939.
Myers, C. S. 1922. “The Influence of the Late W. H. R. Rivers on the Development of Psychology in Great
Britain”. Nature 110: 485–490.
Neumann, J. e O. Morgenstern. 1944. Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Ng, Y-K. 1981. “Bentham or Nash? On the Acceptable Form of Social Welfare Functions”. Economic Record
(3): 238–250.
Oliveira, T. D. e A. L. Portella. 2017. “Two Faces of the Same Georgescu-Roegen: from Path-Dependency and the Imperfection of the Human Mind to Institutional Change and Biophysical Constraints”. História Econômica & História de Empresas 20 (1): 243-261.
Pareto, V. 1996 [1909]. Manual de Economia Política. São Paulo: Nova Cultural.
Roberts, F. S., C. P. Davis-Stober e M. Regenwetter. 2024. “The Mathematical Psychology of Peter Fishburn”. Journal of Mathematical Psychology 120-121:102845.
Rothenberg, J. 1953. “Marginal Preference and the Theory of Welfare”. Oxford Economic Papers 5 (3): 248–263.
Rothenberg, J. 1954. “Reconsideration of a Group Welfare Index: A Rejoinder on Marginal Preference”. Oxford Economic Papers 6 (2): 164–180.
Samuelson, P. A. 1938a. “A Note on the Pure Theory of Consumer’s Behaviour”. Economica 5 (17): 61–71.
Samuelson, P. A. 1938b. “The Empirical Implications of Utility Analysis”. Econometrica 6 (4): 344–356.
Sen, A. 1969. “Quasi-Transitivity, Rational Choice and Collective Decisions”. The Review of Economic Studies
(3): 381–393.
Sen, A. 1971. “Choice Functions and Revealed Preference”. The Review of Economic Studies 38 (3): 307–317.
Sen, A. 1986. “Social Choice Theory”. In Handbook of Mathematical Economics, edited by K. J. Arrow e M. D.
Intriligator, 3:1073–1181. Amsterdam: North-Holland.
Tribe, K. 2022. Constructing Economic Science: The Invention of a Discipline 1850-1950. Oxford: Oxford
University Press.
Tullock, G. 1964. “The Irrationality of Intransitivity”. Oxford Economic Papers 16 (3): 401–406.
Urry, J. 1985. “W. E. Armstrong and Social Anthropology at Cambridge 1922-1926”. Man 20 (3): 412–433.
Vickrey, W. 1960. “Utility, Strategy, and Social Decision Rules”. The Quarterly Journal of Economics 74 (4):
–535.
Ward, J. 1891. The Moral Sciences Tripos. Cambridge: Deighton, Bell & CO
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