Cardinal Utility: A History of Hedonimetry

The paper chronicles the scientific use and abuse of cardinal utility during more than two centuries. Surveying the contributions from moral philosophers, economists, psychologists and mathematicians, it is shown that cardinal utility is used as a name not only for one but for a large number of formally distinct concepts. Throughout the years these have become extensively confused, and still are.

[1]  H. P. Young,et al.  Progressive Taxation and Equal Sacrifice , 1990 .

[2]  Alan T. Peacock,et al.  Classics in the theory of public finance , 1959 .

[3]  Francis Hutcheson,et al.  An Essay on the Nature and Conduct of the Passions and Affections: With Illustrations on the Moral Sense , 1972 .

[4]  Milton Friedman,et al.  Choice, Chance, and the Personal Distribution of Income , 1953, Journal of Political Economy.

[5]  John C. Harsanyi,et al.  Nonlinear social welfare functions , 1975 .

[6]  Y. Ng Interpersonal level comparability implies comparability of utility differences: A reply , 1984 .

[7]  Yew-Kwang Ng,et al.  On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions , 1976 .

[8]  J. Viner The Utility Concept in Value Theory and Its Critics , 1925, Journal of Political Economy.

[9]  Geoff Riddington,et al.  Progress in Utility and Risk Theory , 1985 .

[10]  D. Robertson,et al.  Utility and all that , 1954 .

[11]  David. I. MAYSTON The generation of a social welfare function under ordinal preferences , 1982, Math. Soc. Sci..

[12]  I. Fisher,et al.  A statistical method for measuring "marginal utility" and testing the justice of a progressive income tax , 1927 .

[13]  Robert P. Parks,et al.  An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function , 1976 .

[14]  John C. Harsanyi,et al.  Cardinal Utility in Welfare Economics and in the Theory of Risk-taking , 1953, Journal of Political Economy.

[15]  R. Luce Semiorders and a Theory of Utility Discrimination , 1956 .

[16]  Ragnar Frisch,et al.  SUR UN PROBLÈME D'ÉCONOMIE PURE * , 1957 .

[17]  C H COOMBS,et al.  Psychological scaling without a unit of measurement. , 1950, Psychological review.

[18]  Roman Krzysztofowicz,et al.  Risk Attitude Hypotheses of Utility Theory , 1983 .

[19]  J. Kagel,et al.  Animals' Choices over Uncertain Outcomes: Some Initial Experimental Results , 1985 .

[20]  Aldo Montesano,et al.  Recent Developments in the Foundations of Utility and Risk Theory , 1986 .

[21]  R. Wilkinson,et al.  Economics and Consumer Behaviour , 1981 .

[22]  A. N. Page Utility Theory: A Book of Readings , 1968 .

[23]  P. Schoemaker The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations , 1982 .

[24]  D. Ellsberg Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[25]  On the Determinateness of the Utility Function , 1937 .

[26]  The Collected Scientific Papers of Paul A. Samuelson. , 1967 .

[27]  Amos Tversky,et al.  A general theory of polynomial conjoint measurement , 1967 .

[28]  Neil R. Paine Introspective utility and the group choice problem , 1975 .

[29]  Nicholas Georgescu-Roegen,et al.  Threshold in Choice and the Theory of Demand , 1958 .

[30]  Rakesh K. Sarin,et al.  Group Preference Aggregation Rules Based on Strength of Preference , 1979 .

[31]  Peter A. Diamond,et al.  Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment , 1967, Journal of Political Economy.

[32]  Tjalling C. Koopmans,et al.  Additively decomposed quasiconvex functions , 1982, Math. Program..

[33]  L. Hurwicz,et al.  Social goals and social organization : essays in memory of Elisha Pazner , 1985 .

[34]  K. Basu Determinateness of the Utility Function: Revisiting a Controversy of the Thirties , 1982 .

[35]  M. Allais,et al.  The So-Called Allais Paradox and Rational Decisions under Uncertainty , 1979 .

[36]  J. Simon Interpersonal Welfare Comparisons Can be Made-and Used for Redistribution Decisions , 1974 .

[37]  W. Wilson Correlates of avowed happiness. , 1967, Psychological bulletin.

[38]  Y. Ng Beyond pareto optimality: The necessity of interpersonal cardinal utilities in distributional judgements and social choice , 1982 .

[39]  Amartya Sen,et al.  Informational bases of alternative welfare approaches: Aggregation and income distribution , 1974 .

[40]  Wilhelm Krelle,et al.  Präferenz- und Entscheidungstheorie , 1968 .

[41]  M. Allais Le comportement de l'homme rationnel devant le risque : critique des postulats et axiomes de l'ecole americaine , 1953 .

[42]  Arie Kapteyn,et al.  Empirical comparison of the shape of welfare functions , 1981 .

[43]  Richard de Neufville,et al.  Empirical Demonstration that Expected Utility Decision Analysis is Not Operational , 1983 .

[44]  P. Rappoport Reply to Professor Hennipman , 1988 .

[45]  R. Tollison,et al.  The utilitarian contract: A generalization of Rawls' theory of justice , 1974 .

[46]  A. Gabor,et al.  On Measuring Utility , 1979 .

[47]  Georges Bernard On utility functions. The present state , 1984 .

[48]  E. Kauder History of Marginal Utility Theory , 1965 .

[49]  B. D. Finetti A Short Confirmation of my Standpoint , 1979 .

[50]  Clyde H. Coombs,et al.  Tests of the betweenness property of expected utility , 1976 .

[51]  Y. Ng Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions , 1975 .

[52]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[53]  H. Jevons An Economist's View , 1932 .

[54]  John S. Chipman,et al.  Preferences, Utility, and Demand. , 1972 .

[55]  M. Allais The Foundations of the Theory of Utility and Risk Some Central Points of The Discussions at the Oslo Conference , 1984 .

[56]  Amartya Sen SOCIAL WELFARE FUNCTIONS , 1970 .

[57]  D. Ellsberg Classic and Current Notions of “Measurable Utility” , 1954 .

[58]  P. Suppes,et al.  An Axiomatization of Utility Based on the Notion of Utility Differences , 1955 .

[59]  H. Sinn Psychophysical laws in risk theory , 1985 .

[60]  J. Harsanyi Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility , 1955 .

[61]  I. Pearce An Exact Method of Consumer Demand Analysis , 1961 .

[62]  B. Ratchford The individual welfare function: A comment , 1985 .

[63]  William Vickrey,et al.  Utility, Strategy, and Social Decision Rules , 1960 .

[64]  W. Mitchell Bentham's Felicific Calculus , 1918 .

[65]  Tapas Majumdar Behaviourist Cardinalism in Utility Theory , 1958 .

[66]  The Determinateness of the Utility Function , 1934 .

[67]  A. Lerner Marginal Cost Pricing in the 1930's , 1977 .

[68]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[69]  M. Friedman,et al.  Capitalism and Freedom , 1963 .

[70]  Amartya Sen,et al.  The Standard of Living. , 1988 .

[71]  Yew-Kwang Ng,et al.  Expected subjective utility: Is the Neumann-Morgenstern utility the same as the Neoclassical's? , 1984 .

[72]  G. Ekman,et al.  Is the Power Law a Special Case of Fechner's Law? , 1964, Perceptual and motor skills.

[73]  Peter P. Wakker,et al.  Cardinal coordinate independence for expected utility , 1984 .

[74]  W. E. Armstrong UTILITY AND THE THEORY OF WELFARE , 1951 .

[75]  The End of Marginal Utility: A Note on Dr. Bernardelli's Article , 1939 .

[76]  J. Rothenberg MARGINAL PREFERENCE AND THE THEORY OF WELFARE , 1953 .

[77]  V. Pareto Manuel D'Economie Politique , 1988 .

[78]  Jeannine Buyze,et al.  The estimation of welfare levels of a cardinal utility function , 1982 .

[79]  The End of the Marginal Utility Theory , 1938 .

[80]  W. G. Mellon,et al.  Priority ratings in more than one dimension , 1960 .

[81]  W. E. Armstrong,et al.  The Measurement of Utility , 1958 .

[82]  L. J. Savage,et al.  The Expected-Utility Hypothesis and the Measurability of Utility , 1952, Journal of Political Economy.

[83]  Yew-Kwang Ng,et al.  Welfare Economics: Introduction and Development of Basic Concepts , 1979 .

[84]  W. Vickrey Measuring Marginal Utility by Reactions to Risk , 1945 .

[85]  R. Cooter,et al.  Were the Ordinalists Wrong About Welfare Economics , 1984 .

[86]  A. Camacho,et al.  On cardinal utility , 1979 .

[87]  Werner Leinfellner,et al.  Generalization of Classical Decision Theory , 1968 .

[88]  Yew-Kwang Ng,et al.  More on Social Welfare Functions: The Incompatibility of Individualism and Ordinalism , 1977 .

[89]  Paul A. Samuelson,et al.  The Numerical Representation of Ordered Classifications and the Concept of Utility , 1938 .

[90]  B. V. Praag,et al.  Individual welfare functions and consumer behavior. : A theory of rational irrationality. , 1968 .

[91]  Johann Pfanzag A general theory of measurement applications to utility , 1959 .

[92]  William J. Baumol,et al.  The Cardinal Utility Which is Ordinal , 1958 .

[93]  Jerome Rothenberg,et al.  The measurement of social welfare , 1963 .

[94]  P. Gärdenfors,et al.  Decision, Probability, and Utility , 1988 .

[95]  W. Jevons Theory of Political Economy , 1965 .

[96]  P. Samuelson,et al.  Foundations of Economic Analysis. , 1948 .

[97]  J. Milnor,et al.  AN AXIOMATIC APPROACH TO MEASURABLE UTILITY , 1953 .

[98]  Ernst Heinrich Weber Die Lehre vom Tastsinne und Gemeingefühle auf Versuche gegründet , 1851 .

[99]  Risk and Uncertainty , 1969 .

[100]  Marvin K. Opler,et al.  Reports on happiness , 1965 .

[101]  Paul A. Samuelson,et al.  Reaffirming The Existence of "Reasonable" Bergson-Samuelson Social Welfare Functions , 1977 .

[102]  Bengt Hansson,et al.  Decision, probability, and utility: Risk aversion as a problem of conjoint measurement , 1988 .

[103]  K. MacCrimmon,et al.  Utility Theory: Axioms Versus ‘Paradoxes’ , 1979 .

[104]  R. Easterlin Does Economic Growth Improve the Human Lot? Some Empirical Evidence , 1974 .

[105]  D. Scott Measurement structures and linear inequalities , 1964 .

[106]  The utilitarian criterion, finite sensibility, and the weak majority preference principle , 1985 .

[107]  André Blais,et al.  A Survey Measure of Risk Aversion , 1986 .

[108]  F. Alt Über die Meßbarkeit des Nutzens , 1936 .

[109]  Frederick Mosteller,et al.  An Experimental Measurement of Utility , 1951, Journal of Political Economy.

[110]  I. Waldner The Empirical Meaningfulness of Interpersonal Utility Comparisons , 1972 .

[111]  W. E. Armstrong Uncertainty and the Utility Function , 1948 .

[112]  W. Marx THE LAW OF DIMINISHING MARGINAL UTILITY OF INCOME AN INVESTIGATION OF ITS VALIDITY , 1949 .

[113]  Tom Wansbeek,et al.  The individual welfare function : A rejoinder , 1985 .

[114]  Mark R. McCord,et al.  Assessment response surface: Investigating utility dependence on probability , 1985 .

[115]  W. E. Armstrong CONCERNING MARGINAL UTILITY , 1955 .

[116]  Rakesh Kumar Sarin,et al.  Strength of Preference and Risky Choice , 1982, Oper. Res..

[117]  H. P. Young,et al.  Progressive taxation and the equal sacrifice principle , 1987 .

[118]  E. H. P. Brown Notes on the Determinateness of the Utility Function: I , 1934 .

[119]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[120]  P. Pattanaik Risk, Impersonality, and the Social Welfare Function , 1968, Journal of Political Economy.

[121]  K. Arrow Social Choice and Individual Values , 1951 .

[122]  Hadley Cantril,et al.  The pattern of human concerns , 1965 .

[123]  J. Harsanyi Use of Subjective Probabilities in Game Theory , 1983 .

[124]  Y. Ng Some Fundamental Issues in Social Welfare , 1985 .

[125]  Yew-Kwang Ng,et al.  The incompatibility of individualism and ordinalism , 1982, Math. Soc. Sci..

[126]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[127]  H. Sinn Economic Decisions Under Uncertainty , 1983 .

[128]  Alex Inkeles,et al.  Industrial Man: The Relation of Status to Experience, Perception, and Value , 1960, American Journal of Sociology.

[129]  P. Fishburn,et al.  Utility theory , 1980, Cognitive Choice Modeling.

[130]  C. West Churchman,et al.  Measurement: Definitions and Theories , 1960 .

[131]  J. Marschak Rational Behavior, Uncertain Prospects, and Measurable Utility (1950) , 1950 .

[132]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[133]  Jean-Yves Jaffray,et al.  Individual behavior under risk and under uncertainty: An experimental study , 1985 .

[134]  J. Harsanyi Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen , 1977 .

[135]  M. Allais Determination of Cardinal Utility According to an Intrinsic Invariant Model , 1986 .

[136]  P. Samuelson A Note on Measurement of Utility , 1937 .

[137]  Tom Wansbeek,et al.  THE INDIVIDUAL WELFARE FUNCTION - A REVIEW , 1985 .

[138]  R. Luce A PROBABILISTIC THEORY OF UTILITY , 1958 .

[139]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[140]  B. V. Praag Linking economics with psychology an economist's view , 1985 .

[141]  A Note on Measures of Utility , 1950 .

[142]  W. E. Armstrong Utility and the "Ordinalist Fallacy" , 1958 .

[143]  A. Sen Non-Linear Social Welfare Functions: A Reply to Professor Harsanyi , 1977 .

[144]  K. Basu Revealed Preference of Government , 1980 .

[145]  F. Y. Edgeworth The Pure Theory of Taxation , 1897 .

[146]  J. Mill Principles of Political Economy , 2011, Forerunners of Realizable Values Accounting in Financial Reporting.

[147]  D. Mueller Constitutional Democracy and Social Welfare , 1973 .

[148]  K. Spence,et al.  The logic of psychophysical measurement , 1944 .

[149]  A. Marshall Principles of Economics , .

[150]  N. Georgescu-Roegen The Pure Theory of Consumers Behavior , 1936 .

[151]  A. Gabor,et al.  ON MEASURING UTILITY: Preliminary Considerations , 1958 .

[152]  Ragnar Frisch,et al.  A Complete Scheme for Computing all Direct and Cross Demand Elasticities in a Model with many Factors , 1959 .

[153]  G. Debreu,et al.  Stochastic Choice and Cardinal Utility , 1958 .

[154]  Georges Bernard A discussion of the present state of utility theory (FUR II, Venice, 1984) , 1986 .

[155]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[156]  Georges Bernard On utility functions , 1974 .

[157]  A mistaken argument against the expected utility theory of rationality , 1985 .

[158]  R. G. D. Allen A Note on the Determinateness of the Utility Function , 1935 .

[159]  L. Robbins,et al.  An Essay on the Nature and Significance of Economic Science. , 1934 .

[160]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[161]  W. E. Armstrong The Determinateness of the Utility Function , 1939 .

[162]  I. Fisher,et al.  Is "Utility" the Most Suitable Term for the Concept It is Used to Denote? , 1918 .

[163]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

[164]  I. Fisher Mathematical Investigations in the Theory of Value and Prices , 1893 .

[165]  G. Debreu Topological Methods in Cardinal Utility Theory , 1959 .

[166]  Moses Abramovitz,et al.  Nations and households in economic growth : essays in honor of Moses Abramovitz , 1974 .

[167]  M. Machina Choice under Uncertainty: Problems Solved and Unsolved , 1987 .

[168]  G. Stigler The Development of Utility Theory. I , 1950, Journal of Political Economy.

[169]  S. S. Stevens Mathematics, measurement, and psychophysics. , 1951 .

[170]  A. Lerner,et al.  The Economics of Control , 1944 .

[171]  N. Bradburn The structure of psychological well-being , 1969 .

[172]  I. Little A critique of welfare economics , 1951 .

[173]  Dagobert D. Runes The Dictionary Of Philosophy , 1951 .

[174]  Moses Abramovitz Economic Growth and Its Discontents , 1973 .

[175]  Paul A. Samuelson,et al.  The Collected Scientific Papers of Paul A. Samuelson , 1970 .

[176]  Bernt P. Stigum,et al.  Foundations of utility and risk theory with applications , 1983 .

[177]  A. Camacho,et al.  Approaches to cardinal utility , 1980 .

[178]  Beyond pareto optimality! A response to Christian Seidl , 1986 .

[179]  R. Kanbur The Standard of Living : Uncertainty, Inequality and Opportunity , 1985 .

[180]  John C. Harsanyi,et al.  Bayesian Decision Theory and Utilitarian Ethics , 1978 .

[181]  A. Sandmo Ex Post Welfare Economics and the Theory of Merit Goods , 1983 .

[182]  W. Rudin Principles of mathematical analysis , 1964 .

[183]  I. Fisher,et al.  Ten economic studies in the tradition of Irving Fisher , 1967 .

[184]  A. Sen,et al.  Chapter 22 Social choice theory , 1986 .

[185]  C. Seidl Beyond pareto optimality? A comment to Yew-Kwang Ng , 1986 .

[186]  William J. Baumol,et al.  The Neumann-Morgenstern Utility Index--An Ordinalist View , 1951, Journal of Political Economy.

[187]  Mamoru Kaneko,et al.  The optimal progressive income tax : The existence and the limit tax rates , 1982, Math. Soc. Sci..

[188]  G. Antonides,et al.  Empirical testing of the expected utility model , 1984 .

[189]  P. Gärdenfors,et al.  Decision, Probability, and Utility : Selected Readings , 1988 .

[190]  A. Camacho,et al.  Cardinal Utility and Decision Making under Uncertainty , 1983 .

[191]  Emil Kauder,et al.  Genesis of the Marginal Utility Theory: From Aristotle to the End of the Eighteenth Century , 1953 .

[192]  A Rehabilitation of the Classical Theory of Marginal Utility , 1952 .

[193]  George R. Feiwel,et al.  Issues in contemporary microeconomics and welfare , 1985 .

[194]  A. Sen,et al.  Interpersonal Comparisons of Welfare , 1979 .

[195]  S. Karlin,et al.  Mathematical Methods in the Social Sciences , 1962 .

[196]  Abram Bergson,et al.  On the Concept of Social Welfare , 1954 .

[197]  A. Barten,et al.  Consumer Demand Functions under Conditions of Almost Additive Preferences , 1964 .

[198]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[199]  Introduction to part 2 , 1988 .

[200]  G. Debreu Mathematical Economics: Representation of a preference ordering by a numerical function , 1983 .