What are axiomatizations good for?

Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their implications for axiomatic decision theory.

[1]  R. Carnap,et al.  Über die Aufgabe der Physik , 1923 .

[2]  J. Habermas Theory of Communicative Action , 1981 .

[3]  P. Slovic,et al.  Reversals of preference between bids and choices in gambling decisions. , 1971 .

[4]  K. Arrow Alternative Approaches to the Theory of Choice in Risk-Taking Situations , 1951 .

[5]  I. Gilboa Theory Of Decision Under Uncertainty , 2009 .

[6]  Maurice Allais,et al.  Fondements d'une Theorie Positive des Choix Comportant un Risque et Critique des Postulats et Axiomes de l'Ecole Americaine. , 1956 .

[7]  P. Fishburn,et al.  On Handa's "New Theory of Cardinal Utility" and the Maximization of Expected Return , 1978, Journal of Political Economy.

[8]  H. Simon,et al.  Models of Man. , 1957 .

[9]  Ivan Moscati,et al.  Measuring Utility: From the Marginal Revolution to Behavioral Economics. Prologue , 2018 .

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

[11]  Niels Erik Jensen,et al.  An Introduction to Bernoullian Utility Theory: II. Interpretation, Evaluation and Application; A Critical Survey , 1967 .

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

[13]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[14]  Itzhak Gilboa,et al.  Rationality of Belief , 2004 .

[15]  F. Ramsey Truth and Probability , 2016 .

[16]  F. Ramsey The Foundations of Mathematics and Other Logical Essays , 2001 .

[17]  Jonathan Barzilai,et al.  On the foundations of measurement , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[18]  Brian Hill,et al.  Representation theorems and the semantics of decision-theoretic concepts , 2015 .

[19]  H. Lindman Inconsistent preferences among gambles. , 1971 .

[20]  Itzhak Gilboa,et al.  A theory of case-based decisions , 2001 .

[21]  Amartya Sen,et al.  INTERNAL CONSISTENCY OF CHOICE , 1993 .

[22]  A. K. Basu A Theory of Decision-Making , 1973, The Journal of Sociology & Social Welfare.

[23]  Larry Samuelson,et al.  Economic Models as Analogies , 2011 .

[24]  Edi Karni,et al.  Probabilities and beliefs , 1996 .

[25]  A. Tversky,et al.  Foundations of Measurement, Vol. III: Representation, Axiomatization, and Invariance , 1990 .

[26]  I. Gilboa,et al.  IS IT ALWAYS RATIONAL TO SATISFY SAVAGE'S AXIOMS? , 2009, Economics and Philosophy.

[27]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[28]  J. Schreiber Foundations Of Statistics , 2016 .

[29]  J. Quiggin A theory of anticipated utility , 1982 .

[30]  Larry Samuelson,et al.  Economics: Between Prediction and Criticism , 2016 .

[31]  Geoffrey Brennan,et al.  An economic theory of military tactics : Methodological individualism at war , 1982 .

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

[33]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

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

[35]  A. Marshall Principles of Economics , .

[36]  C. Plott,et al.  Economic Theory of Choice and the Preference Reversal Phenomenon , 1979 .

[37]  David Schmeidleis SUBJECTIVE PROBABILITY AND EXPECTED UTILITY WITHOUT ADDITIVITY , 1989 .

[38]  Eddie Dekel,et al.  How (Not) to Do Decision Theory , 2010 .

[39]  I. Gilboa,et al.  Objective and Subjective Rationality in a Multiple Prior Model , 2010 .

[40]  Jagdish Handa,et al.  Risk, Probabilities, and a New Theory of Cardinal Utility , 1977, Journal of Political Economy.

[41]  B. Finetti Sul significato soggettivo della probabilità , 1931 .

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

[43]  Ivan Moscati Retrospectives: How Economists Came to Accept Expected Utility Theory: The Case of Samuelson and Savage , 2016 .

[44]  M. Yaari The Dual Theory of Choice under Risk , 1987 .

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

[46]  B. D. Finetti La prévision : ses lois logiques, ses sources subjectives , 1937 .

[47]  George Loewenstein,et al.  The fall and rise of psychological explanations in the economics of intertemporal choice. , 1992 .

[48]  Ghanshyam B. Mehta Existence of a continuous utility function with path monotonicity: the Wold approach , 1993 .

[49]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[50]  J. Jaffray Existence of a Continuous Utility Function: An Elementary Proof , 1975 .

[51]  Itzhak Gilboa,et al.  Rationality of belief or: why savage’s axioms are neither necessary nor sufficient for rationality , 2007, Synthese.

[52]  Carus Paul The Foundation of Mathematics. , 1920 .