Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents.

Kontek, Krzysztof (2015): Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents.

Abstract

This paper introduces a new method of estimating indifference curves in the Marschak-Machina triangle. The method involves posing questions about indifference. Contrary to previous attempts, where subjects were required to identify those lotteries to which they were indifferent vis-à-vis a given lottery, the subjects are here required to determine its certainty equivalent. The procedure is repeated for a large number of lotteries inside the triangle. Simple, linear interpolation of certainty equivalent values between adjacent points representing the lotteries under consideration allows any indifference curve inside the triangle to be plotted. The experimental results presented in the paper shed new light on the shape of indifference curves inside the Marschak-Machina triangle, where curve parallelism, fanning-out, fanning-in and boundary effects, including (possibly discontinuous) jumps, are all common. As shown, those decision-making models, which can predict jumps on the triangle legs, offer the best econometric fit of the indifference curves obtained in the study.

• Item Type: MPRA Paper
• Language: English
• Keywords: Marschak-Machina triangle, indifference curves, fanning-out, fanning-in, models of decision-making under risk, certainty equivalents, Wolfram Mathematica®
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data ; Data Access; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C88 - Other Computer Software; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

References

Abdellaoui, M., Munier, B. (1994). “The Closing-in Method: An Individual Tool to Investigate Individual Choice Patterns Under Risk” in Munier B., Machina M. J. (Eds.) “Models and experiments in risk and rationality”, Kluwer Academic Publishers.

Abdellaoui, M., Munier, B. (1998). “The Risk-structure Dependence Effect: Experimenting with an Eye to Decision-aiding”, Annals of Operations Research 80 (1998), 237-252.

Bardsley, N., Cubbit, R., Loomes, G., Moffat P., Starmer C., Sugden R. (2010). “Experimental Economics: Rethinking the Rules”. Princeton University Press.

Becker, J. L., Sarin, R. K. (1987). “Lottery Dependent Utility”. Management Science, 33(11) 1367-1382).

Birnbaum, M. H. (1997). “Violations of monotonicity in judgment and decision making”. In A. A. J. Marley (Ed.) “Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce (73-100). Mahwah, NJ: Erlbaum.

Blavatskyy, P. (2006). “Axiomatization of a Preference for Most Probable Winner”. Theory and Decision, 60: 17-33.

Camerer, Colin, (1989). “An Experimental Test of Several Generalized Utility Theories”, Journal of Risk and Uncertainty, 2: 61-104.

Carbone, E., Hey, J. D. (1994). “Estimation of Expected Utility and Non-Expected Utility Preference Functionals Using Complete Ranking Data” in Munier B., Machina M. J. (Eds.) “Models and Experiments in Risk and Rationality”, Kluwer Academic Publishers.

Cavagnaro, D., Gonzales, R., Myung, J. I., Pitt, M. A. (2013). “Optimal Decision Stimuli for Risky Choice Experiments: An Adaptive Approach”. Management Science, 59 (2), 358–375.

Chew, S. H., MacCrimmon, K. R. (1979). “Alpha-Nu Choice Theory: An Axiomatization of Expected Utility”. University of British Columbia Working Paper 669.

Chew, S. H. (1983). “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox”. Econometrica, 51(4), 1065-1092.

Chew, S. H., Waller, W. S. (1986). “Empirical Tests of Weighted Utility Theory”. Journal of Mathematical Psychology, 30, 55-72.

Cohen, M. (1992). “Security Level, Potential Level, Expected Utility: A Three Criteria Decision Model under Risk”, Theory and Decision, 33:2, 101-134.

Conlisk, John, (1989). “Three Variants on the Allais Example”, American Economic Review, vol. 79(3), 392-407.

Dekel, E. (1986). “An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom”. Journal of Economic Theory, 40, 304-318.

Fishburn, P. C. (1983). “Transitive Measurable Utility”. Journal of Economic Theory”, 31, 293-317.

Gonzales, R., Wu, G. (1999). “On the Shape of the Probability Weighting Function”. Cognitive Psychology, 38, 129-166.

Gul, F. (1991). A Theory of Disappointment Aversion”. Econometrica, 59, 667-686.

Harless, D. (1992). “Predictions about Indifference Curves Inside the Unit Triangle”. Journal of Economic Behavior and Organization, 18, 391-414.

Harless, W., Camerer, C. (1994). “The Predictive Utility of Generalized Expected Utility Theories”. Econometrica, 62(6), 1251-1289.

Hey, J. D., Strazzera E., (1989). “Estimation of Indifference Curves in the Marschak-Machina Triangle”, Journal of Behavioral Decision Making, Vol. 2. 239-260.

Hey, J., D., Di Cagno, D. (1990). “Circles and Triangles: An Experimental Estimation of Indifference Lines in the Marschak-Machina Triangle”, Journal of Behavioral Decision Making, Vol. 3, 279-306.

Hey, J. D., Orme, C. (1994). “Investigating Generalizations of Expected Utility Theory Using Experimental Data”. Econometrica, 62(6), 1291-1326.

Jia, J., Dyer, J. S., Butler, J. C. (2001). “Generalized Disappointment Models”. Journal of Risk and Uncertainty, 22(1), 59-78.

Kagel, J. H., MacDonald, D. N., Battalio R. (1990). “Tests of “Fanning out” of Indifference Curves: Results from Animal and Human Experiments”, The American Economic Review Vol. 80 (4), 912-921.

Kahneman, D., Tversky, A. (1979). “Prospect Theory: An Analysis of Decision under Risk”. Econometrica, 47(2) 263-291.

Kontek, K., Lewandowski, M. (2013). “Range-Dependent Decision Utility”. ssrn.com/abstract=2307858.

Loomes, G., Sugden, R. (1982). “Regret Theory: An Alternative Theory of Rational Choice under Uncertainty”. The Economic Journal, 92, 805-824.

MacDonald, D. N., Kagel, J. H., Battalio, R. C. (1991). Animals’ “Choices over Uncertain Outcomes: Further Experimental Results”, The Economic Journal, 101, 1067-1084.

Machina, M. (1982). “Expected Utility Analysis without the Independence Axiom”. Econometrica, 50, 277-323.

Machina, M. (1987). "Choice Under Uncertainty: Problems Solved and Unsolved", Journal of Economic Perspectives, Vol. 1, No. 1.

Marschak, J. (1950). “Rational Behavior, Uncertain Prospects, and Measurable Utility”. Econometrica, Vol. 18(2), 111-141.

Neilson, W. S. (1992). “Some mixed results on boundary effects”, Economics Letters, Vol. 39, 275-278.

Noguchi, T., Sanborn, A., Stewart N. (2013). “Non-parametric estimation of the individual’s utility map”, in M. Knauff, M. Pauen, N. Sebanz & I. Wachsmuth (Eds.), Proceedings of the thirty-fifth annual conference of the Cognitive Science Society (pp. 3145–3150). Austin, TX: Cognitive Science Society.

Quiggin, J. (1982). “A Theory of Anticipated Utility”. Journal of Economic Behavior and Organization, 3(4), 323-343.

Sopher, B., Gigliotti, G. (1993). “A Test of Generalized Expected Utility Theory”. Theory and Decision, 35, 75-106.

Tversky, A., Kahneman, D. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty”. Journal of Risk and Uncertainty, 5: 297-323.

Viscusi, K. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes”. Journal of Risk and Uncertainty, 2, 235-264.

Wu, G., Gonzales, R. (1998). “Common Consequence Conditions in Decision Making under Risk”, Journal of Risk and Uncertainty, 16: 115-139.