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Testing transitivity in choice under risk

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Abstract

Recently proposed models of risky choice imply systematic violations of transitivity of preference. This study explored whether people show the predicted intransitivity of the two models proposed to account for the certainty effect in Allais paradoxes. In order to distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Results showed that few people repeated intransitive patterns. We can retain the hypothesis that all participants were transitive.

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References

  • Birnbaum M.H. (1999) Testing critical properties of decision making on the Internet. Psychological Science 10: 399–407

    Article  Google Scholar 

  • Birnbaum M.H. (2004) Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting. Organizational Behavior and Human Decision Processes 95: 40–65

    Article  Google Scholar 

  • Birnbaum M.H. (2005a) A comparison of five models that predict violations of first-order stochastic dominance in risky decision making. Journal of Risk and Uncertainty 31: 263–287

    Article  Google Scholar 

  • Birnbaum, M. H. (2005b). Testing properties of decision making models with fallible data. Working manuscript, available from M. Birnbaum.

  • Birnbaum M.H. (2005c) Three new tests of independence that differentiate models of risky decision making. Management Science 51: 1346–1358

    Article  Google Scholar 

  • Birnbaum M.H., Gutierrez R. (2007) Testing for intransitivity of preferences predicted by a lexicographic semiorder. Organizational Behavior and Human Decision Processes 104: 97–112

    Article  Google Scholar 

  • Birnbaum M.H., Patton J.N., Lott M.K. (1999) Evidence against rank-dependent utility theories: Violations of cumulative independence, interval independence, stochastic dominance, and transitivity. Organizational Behavior and Human Decision Processes 77: 44–83

    Article  Google Scholar 

  • Blavatskyy, P. (2003). Content-dependent preferences in choice under risk: Heuristic of relative probability comparisons. International Institute for Applied Systems Analysis. Interim Report 03-031, http://www.iiasa.ac.at/Publications/Documents/IR-03-031.pdf.

  • Blavatskyy P. (2006) Axiomatization of a preference for most probable winner. Theory and Decision 60: 17–33

    Article  Google Scholar 

  • Bleichrodt H., Schmidt U. (2002) A context-dependent model of the gambling effect. Management Science 48: 802–812

    Article  Google Scholar 

  • Bleichrodt, H., & Schmidt, U. (2007). Context- and reference-dependent utility. Working Paper, available from U. Schmidt.

  • Bordley R.F. (1992) An intransitive expectations-based Bayesian variant of prospect theory. Journal of Risk and Uncertainty 5: 127–144

    Article  Google Scholar 

  • Bordley R., Hazen G.B. (1991) SSB and weighted linear utility as expected utility with suspicion. Management Science 37: 396–408

    Article  Google Scholar 

  • Brandstaetter E., Gigerenzer G., Hertwig R. (2006) The priority heuristic: Choices without tradeoffs. Psychological Review 113: 409–432

    Article  Google Scholar 

  • Busemeyer J.R., Townsend J.T. (1993) Decision field theory: A dynamic cognition approach to deci- sion making. Psychological Review 100: 432–459

    Article  Google Scholar 

  • Carbone E., Hey J.D. (2000) Which error story is best?. Journal of Risk and Uncertainty 20(2): 161–176

    Article  Google Scholar 

  • Diecidue E., Schmidt U., Wakker P.P. (2004) The gambling effect reconsidered. Journal of Risk and Uncertainty 29: 241–259

    Article  Google Scholar 

  • Edwards W. (1954) The theory of decision making. Psychological Bulletin 51: 380–417

    Article  Google Scholar 

  • Fishburn P.C. (1980) A simple model for the utility of gambling. Psychometrika 45: 435–448

    Article  Google Scholar 

  • Fishburn P.C. (1982) Nontransitive measurable utility. Journal of Mathematical Psychology 26: 31–67

    Article  Google Scholar 

  • Fishburn P.C. (1991) Nontransitive preferences in decision theory. Journal of Risk and Uncertainty 4: 113–134

    Article  Google Scholar 

  • Fishburn P. (1992) Nontransitive preferences and normative decision theory. In: Geweke J. (eds) Decision making under risk and uncertainty: New models and empirical findings. Kluwer, Dordrecht, pp 3–10

    Google Scholar 

  • Harless D.W., Camerer C.F. (1994) The predictive utility of generalized expected utility theories. Econometrica 62: 1251–1290

    Article  Google Scholar 

  • Hey J.D. (2005). Comparing theories: What are we looking for?. In: Schmidt U., Traub S. (eds). Advances in public economics: Utility, choice, and welfare: A Festschrift for Christian Seidl. Dordrecht, The Netherlands: Springer, pp. 213–234

  • Hey J.D., Orme C. (1994) Investigating generalizations of expected utility theory using experi- mental data. Econometrica 62: 1291–1326

    Article  Google Scholar 

  • Humphrey S.J. (2001) Non-transitive choice: Event-splitting effects or framing effects?. Economica 68: 77–96

    Article  Google Scholar 

  • Iverson G., Falmagne J.-C. (1985) Statistical issues in measurement. Mathematical Social Sciences 10: 131–153

    Article  Google Scholar 

  • Iverson, G. J., Myung, J. I., & Karabatsos, G. (2006). Intransitivity of preference: Revisited. Working Paper, available from Geoffrey J. Iverson, Institute for Mathematical Behavioral Sciences, UCI, Irvine, CA 92697, USA.

  • Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291

    Article  Google Scholar 

  • Leland J.W. (1994) Generalized similarity judgments: An alternative explanation for choice anomalies. Journal of Risk and Uncertainty 9: 151–172

    Article  Google Scholar 

  • Loomes G., Starmer C., Sugden R. (1989) Preference reversal: information-processing effect or rational non-transitive choice?. Economic Journal 99: 140–151

    Article  Google Scholar 

  • Loomes G., Starmer C., Sugden R. (1991) Observing violations of transitivity by experimental methods. Econometrica 59: 425–440

    Article  Google Scholar 

  • Loomes G., Sugden R. (1982) Regret theory: An alternative theory of rational choice under uncertainty. Economic Journal 92: 805–824

    Article  Google Scholar 

  • Loomes G., Taylor C. (1992) Non-transitive preferences over gains and losses. The Economic Journal 102: 357–365

    Article  Google Scholar 

  • Luce R.D. (1994) Thurstone and sensory scaling: Then and now. Psychological Review 101: 271–277

    Article  Google Scholar 

  • Luce R.D. (2000) Utility of gains and losses: Measurement-theoretical and experimental approaches. Lawrence Erlbaum Associates, Mahwah, NJ

    Google Scholar 

  • Markowitz H. (1952) The utility of wealth. Journal of Political Economy 60: 151–158

    Article  Google Scholar 

  • Marley A.A.J., Luce R.D. (2005) Independence properties vis-à-vis several utility representations. Theory and Decision 58: 77–143

    Article  Google Scholar 

  • Regenwetter, M., & Stober, C. (2006). Testing transitivity by testing the triangle inequality instead of weak stochastic transitivity. Edwards Bayesian Research Conference, Fullerton, CA, January, 2006.

  • Schmidt U. (1998) A measurement of the certainty effect. Journal of Mathematical Psychology 42: 32–47

    Article  Google Scholar 

  • Sopher B., Gigliotti G. (1993) Intransitive cycles: Rational Choice or random error? An answer based on estimation of error rates with experimental data. Theory and Decision 35: 311–336

    Article  Google Scholar 

  • Starmer C. (1999) Cycling with rules of thumb: An experimental test for a new form of non-transitive behaviour. Theory and Decision 46: 141–158

    Article  Google Scholar 

  • Starmer C. (2000) Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. Journal of Economic Literature 38: 332–382

    Google Scholar 

  • Starmer C., Sugden R. (1998) Testing alternative explanations of cyclical choices. Economica 65: 347–361

    Article  Google Scholar 

  • Stevenson M.K., Busemeyer J.R., Naylor J.C. (1991). Judgment and decision-making theory. In: Dunnette M., Hough L.M. (eds). New handbook of industrial-organizational psychology. Palo Alto CA, Consulting Psychologist Press, pp. 283–374

  • Sugden R. (2003) Reference-dependent subjective expected utility. Journal of Economic Theory 111: 172–191

    Article  Google Scholar 

  • Thurstone L.L. (1927) A law of comparative judgment. Psychological Review 34: 273–286 (Reprinted in 1994, 101, 266–270)

    Article  Google Scholar 

  • Tversky A. (1969) Intransitivity of preferences. Psychological Review 76: 31–48

    Article  Google Scholar 

  • Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323

    Article  Google Scholar 

  • Viscusi W.K. (1989) Prospective reference theory: Toward an explanation of the paradoxes. Journal of Risk and Uncertainty 2: 235–264

    Article  Google Scholar 

  • Wu G., Zhang J., Gonzalez R. (2004) Decision under risk. In: Koehler D., Harvey N. (eds) Blackwell handbook of judgment and decision making. Oxford University Press, Oxford, pp 399–423

    Chapter  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Psychology, California State University, Fullerton, USA

    Michael H. Birnbaum

  2. Department of Economics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Ulrich Schmidt

  3. Kiel Institute for the World Economy, Kiel, Germany

    Ulrich Schmidt

Authors
  1. Michael H. Birnbaum
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  2. Ulrich Schmidt
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Correspondence to Ulrich Schmidt.

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Birnbaum, M.H., Schmidt, U. Testing transitivity in choice under risk. Theory Decis 69, 599–614 (2010). https://doi.org/10.1007/s11238-009-9147-1

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  • DOI: https://doi.org/10.1007/s11238-009-9147-1

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