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Preference reversals: Time and again

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Abstract

This paper sheds new light on the preference reversal phenomenon by analyzing decision times in the choice task. In a first experiment, we replicated the standard reversal pattern and found that choices associated with reversals take significantly longer than non-reversals, and non-reversal choices take longer whenever long-shot lotteries are selected. These results can be explained by a combination of noisy lottery evaluations (imprecise preferences) and an overpricing phenomenon associated with the compatibility hypothesis. The first cause explains the existence of reversals, while the second explains the predominance of a particular type thereof. A second experiment showed that the overpricing phenomenon can be shut down, greatly reducing reversals, by using ranking-based, ordinally-framed evaluation tasks. This experiment also disentangled the two determinants of reversals, because imprecise evaluations still deliver testable predictions on decision times even in the absence of the overpricing phenomenon. Strikingly, when unframed ranking tasks were used, decision times in the choice phase were greatly reduced, even though this phase was identical across treatments. This observation is consistent with psychological insights on conflicting decision processes.

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Notes

  1. Reference dependence states that a subject’s reference point when asked for a minimum selling price is the lottery at hand. Exchanging the lottery for a certain amount of cash involves a probabilistic loss which is higher for the $-bet than for the P-bet leading to a higher stated price for the $-bet. We thank an anonymous referee for referring us to this strand of literature.

  2. The measurement of decision times is a standard tool in psychology (see, e.g., Bargh and Chartrand. 2000). To our knowledge, the first studies in economics employing them to study risky choice were those of Wilcox (1993, 1994). Decision times were also used by Moffatt (2005) relying on risky-choice data from Hey (2001). Rubinstein (2007) advocated the measurement of decision times in large-scale, web-based experiments to better understand economic decisions. Achtziger and Alós-Ferrer (2014) measured response times within a Bayesian-updating paradigm in order to study intuitive decision making in economic contexts.

  3. Since u P and u $ are i.i.d, u P −u $ and u $ −u P have the same distribution. If the distribution of u P and u $ has density v then h = (v∗v −), where v −(s) = v(−s) for all s and the symbol ∗ denotes the convolution operator.

  4. See Blavatskyy (2009) for a formal model focused on those findings.

  5. An alternative interpretation of u P and u $ is hence that they correspond to the expected monetary valuations of the lotteries, in the absence of (over)pricing biases. The second part of the assumption is for technical convenience. The analysis goes through, with more cumbersome proofs, if the error terms have bounded support.

  6. Tversky et al. (1990) used a design with additional choices between the bets and cash amounts and showed that at least part of the predicted reversals arise because of an overpricing of $-bets. Tversky et al. (1988) also proposed the prominence hypothesis, which assumes a bias in the choice stage rather than in the evaluation stage (see also Fischer et al. 1999). Cubitt et al. (2004) investigated a number of alternative hypotheses including prominence and compatibility and dismissed each of them in isolation, concluding that a combination of hypotheses would be a more reasonable explanation of their findings.

  7. In particular, the arguments in the proof of this result hold only for non-reversals. No analogous version of Proposition 3 for reversals can be established.

  8. Although this classical task has recently been shown to be affected by statistical biases (see Alós-Ferrer and Shi 2015, and the references therein), improved versions of the task have meanwhile re-established the basic effect. See e.g. Alós-Ferrer et al. (2012).

  9. Of the 20 lottery pairs, pairs 3 to 8 were such that the expected value of the P-bet was higher than the expected value of the $-bet (with a difference between €1.00 to €3.40). Pairs 9 to 14, which most closely resemble the ones commonly used in the literature, had roughly equal expected values. In pairs 15 to 20, the $-bet had a higher expected value than the P-bet (difference between €1.60 to €4.80). Finally, lottery pairs 1 and 2 were such that one bet dominated the other strictly and were only included as a basic rationality check. Only 2 out of 141 subjects chose one of the two strictly dominated lotteries in phase 2. These two lottery pairs are therefore excluded from the analysis.

  10. The tests for reversal rates include of course only the participants for which both rates can be computed. For instance, if a participant never chose a $-bet, no rate of unpredicted reversals can be computed.

  11. Four participants made only one $-bet choice yielding an unpredicted reversal in choice-price but not in price-choice, resulting in increases of 100% in the reversal rate. Including these four data points, the effect is not significant anymore (N = 71, z = −1.339, p = 0.181).

  12. Every test on decision times was conducted for the population of subjects for which the involved average decision times could be computed. For instance, if a subject did not display any unpredicted reversal, no decision time can be computed for this category.

  13. We used 18 of the lottery pairs from Experiment 1, excluding the two pairs which contained stochastically dominated lotteries.

  14. Our experimental setup does not allow distinguishing between the scale compatibility hypothesis and reference dependence (Sugden 2003; Schmidt et al. 2008; Lindsay 2013) as an explanation for the overpricing of $-bets. This is due to the fact that when asking subjects to think about their minimum selling price (be it in a pricing or a framed ranking task) both effects would be present whereas in an unframed ranking task both effects would be absent.

  15. The difference between decision times in treatments Rank-Framed and BDM2 missed significance, z = −1.596, p = 0.111.

  16. For the two ranking treatments, StatedDiff-1 and StatedDiff-3 refer to the difference in stated ranks between the two lotteries within a pair in phases 1 and 3, respectively.

  17. We consider the framing “indirect” because, contrary to the tasks in Experiment 1 or Treatment BDM2, participants did not actually write down prices.

  18. Participants were asked for the probability p making them indifferent between a given lottery and receiving a fixed, high monetary outcome X with probability p. Hence monetary outcomes remained an important part of the frame.

  19. We present this discussion after the fact for readability reasons only. For a detailed discussion of decision times and conflicting decision processes under risk and uncertainty, see Achtziger and Alós-Ferrer (2014).

  20. Such an assumption would also capture the observation that preference reappraisal and process conflict resolution in the Free-Choice Paradigm occur during the choice phase, as observed in fMRI (Jarcho et al. 2011) and response time studies (Alós-Ferrer et al. 2012).

References

  • Achtziger, A., & Alós-Ferrer, C. (2014). Fast or rational? A response-times study of Bayesian updating. Management Science, 60(4), 923–938.

    Article  Google Scholar 

  • Alós-Ferrer, C., & Shi, F. (2015). Choice-induced preference change and the free-choice paradigm: a clarification. Judgment and Decision Making, 10(1), 34–49.

    Google Scholar 

  • Alós-Ferrer, C., & Strack, F. (2014). From dual processes to multiple selves: implications for economic behavior. Journal of Economic Psychology, 41, 1–11.

    Article  Google Scholar 

  • Alós-Ferrer, C., Granić, D.G., Shi, F., & Wagner, A.K. (2012). Choices and preferences: evidence from implicit choices and response times. Journal of Experimental Social Psychology, 48(6), 1336–1342.

    Article  Google Scholar 

  • Bargh, J.A., & Chartrand, T.L. (2000). The mind in the middle: a practical guide to priming and automaticity research. In Reis, H.T., & Judd, C.M. (Eds.) Handbook of research methods in social and personality psychology (pp. 253–285). NY: Cambridge University Press.

  • Bateman, I., Day, B., Loomes, G., & Sugden, R. (2007). Can ranking techniques elicit robust values? Journal of Risk and Uncertainty, 34(1), 49–66.

    Article  Google Scholar 

  • Becker, G.M., DeGroot, M.H., & Marschak, J. (1964). Measuring utility by a single response sequential method. Behavioral Science, 9(3), 226–232.

    Article  Google Scholar 

  • Bem, D. (1967). Self-perception: an alternative interpretation of cognitive dissonance phenomena. Psychological Review, 74(3), 183–200.

    Article  Google Scholar 

  • Blavatskyy, P.R. (2009). Preference reversals and probabilistic decisions. Journal of Risk and Uncertainty, 39(3), 237–250.

    Article  Google Scholar 

  • Bleichrodt, H., & Pinto Prades, J.L. (2009). New evidence of preference reversals in health utility measurement. Health Economics, 18(6), 713–726.

    Article  Google Scholar 

  • Brehm, J.W. (1956). Postdecision changes in the desirability of alternatives. Journal of Abnormal and Social Psychology, 52(3), 384–389.

    Article  Google Scholar 

  • Butler, D.J., & Loomes, G. (2007). Imprecision as an account of the preference reversal phenomenon. The American Economic Review, 97(1), 277–297.

    Article  Google Scholar 

  • Casey, J.T. (1991). Reversal of the preference reversal phenomenon. Organizational Behavior and Human Decision Processes, 48(2), 224–251.

    Article  Google Scholar 

  • Casey, J.T. (1994). Buyers’ pricing behavior for risky alternatives: Encoding processes and preference reversals. Management Science, 40(6), 730–749.

    Article  Google Scholar 

  • Chabris, C.F., Laibson, D.I., Morris, C.L., Schuldt, J.P., & Taubinsky, D. (2009). The allocation of time in decision-making. Journal of the European Economic Association, 7(2), 682–637.

    Google Scholar 

  • Cubitt, R.P., Munro, A., & Starmer, C. (2004). Testing explanations of preference reversal. The Economic Journal, 114(497), 709–726.

    Article  Google Scholar 

  • Delquié, P. (1993). Inconsistent trade-offs between attributes: new evidence in preference assessment biases. Management Science, 39(11), 1382–1395.

    Article  Google Scholar 

  • Evans, JS.B.T. (2008). Dual-processing accounts of reasoning, judgment, and social cognition. Annual Review of Psychology, 59(1), 255–278.

    Article  Google Scholar 

  • Festinger, L. (1957). A theory of cognitive dissonance. Stanford: Stanford University Press.

    Google Scholar 

  • Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2), 171–178.

    Article  Google Scholar 

  • Fischer, G.W., Carmon, Z., Ariely, D., & Zauberman, G. (1999). Goal-based construction of preferences: task goals and the prominence effect. Management Science, 45(8), 1057–1075.

    Article  Google Scholar 

  • Goldstein, W.M., & Einhorn, H.J. (1987). Expression theory and the preference reversal phenomena. Psychological Review, 94(2), 236–254.

    Article  Google Scholar 

  • Grether, D.M., & Plott, C.R. (1979). Theory of choice and the preference reversal phenomenon. The American Economic Review, 69(4), 623–638.

    Google Scholar 

  • Hershey, J.C., & Schoemaker, P.J.H. (1985). Probability versus certainty equivalence methods in utility measurement: are they equivalent? Management Science, 31(10), 1213–1231.

    Article  Google Scholar 

  • Hey, J.D. (2001). Does repetition improve consistency? Experimental Economics, 4(1), 5–54.

    Article  Google Scholar 

  • Jarcho, J.M., Berkman, E.T., & Lieberman, M.D. (2011). The neural basis of rationalization: cognitive dissonance reduction during decision-making. Social Cognitive and Affective Neuroscience, 6(4), 460–467.

    Article  Google Scholar 

  • Johnson, E.J., & Schkade, D.A. (1989). Bias in utility assessments: further evidence and explanations. Management Science, 35(4), 406–424.

    Article  Google Scholar 

  • Lindman, H.R. (1971). Inconsistent preferences among gambles. Journal of Experimental Psychology, 89(2), 390–397.

    Article  Google Scholar 

  • Lindsay, L. (2013). The arguments of utility: preference reversals in expected utility of income models. Journal of Risk and Uncertainty, 46, 175–189.

    Article  Google Scholar 

  • Moffatt, P.G. (2005). Stochastic choice and the allocation of cognitive effort. Experimental Economics, 8(4), 369–388.

    Article  Google Scholar 

  • Oliver, A. (2013). Testing procedural invariance in the context of health. Health Economics, 22(3), 272–288.

    Article  Google Scholar 

  • Rubinstein, A. (2007). Instinctive and cognitive reasoning: a study of response times. Economic Journal, 117(523), 1243–1259.

    Article  Google Scholar 

  • Schkade, D.A., & Johnson, E.J. (1989). Cognitive processes in preference reversals. Organizational Behavior and Human Decision Processes, 44(2), 203–231.

    Article  Google Scholar 

  • Schmidt, U., & Hey, J.D. (2004). Are preference reversals errors? An experimental investigation. The Journal of Risk and Uncertainty, 29(3), 207–218.

    Article  Google Scholar 

  • Schmidt, U., Starmer, C., & Sugden, R. (2008). Third-generation prospect theory. Journal of Risk and Uncertainty, 36(3), 203–223.

    Article  Google Scholar 

  • Seidl, C. (2002). Preference reversal. Journal of Economic Surveys, 16(5), 621–655.

    Article  Google Scholar 

  • Sharot, T., De-Martino, B., & Dolan, R.J. (2009). How choice reveals and shapes expected hedonic outcome. The Journal of Neuroscience, 29(12), 3760–3765.

    Article  Google Scholar 

  • Shultz, T.R., Léveillé, E., & Lepper, M.R. (1999). Free choice and cognitive dissonance revisited: choosing “lesser evils” versus “greater goods”. Personality and Social Psychology Bulletin, 25(1), 40–48.

    Article  Google Scholar 

  • Slovic, P., & Lichtenstein, S. (1968). Relative importance of probabilities and payoffs in risk taking. Journal of Experimental Psychology Monograph, 78(3, Part 2), 1–18.

    Article  Google Scholar 

  • Stalmeier, P.F.M., Wakker, P.P., & Bezembinder, T.G.G. (1997). Preference reversals: violations of unidimensional procedure invariance. Journal of Experimental Psychology: Human Perception and Performance, 23(4), 1196–1205.

    Google Scholar 

  • Strack, F., & Deutsch, R. (2004). Reflective and impulsive determinants of social behavior. Personality and Social Psychology Review, 8(3), 220–247.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tversky, A., Sattath, S., & Slovic, P. (1988). Contingent weighting in judgment and choice. Psychological Review, 95(3), 371–384.

    Article  Google Scholar 

  • Tversky, A., Slovic, P., & Kahneman, D. (1990). The causes of preference reversal. The American Economic Review, 80(1), 204–217.

    Google Scholar 

  • Weber, E.U., & Johnson, E.J. (2009). Mindful judgment and decision making. Annual Review of Psychology, 60, 53–85.

    Article  Google Scholar 

  • Wilcox, N.T. (1993). Lottery choice: incentives, complexity, and decision time. Economic Journal, 103(421), 1397–1417.

    Article  Google Scholar 

  • Wilcox, N.T. (1994). On a lottery pricing anomaly: time tells the tale. Journal of Risk and Uncertainty, 8(7), 311–324.

    Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge helpful comments from an anonymous referee, Mónica Capra, Urs Fischbacher, Nikos Georgantzis, Werner Güth, and seminar participants at Ca’ Foscari University (Venice), Emory University (Atlanta), University of Indiana at Bloomington, University of Innsbruck, Universidad Jaume I (Castellón), the TIBER XI conference in Tilburg, the Economic Science Association 2012 conference in Cologne, and the FUR XVI conference in Rotterdam. Wagner also gratefully acknowledges financial support from the German Research Foundation (DFG) through research fellowship WA3559/1-1.

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Author notes

  1. Ðura-Georg Granić

    Present address: Erasmus School of Economics, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, Netherlands

  2. Alexander K. Wagner

    Present address: Vienna Center for Experimental Economics and Department of Economics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

Authors and Affiliations

  1. Department of Economics, University of Cologne, Albertus-Magnus Platz, 50923, Cologne, Germany

    Carlos Alós-Ferrer, Ðura-Georg Granić, Johannes Kern & Alexander K. Wagner

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  1. Carlos Alós-Ferrer
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Correspondence to Carlos Alós-Ferrer.

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Alós-Ferrer, C., Granić, ÐG., Kern, J. et al. Preference reversals: Time and again. J Risk Uncertain 52, 65–97 (2016). https://doi.org/10.1007/s11166-016-9233-z

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