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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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.
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.
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.
See Blavatskyy (2009) for a formal model focused on those findings.
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.
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.
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.
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.
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.
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).
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.
We used 18 of the lottery pairs from Experiment 1, excluding the two pairs which contained stochastically dominated lotteries.
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.
The difference between decision times in treatments Rank-Framed and BDM2 missed significance, z = −1.596, p = 0.111.
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.
We consider the framing “indirect” because, contrary to the tasks in Experiment 1 or Treatment BDM2, participants did not actually write down prices.
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.
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).
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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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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
- Preference reversals
- Decision times
- Imprecise preferences
- Compatibility hypothesis