Loss aversion or mistakes?

Super-neat paper coming out in the AER by Ryan Oprea: Decisions under risk are decisions under complexity. 

The abstract:

We provide evidence that classic lottery anomalies like probability weighting and loss aversion are not special phenomena of risk. They also arise (and often with equal strength) when subjects evaluate deterministic, positive monetary payments that have been disaggregated to resemble lotteries. Thus, we find, e.g., apparent probability weighting in settings without probabilities and loss aversion in settings without scope for loss. Across subjects, anomalies in these deterministic tasks strongly predicts the same anomalies in lotteries. These findings suggest that much of the behavior motivating our most important behavioral theories of risk derive from complexity-driven mistakes rather than true risk preferences.

There are piles of experiments showing what seem to be anomalies from rational choice; behavioural economists lump these into categories like loss aversion. 

But experiments testing for these things require participants to make complicated choices. That complexity can matter.

Oprea sets experiments where people are faced with risky choices, and equally complicated variants of the choices where there is no risk. People have to compute expected value in both cases, and not everybody is good at that on the fly in the lab. In the deterministic treatment, people get the expected value of the choice with certainty. In the risky treatment, they only get it probabilistically. But the computational complexity is the same across treatments.

While the literature interprets the resulting valuations of lotteries as certainty equivalents –

the certain dollar payments subjects value equivalently to risky lotteries – the same interpretation cannot be applied to mirrors which contain no uncertainty. Instead values for mirrors are simplicity equivalents: the simply-described payment amount subjects value equivalently to the more complexly described (but no less certain) mirror. Our question throughout the paper is whether simplicity equivalents have the same properties and suffer the same anomalies as certainty equivalents.

To the degree the classical pattern is indeed driven by risk preferences (i.e. tastes for risk

that cause valuations to deviate from expected value), it should disappear when we remove risk from lotteries in our Mirror treatment. Because mirrors pay expected value with certainty, they effectively induce risk neutral EUT preferences in subjects, making any valuations that depart from expected value dominated mistakes under any rational theory of subjects’ own native preferences. Thus, to the degree this distinctive pattern continues to arise in the absence of risk, we have evidence for an alternative interpretation of the classical pattern: that it is a pattern of systematic mistakes, arising not because lotteries are risky, per se, but rather because they are complex (costly or difficult to properly value).5

Oprea then finds that situations without risk generate the same kinds of patterns that people have interpreted as loss aversion in risky contexts. 

What predicts errors that look like loss aversion etc?

Finally, we collected a number of additional pieces of data in our main experiment that we correlate with the severity of the classical pattern in lotteries and mirrors (see Supplemental Appendix A.5 for details), giving us some insight into the behaviors that drive the classical pattern. For instance, we find that (i) fast decision-making, (ii) noisy, inconsistent choices in repeated instances of the same task and (iii) poor performance on cognitive reflection tasks administered post-experiment are all positively correlated with the severity of the classical pattern. We also asked subjects after the experiment (iv) how likely they believed it was that they made suboptimal choices (measuring “cognitive uncertainty,” a’la Enke & Graeber (2023)), (v) how imprecise they thought their decision-making process was (on a 100-point Likert scale) and (vi) how little attention subjects believe they themselves paid to payoffs and proportions in the descriptions of mirrors (again, using a 100-point Likert scale), and found that all of these were significantly correlated with the pattern too. These results therefore link the classical pattern in both lotteries and mirrors to hasty, noisy, imprecise and inattentive decision-making and suggest that subjects were largely aware that they were making imperfect decisions in these valuations (i.e. in important respects they know they are heuristically valuing these objects). Importantly, this is virtually identically true in lotteries and mirrors: we find highly consistent correlations between the classical pattern and all of these measures in the two settings, reinforcing our conclusion that the pattern is driven by the same behavioral mechanism in lotteries and mirrors.

Putting these strands of evidence together, the twin appearance of the classical pattern in lotteries and mirrors suggests that it represents a response not to risk but rather to the complexity of valuation. Perhaps surprisingly, this complexity does not seem to be primarily rooted in the arithmetic required in valuation, but in other cognitively taxing aspects of the task. For instance simply thinking through how one’s preferences connect to the primitives of lotteries and mirrors and articulating the implications for behavior plausibly requires significant mental effort, even if one has little diffculty with the math once the problem is “set up.” We speculate that subjects make a kind of “extensive margin” choice when deciding how to approach valuation tasks like these, deciding first whether to (i) do a precise, careful job of evaluation, or instead to (ii) casually or informally approximate value using heuristic methods. Following approach (i) requires more mental effort, strain and time than approach (ii), leading many subjects to pursue approach (ii) instead. Auxiliary evidence from Supplemental Appendix A.5 seems consistent with this account, since this evidence shows that features of behavior that we would expect to accompany casual or informal valuation procedures (e.g., hasty, inconsistent, imprecise inattentive and error-prone choices) are highly predictive of the severity of the classical pattern.

Just a super important result. And the kind of test that when it's pointed out, you have to wonder why nobody had tried it before. Great stuff.