Specific Sensitivity to Rare and Extreme Events: Quasi-Complete Black Swan Avoidance vs Partial Jackpot Seeking in Rat Decision-Making

Reviewer #1 (Public Review):

Summary:

In this manuscript, the authors investigate the impact of rare and extreme events on rodents' decision-making under risk, in gain and loss contexts. They describe the behavior of 20 rats performing a four-armed bandit task, where probabilistic gains (sugar pellets) and losses (time-out punishments) can - in some arms - incorporate extremely large - but rare - outcomes. They report that most rats are sensitive to rare and extreme outcomes despite their infrequent occurrence, and that this sensitivity is primarily driven by extreme loss events which they try to avoid, rather than extreme gains that they seek to obtain.

They finally propose a modification of standard reinforcement-learning, which features a specific sensitivity to rare and extreme outcomes and can account for the observed behavior.

Strengths:

The manuscript really taps into a surprisingly neglected but very relevant aspect of decision-making: the effect of rare and extreme events (REE). The authors have developed an experimental setup that seemingly allows investigation of this aspect, which is not trivial given the idiosyncratic properties of rare and extreme events.

The parameters of the experimental setup seem also to be well thought off: basically, in the absence of REE, some options are objectively better than others (because, in expectation, they overall deliver more food, or minimize time-out punishments), but this ordering reverses if REE are taken into account. This allows for a clean test of the integration of REE in the rodent's decision-making model.

The data is presented and analyzed in a very descriptive but exhaustive and transparent way, down to the description of individual rodent's behavior.

Weaknesses:

While the description and analyses of the behavioral patterns are rigorously done under the economic lens of risky decision-making, the authors' interpretation heavily relies on the assumption that rodents have built the correct model of the task during the training. Extensive details are provided about the training procedure, and the observed behavior at the end of the training, but it remains virtually impossible to disambiguate choices due to imperfect learning to choices made due to intrinsic preferences for risk or REE.

By nature, gains (food pellets) and losses (time-out punishments) are somewhat incommensurable so the interpretation of the asymmetry due to outcome valence is also subject to interpretation. There might be some additional subtleties due e.g. satiety that could come from gaining REE (i.e. the delivery of 80 pellets from the Jackpot).

In its current form, the paper is quite hard to digest. This is naturally the case with interdisciplinary work (here mixing economists and neurobiologists). But I am afraid that with the current frame, the paper is going to miss its target, in terms of audience.

The proposed model seems somewhat disconnected from the behavioral patterns: while the model suggests an effect of REE at the decision stage (i.e. with specific decision weights for those rare events), this formalism seems at odds with the observation that REE (notably in the loss domain) has an impact of subsequent behavior - (Black Swans tend to reinforce Total Sensitivity to REE) which rather suggests an effect at the learning stage.

Discussion:

This study convincingly demonstrates that REEs are processed rather uniquely, which makes sense given their evolutionary relevance. REE has indeed been somewhat neglected in previous research, and this study therefore opens an interesting new front on the fundamental aspects of decision under risk. The authors have devised an original theoretical and empirical framework that will be useful for the community, and the combination of economics analysis and rodent behavior constitutes a thought-provoking ground to think about the nature of risk preferences. The interpretation and mechanistic account of these aspects, as well as their generalizability outside the specific context of this study, remain to be strengthened.

Reviewer #2 (Public Review):

Summary:

This paper attempts to examine how rare, extreme events impact decision-making in rats. The paper used an extensive behavioural study with rats to evaluate how the probability and magnitude of outcomes impact preference. The paper, however, provides limited evidence for the conclusions because the design did not allow for the isolation of the rare, extreme events in choice. There are many confounding factors, including the outcome variance and presence of less-rare, and less-extreme outcomes in the same conditions.

Strengths:

(1) The major strength of the paper is the significant volume of behavioural data with a reasonable sample size of 20 rats.

(2) The paper attempts to examine losses with rats (a notoriously tricky problem with non-human animals) by substituting time-outs as a proxy for losses. This allows for mixed gambles that have both gain and loss possible outcomes.

(3) The paper integrates both a behavioural and a modelling approach to get at the factors that drive decision-making.

(4) The paper takes seriously the question of what it means for an event to be rare, pushing to less frequent outcomes than usually used with non-human animals.

Weaknesses:

(1) The primary issue with this work is that the primary experimental manipulation fails to isolate the rare, extreme events in choice. As I understand the task, in all the conditions with a rare extreme event (e.g., 80 pellets with probability epsilon), there is also a less-rare, less-extreme event (e.g., 12 pellets with probability 5). In addition, the variance differs between the two conditions. So, any impact attributable to the rare, extreme event could be due to the less rare event or due difference in the variance. The design does not support the conclusions. Finally, by deliberately confounding rarity and extremity, the design does not allow for assessing the impact of either aspect.

(2) The RL-modelling work also fails to show a specific impact of the rare extreme event. As best as I can understand Eq 2, the model provides a free parameter that adds a bonus to the value of either the two options with high-variance gains (A and V in the paper) or to the two options with high-variance losses (F and V in the paper). This parameter only depends on whether this option could have possibly yielded the rare, extreme outcome (i.e., based on the generative probability) and was not connected to its actual appearance. That makes it a free parameter that just bumps up (or down) the probability of selecting a pair of options. In the case of the "black swan" or high-variance loss conditions, this seems very much like a loss aversion parameter, but an additive one instead of a multiplicative one.

(3) The paper presented the methods and results with lots of neologisms and fairly obscure jargon (e.g., fragility, total REE sensitivity). That made it very hard to decipher exactly what was done and what was found. For example, on p. 4, the use of concave and convex was very hard to decipher; the text even has to repeat itself 3 times (i.e., "to repeat" and "in other words") and is still not clear. It would be much clearer (and probably accurate) to say that the options varied along the variance dimension, separately for gains and losses. Option A was low-variance gains and losses. Option B was low-variance losses and high-variance gains. Option C was high-variance losses and low-variance gains, and Option D was high-variance losses and gains. That tells much more clearly what the animals experienced without the reader having to master a set of new terminologies around fragility and robustness, which brings a set of theoretical assumptions unnecessarily into the description of the experimental design. In terms of results, "Black Swan" avoidance is more simply known as risk aversion for losses.

(4) Were the probabilities shuffled or truly random (seem to be fixed sequences, so neither)? What were the experienced probabilities? Given the fixed sequences, these experienced ("ex-post") probabilities, could differ tremendously from the scheduled ("ex ante") probabilities. It's quite possible that an animal never experienced the rare, extreme event for a specific option. It's even possible (if they only picked it on the 10th/60th choices by chance), that they only ever experienced that rare extreme event. This cannot be known given the information provided. The Supplemental info on p.55 only gives gross overall numbers but does not indicate what the rats experienced for each choice/option-which is what matters here. A simple table that indicates for each of the 4 options, how often they were selected, and how often the animals experienced each of the 6-8 possible outcome would make it much clearer how closely the experience matched the planned outcomes. In addition, by restricting the rare outcome to either the 10th or 60th activations in a session, these are not random. Did the animals learn this association?

(5) The choice data are only presented in an overprocessed fashion with a sum and a difference (in both figures and tables). The basic datum (probability/frequency of selecting each of the 4 options) is not provided directly, even if it can theoretically be inferred from the sum and the difference. To understand what the rats actually do, we first need to see how often they select each option, without these transformations.

(6) There is insufficient detail provided on the inferential statistical tests (e.g., no degrees of freedom or effect sizes), and only limited information on exactly what tests were run and how (bootstrapping, but little detail). Without code or data (only summary information is provided in the supplement), this is difficult to evaluate. In addition, the studies seem not to be pre-registered in any way, leaving many researchers with degrees of freedom. Were any alternative analysis pipelines attempted? Similarly, there were many sub-groupings of the animals, and then comparisons between them - were these post-hoc?

(7) On p. 17, there is an attempt to look at the impact of a rare, extreme event by plotting a measure of preference for the 10 trials before/after the rare, extreme event. In the human literature, the main impact of experiencing a rare, extreme event is what is known as the wavy recency effect (See Plonsky et al. 2015 in Psych Review for example). What this means is that there tends to be some immediate negative recency (e.g., avoiding a rare gain) followed by positive recency (e.g., chasing the rare gain). Using a 10-trial window would thus obscure any impact of this rare, extreme event. An analysis that looks at a time course trial-by-trial could reveal any impact.

(8) As I understood the method (p. 31), the assignment of options to physical locations was not random or counterbalanced, but deliberately biased to have one of the options in the preferred location. This would seem to create a bias towards a particular option and a bias away from the other options, which confounds the preference data in subsequent analyses.

(9) Are delays really losses? This is a big assumption. Magnitude and delay are different aspects of experience, which are not necessarily commensurable and can be manipulated independently. And, for the model, how were these delays transformed into outcomes for the model? Eq 1 skips over that. Is there an assumption of linearity? In addition, I was not wholly clear if the delays meant fewer trials in a session or if the delays merely extended the session and meant longer delays until the next choice period.

(10) The paper does not sufficiently accurately represent the existing literature on human risky decision-making (with and without rare events). Here are a few examples of misrepresented and/or missing literature:
-Most studies on decision-making do not only rely on p > 10% (as per p. 2). Maybe that is true with animals, but not a fair statement generally. Some do, and some don't. There is substantial literature looking at rarer events in both descriptions (most famously with Kahneman & Tversky's work), but also in experience (which is alluded to in reference 19). That reference is not only about the situation when choices are not repeated (e.g. the sampling paradigm), but also partial feedback and full-feedback situations.

The literature on learning from rewarding experiences in humans is obliquely referenced but not really incorporated. In short, there are two main findings - firstly people underweight rare events in experience; second, people overweight extreme outcomes in experience (both contrary to description). Some related papers are cited, but their content is not used or incorporated into the logic of the manuscript.

One recent study systematically examined rarity and extremity in human risky decision-making, which seems very relevant here: Mason et al. (2024). Rare and extreme outcomes in risky choice. Psychonomic Bulletin & Review, 31, 1301-1308.

There is a fair bit of research on the human perception of the risk of rare events (including from experience) and important events like climate. One notable paper is Newell et al (2015) in Nature Climate Change.