1 Introduction

Much of the research on biases has focused on choices about risks to oneself, called here “risky choice”. These are biases of risk aversion and seeking. In contrast, this study focuses on choices about risks to a group of others, called “distributional choices”. These are biases of inequality aversion or fairness. Choices about risk and inequality may be directly linked. If so, they may share some of the same biases, and may even share psychological mechanisms like heuristics.

In philosophy, risky and distributional choices have a strong connection that results from a method for trying to make objective decisions about inequality and fairness. Harsanyi and Rawls each suggested imagining that one could be randomly reassigned to be any member of society, from poorest to wealthiest (Reference HarsanyiHarsanyi, 1955; Reference RawlsRawls, 1957). They proposed that the choices one would make from this perspective, Rawls’ “original position”, would be objectively fair. In this thought experiment, it turns out that choices about inequality and risk are also literally the same. For example, “2% of society lives in poverty” is a statement about inequality. “You have a 2% chance of being assigned to living in poverty” is a statement about risk. In this scenario, those two statements are equivalent. This principle of an “assignment gamble”—or “veil of ignorance”, as Rawls calls it—is applicable whether we are discussing income in large societies or who will get the largest piece of cake.

In general, for a decision maker in the original position and behind the veil of ignorance, percentages regarding distributions in the group are equivalent to probabilities of outcomes in the assignment gamble. Rawls argued that it is most rational to be highly risk averse when deciding from the original position, given the huge stakes, and he proposed a “maximin” decision rule for justice (maximizing the interests of the least well off), which he called the “difference principle” (Reference RawlsRawls, 1971). In recommending this type of high risk aversion as part of fairness, he was also advocating for high inequality aversion and reducing the distribution of outcomes in society (from the bottom up). Harsanyi, on the other hand, advocated for individuals to make choices about fairness the same way he believed they should about risk, based upon their expected utility using a von Neumann-Morgenstern utility function (Reference HarsanyiHarsanyi, 1975). With this debate began the literature on exactly which decision rules, preferences, and utility functions individuals should exhibit when making distributional choices.

Economists have also explored the link between distributional and risk preferences with quantitative methods. Economic theorists have established, at least in the mathematics of utility functions, that having more risk aversion results in more inequality aversion (Reference VickreyVickrey, 1945), and that the reverse is also true, more inequality aversion results in more risk aversion (Reference ChambersChambers, 2012). Consistent with this theory, empirical studies have found that the degrees to which individuals are risk averse is correlated with their degrees of inequality aversion (Reference Ferrer-i-Carbonell and RamosFerrer-i-Carbonell & Ramos, 2010; Reference Carlsson, Daruvala and Johansson-StenmanCarlsson, Daruvala & Johansson-Stenman, 2005).

But the mathematics of utility functions and cross-sectional correlations of large groups do not reveal much about psychology and decision processes. Not all behavior follows the dictums of economic calculus, and population correlations could be picking up personality trait differences or any number of other attributes. It remains to be established whether the actual decision processes for choices about risk and inequality are similar and what the consequences of this may be. If the same psychological biases appear in both types of decisions, it could serve as evidence of a connection at the decision process level. This follows the established practice of evoking inconsistencies in judgments that should appear only if a decision maker is using some heuristic (Reference Messick, Mellers and BaronMessick, 1993).

In most of the instances in which “heuristics” for distributional choice have been explored, authors have discussed moral commitments that serve as decision rules, rather than “rules of thumb” or “time saving approximations”, as the term “heuristic” has traditionally meant (Reference Baron, Mellers and BaronBaron, 1993). An example of this is the “equality heuristic”, which proposes that the desire for equal outcomes is a durable guidepost across a variety of distributional choice settings and problems (Reference Harris and JoyceHarris & Joyce, 1980; Reference Messick, Mellers and BaronMessick, 1993). Evidence has found the commitment to favor equality (the “equality heuristic”) even in situations where what is equal can have different meanings shaped by context and framing (Reference Bar-Hillel, Yaari, Mellers and BaronBar-Hillel, 1993). A similar result has been found in negotiation settings where this commitment to equality has been referred to as a “reference point”, which is also a recognized heuristic tool (Reference Loewenstein, Thompson and BazermanLoewenstein et al., 1989; Reference Hoffman and SpitzerHoffman & Spitzer, 1985). So, while there is literature on heuristics in distributional choice decisions, so far they are largely different from the heuristics discussed in the literature on risky decision making.

One of the closest findings on a shared heuristic and bias is with the “identifiable victim effect” (Reference Jenni and LoewensteinJenni & Loewenstein, 1997) and related “psychic numbing” effect (Reference SlovicSlovic, 2007): the plight of a specific individual is more concerning than statistics about many similar victims. This appears to be a potential example of the “availability heuristic” and “availability bias”. To see this, consider the risky choice experiment of Johnson et al. (1993) on availability, where the authors found that people were willing to pay more for insurance on their plane crashing due to terrorism than for a general insurance policy covering any form of disaster in their flight. Just as the crash due to terrorism is but a subpart of all plane disasters, so is the one starving child but a subpart of the starvation reflected in a statistic. The paradox in Johnson et al. is that one should not be more concerned about the risk of a terrorist plane crash than all possible forms of crash. Likewise, one should not be more concerned about one starving child than all the starving children. In both cases though, the availability and vividness of the identifiable risk or victim elicits even more concern than the non-specific group of all such risks or victims. This is usually called the “availability heuristic”, when referring to probability and risk choices (Reference Tversky and KahnemanTversky & Kahneman, 1973), and the labels “identifiable victim effect” and “psychic numbing” may be essentially describing a manifestation of the same heuristic in a different context.

Considering the proposition that probabilities in risky choices may be like percentages of people in distributional choices, per the “veil of ignorance” thought experiment, there are several other well-studied biases of risky choice worth examining in the context of distributional choices. That is the focus of this paper.

One bias to be examined is demonstrated in the Allais paradox (Reference AllaisAllais, 1953), a violation of Savage’s (1954) “sure thing principle”, which holds that choices should not be affected by consequences that occur in some state of the world regardless of the option chosen. In the distributional analogy, choices should not be affected by a consequence that affects some group of people regardless of the option chosen.

Another is the “certainty effect”: the anomaly that people “underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty” (Reference Ferrer-i-Carbonell and RamosKahneman & Tversky, 1979). The certainty effect is one explanation of the Allais Paradox. One illustration of the certainty effect involves the “isolation effect” (Reference Ferrer-i-Carbonell and RamosKahneman & Tversky, 1979), in which a gamble is presented in two stages. A common consequence is ignored when it is determined in the first stage, thus isolating the second stage and thus creating apparent certainty for one option in that stage. If risky and distributional choices are similar enough that these biases carry over, the isolation effect should mean that decision-makers will disregard individuals whose outcomes do not depend on the choice, when these are identified in the first stage, and focus only on those whose outcomes vary across choices. The certainly effect suggests that people might highly prefer perfect equality, relative to outcomes that contain merely a small degree of inequality. The small chance of getting a bad outcome in a gamble would translate into a small group or individual being singled out in the distribution to receive a bad outcome. A finding along these lines was reported in Ubel et al. (2001), who found that people would rather offer a less effective screening test to 100% of a Medicaid population than a more effective test to 50% of the population.

Another paradox of risky choice that may apply to distributional fairness is the “peanuts effect”, referring to the observation that the usual risk aversion actually turns into risk seeking as prospective rewards become very low (Weber & Chapman, 2003; Reference MarkowitzMarkowitz, 1952). While it is not impossible to reconcile the peanuts effect with Expected Utility Theory under some utility functions, the experimental results are at least inconsistent with the way risk aversion is traditionally modeled. Usually the assumption of declining marginal utility would mean that risk aversion would be highest in the domain of low amounts of money and diminish as the money goes up; and declining marginal utility, in fact, has been found to apply in other distributional choice experiments (e.g., Reference Greene and BaronGreene & Baron, 2001). However, if the peanuts effect applies to distributional fairness, inequality aversion would also flip direction and become inequality seeking as prospective rewards become very low, just as risk aversion does.