Studies that have tested economic agents' personal theories about distributive justice yield confusing results.
Notions of equity, fairness, status, and "other departures from self-interest" (Matthew Rabin's phrase) play an integral role in how choices in games and various scenarios. It is clear that 'dominant strategies' and 'best-response solutions' to game theoretic problems which involve making "the rational choice" are rarely solved in the way economists would solve them. Even when there are supposed to be clear utility-maximizing solutions to these problems, the utility-maximizing or Pareto-improving solution is not chosen and sometimes not even noticed. Yet these heuristics that economists use, like optimizing outcomes and maximizing profit or utility, are fundamental to the notion of rational public policy decisions and public choice theory.
In the Vitamin F study done by Yaari and Bar-Hillel, for example, the players are told that that one player gets substantially more utility from the Vitamin F in grapefruits another player who gets the same utility from the Vitamin F in avocados as he does from grapefruits. They're asked to divide up the twelve grapefruits and avocados accordingly. Yaari and Bar-Hillel's work demonstrates that decision-makers disproportionately choose outcomes which do not maximize the social utility in this framework but instead distribute foodstuffs equitably or evenly among the players. This should make no sense from a neoclassical perspective. It should be counterintuitive and even "irrational".
These studies tell us something about "behavioral distributive justice", if we can label it that. They show, in non-trivial ways, that decision-making is essentially not neoclassical. It is not Marshallian, or at least not naively so. The standard Marshallian marginal utility model, with all its imperfections (the axes being upside down etc.), does not specify what is "rational" to value, only that it is rational to value utility-maximizing equilibria. What has been pumped into this notion of rationality is today a very simplified, orderly, systematizing, neoclassical set of values. Yet those values contradict most of the data that has sought to describe the values of economic decision-makers, whom, to increase the authority of the generality here, come from different cultural backgrounds and socioeconomic statuses. Their values are typically more closely linked to frameworks that involve social concerns and fairness.
Ancillary conclusions about what institutions and economic policies are necessary will likely not be drawn from these studies, but it ought to be open to criticism whether these ancillary conclusions should be drawn. If rationality is in fact something more like "fairness", why use microeconomic models that do not capture this? Perhaps no ancillary conclusions can be drawn in the first place. Decision-makers are, after all, put in the position of a benevolent dictator. All other variables like rent-seeking opportunities are ruled out. There are serious limitations and few policy insights that can be gleaned from this data.
Yet the most basic conclusion that Vitamin F should suggest is that utility-maximizing paradigms simply do not accurately describe what most economic actors think is "rational", and in that regard microeconomics is still unabashedly autistic. One way economists have interpreted the data is to say that the participants in these studies are simply not well-versed in the study of economics enough to make these decisions, making economists into some kind of vanguard group.
However, this seems highly undemocratic and paternalistic, something American economists are not supposed to do. The profession is constantly striving toward being a "positive" science instead of a "normative" calculus. Yet since these models do not include the "positive" results of scientific study, it makes economic modeling and methodology into a series of normative claims. All the models of economic theory and the solutions economists provide, then, would be nothing more than theories about what economic agents "should" do if they wanted act in a certain way, the way economists are telling them they should act. It reduces everything that was once thought to be "positive" and unbiased into a series of moral imperatives coming from a distinct methodologically individualist and utilitarian perspective, but hardly scientific.