Modeling fairness judgments of splits between multiple parties

Fair divisions are a fundamental problem for moral cognition. Past experimental work has provided evidence in support of three principles of fairness in divisions between two parties: proportional splits, equal splits, and splits that equalize net gains (the Nash bargaining solution). When the number of parties increases, so does the complexity of such decisions, potentially influencing people’s cognitive strategies and their reliance on precise explicit heuristics vs intuitive approximations. We design a novel task in which participants can easily and intuitively sample and select among various distributions of resources between multiple people (2 to 18) by adjusting a continuous slider that updates divisions in real time. In two preregistered experiments (n = 378; 2,268 choices), we quantitatively model participants’ fairness judgments at the individual level. We find that participants can be categorized into three main groups. Overall, around 50% are best fitted by proportionality, 40% by the Nash bargaining solution, and fewer than 10% by equality. At the aggregate level, proportionality and the Nash bargaining solution perform best. Fairness judgments remain stable as the number of involved parties increases. When they only have access to the slider (Experiment 1), participants best fitted by the Nash bargaining solution seem to intuitively approximate it, but in an imprecise way. By contrast, they tend to precisely select it when three buttons (one for each model, Experiment 2) are available to automatically adjust the slider. These results suggest that a substantial proportion of participants rely on intuitive approximations for the Nash bargaining solution, consistent with bargaining-based (contractualist) theories of fairness.