Reservation of Judgment and Robust Collective Decisions

This paper studies preference aggregation under ambiguity when agents have incomplete preference relations due to imprecise beliefs. We introduce the “dual” of the Pareto principle, which respects unanimity among individuals, including those with unexpressed opinions. Our first theorem shows that, in most cases, this principle leads to a dictatorial rule in taste aggregation. We argue that this stems from the problem of spurious unanimity, even when the individuals have the same prior set. By weakening the above principle to avoid respecting spurious unanimity, the second theorem characterizes novel belief-aggregation rules, under which society does not discard any combination of plausible priors.

💡 Research Summary

The paper investigates collective decision‑making when agents face ambiguity and therefore hold incomplete preference relations, modeled by Bewley’s multi‑prior framework. Traditional aggregation theory relies on the Pareto principle, which requires that if every individual weakly prefers alternative X to Y, then society must also weakly prefer X to Y. The authors argue that this formulation ignores the informational content of “reservation of judgment” – cases where agents cannot express a preference because they lack sufficient confidence. To capture this, they introduce a dual axiom, the Pareto* principle: if no individual thinks X is weakly better than Y, then society must also not regard X as weakly better than Y.

The first main result is an impossibility theorem: even when all agents share the same set of plausible priors, any aggregation rule satisfying Pareto* inevitably becomes dictatorial. The underlying mechanism is “spurious unanimity.” Because each agent’s judgment “X is not weakly better than Y” can be based on different priors within the common set, agents may appear to agree while actually relying on opposite beliefs and tastes. Respecting such superficial consensus forces the social rule to discard some individuals’ genuine preferences, leading to a dictatorial outcome. This extends earlier work (e.g., Danan et al. 2016) which showed that the ordinary Pareto principle is compatible with non‑dictatorial aggregation only when a single prior is common to all.

Recognizing the problem, the authors propose a weakened version called the common‑taste Pareto* principle. It requires unanimity only on pairs of acts for which there is no genuine taste disagreement among agents. Under this axiom, the second theorem characterizes a novel class of belief‑aggregation rules: the social belief set must contain every convex combination of the individual prior distributions. In other words, for any selection of priors (p_i) (one from each agent’s plausible set), there must exist a social prior that is a weighted average of those (p_i). This condition is the dual of the convex‑hull requirement identified by Danan et al. (2016); whereas the latter allows the social set to omit some combinations, the new rule guarantees that no combination is discarded. Consequently, if all agents share a particular prior, that prior necessarily belongs to the social belief set, a property lacking in the earlier literature.

The paper illustrates these ideas with a two‑politician example. Both politicians share the same prior interval (