Agents care not only about the outcomes of collective decisions but also about how decisions are made. In many cases, both the outcome and the procedure affect whether agents see a decision as legitimate, justifiable, or acceptable. We propose a novel model for collective decisions that takes into account both the preferences of the agents and their higher order concerns about the process of preference aggregation. To this end we (1) propose natural, plausible preference structures and establish key properties thereof, (2) develop mechanisms for aggregating these preferences to maximize the acceptability of decisions, and (3) characterize the performance of our acceptance-maximizing mechanisms. We apply our general approach to the specific setting of dichotomous choice, and compare the worst-case rates of acceptance achievable among populations of agents of different types. We also show in the special case of rule selection, i.e., amendment procedures, the method proposed by Abramowitz, Shapiro, and Talmon (2021) achieves universal acceptance with certain agent types.

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