  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.
