Bureaucracy in quest of feasibility

A bureaucracy has to determine the values of many decision variables while satisfying a set of constraints. The bureaucracy is not assumed to have any objective function beyond achieving a feasible solution, which can be viewed as “satisficing” à la Simon (1955). We assume that the variables are integer-valued and the constraints are linear. We show that simple and (arguably) natural versions of the problem are already NP-Hard. We therefore look at decentralized decisions, where each office controls but one decision variable and can determine its value as a function of its past values. However, an attempt to consult more than a single past case can lead to Condorcet-style consistency problems. We prove an Arrovian result, showing that, under certain conditions, feasibility is guaranteed only if all offices mimic their decisions in the same past case. This result can be viewed as explaining a status quo bias.