Combining Social Choice and Matching Theory to Understand Institutional Stability

In many organizations, members need to be assigned to certain positions, whether these are legislators to committees, executives to roles, or workers to teams. I show that these assignment problems lead to novel questions about institutional stability. Will the set of agents being assigned prefer or vote in favor of some alternative allocation over their current allocation thereby lobbying to reform the institution? I explore questions of institutional stability where the choice of the institution (i.e., the matching mechanism) is chosen and agreed upon by the very people who are assigned by the assignment procedure. I endogenize an institution's choice of assignment procedures by analyzing an important sub-case of social choice that I call a social allocation choice problem. I discuss a variety of voting rules (plurality, majority, and unanimity) and their institutional stability counterparts in matching theory (popular matching, majority stability, and pareto efficiency). The novel property of majority stability is introduced and its existence and robustness to correlated preferences and interdependent preferences are analyzed. Chains of envy are necessary to overcome the packing problem that arises in reallocating a majority to a new set of assignments under an alternative allocation. This makes majority stability, in sharp contrast to plurality rule, strikingly robust to correlated preferences.