A Notion of Equilibrium and Its Possibility Under Majority Rule

TLDR

A committee must decide how to adjust multiple variables, with majority rule determining agreement, applicable to boards or public‑goods allocation. A change is adopted only if it receives majority support; otherwise the status quo persists, and if no change can gain majority, the current state is an equilibrium.

Abstract

Consider a committee that is faced with the task of deciding on how to change the magnitude of several variables. It is assumed that agreement is defined by majority rule. The decision-making body could be a board of directors attempting to decide on the magnitude of several investment projects, or a group of individuals deciding upon the allocation of a budget among several public goods. The setting makes no difference as long as the variables could conceivably be changed by any amount. If change in the variables is proposed and the change does not receive a majority vote, then the existing state of the variables remains. If no possible change in the variables could receive a majority vote, then the existing state of the variables is an equilibrium.