A Notion of Equilibrium and Its Possibility Under Majority Rule

Abstract

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