Spatial models of simple-majority decision making by committees demonstrate that stable outcomes exist only under very restrictive conditions. In the unlikely event that those conditions are realized, a stable equilibrium proposal can be identified; it would be preferred by a majority to every possible alternative. That stable outcome, the multidimensional median located at the center of the preference space, would be the unique, best possible representation of the individual preferences of all committee members.

Under normal circumstances, absent the restrictive conditions, the multidimensional median does not exist as a single point but as a relatively small subset of ...