A branch of game theory known as social-choice theory studies institutions and methods of collective decision-making. Voting in elections, for example. Social-choice theory deepened enormously from the 1950’s on after Kenneth Arrow laid down five elementary axioms that any rule defining the preferences of a group should satisfy. To widespread dismay, Arrow proved that those axioms are logically inconsistent with each other. There is no rational way to assure fairness when members seek to determine a group’s collective preference (See my post of Aug. 13, 2009: the impossibility theorem of Kenneth Arrow.).
This dispiriting truth David Deutsch explains in The Beginning of Infinity: Explanations that Transform the World (Viking 2011), Chapter 13. Deutsch, however, proposes that this no-go theorem has an out: people can create new choices. To flesh out his point would go beyond the scope of this post. Meanwhile, managers of law departments should not give up on decision-making by votes, but they should recognize that the best plans and techniques do not promise fairness.