Simple majority rule is badly behaved. This is one of the earliest lessons learned by political scientists in the positive political theory tradition. Discovered and rediscovered by theorists over the centuries (including, famously, the Majorcan Franciscan monk Raymon Llull in the thirteenth century, the Marquis de Condorcet in the eighteenth, the Reverend Charles Dodgson (Lewis Carroll) in the eighteenth, and Duncan Black in the twentieth), the method of majority rule cannot be counted on to produce a rational collective choice. In many circumstances (made precise in the technical literature), it is very likely (a claim also made precise) that whatever choice is produced will suffer the property of not being “best” in the preferences of all majorities: for any candidate alternative, there will always exist another alternative that some majority prefers to it. This chapter suggests that while a collection of preferences often cannot provide a collectively “best” choice, institutional arrangements, which restrict comparisons of alternatives, may allow majority rule to function more smoothly. That is, where equilibrium induced by preferences alone may fail to exist, institutional structure may induce stability.
Dynamics of majority rule on hypergraphs
