Majority rule is at once the simplest of institutions and one of humankind's most remarkable inventions. Asking that the few give way to the many is, after all, a simple idea. The remarkable invention is the use of majority voting as the central mechanism in the formation of selftransforming institutions - systems of rules capable of turning themselves into new systems over time, in light of changing conditions and changing beliefs. Following the convenient terminology of H. L. A. Hart (1961) we may call the ordinary rules by which institutions regulate human conduct primary, and the rules by which these primary rules themselves are regulated secondary. It is the integration of primary and secondary rules that institutionalizes self-transformation and, in turn, opens up the high ideals of democracy and freedom. Majority rule is the simplest and most celebrated of secondary rules and this chapter explores the grounds for its celebrity.

Let us distinguish two broad levels of analysis. First, the level of abstract binary choice. Given two abstract options (JC, V), choosexPy, yPx, or xly as the collective decision from the pair. This is the level at which majority rule's elegance is most visible, and the level at which axiomatic justification flourishes. A second level of analysis concerns the general choice problem of forming a collective judgment among m objects, such as (x, y, z). Here, the object is to begin with n individual preferences in the form xRiyRitz, where R denotes preference P or indifference I over the m objects.