The previous chapters have assumed that society's decisions are made by simple majority rule. In the real world, many decisions really are made that way. Many other decisions, however, are made using other means of adding up or counting people's political preferences. In this chapter we consider public decisions more broadly and look at other ways of choosing. Because we are going to cover many topics quickly, it is well to begin with an intuitive overview.

One of the conventions of social choice theory is to describe each of several important results as a “paradox,” a term deriving from paradoxon, a Greek word meaning “beyond opinion or belief.” Thomas Schwartz described the role of paradox in analytical politics: “Deduce a contradiction from reasonable-looking, widely held assumptions, and you have a paradox; the better entrenched the assumptions, the more paradoxical the paradox” (1986, p. 116).

We have argued that the location of a middle within public opinion, given the voting rules of the society, is the key feature in determining both the nature of policy and its stability in a nation. But we have had trouble finding a middle in complicated policy spaces under majority rule. This difficulty suggests that majority rule decisions are susceptible to manipulation, because there is no determinate outcome in many circumstances.