The Logic of Democracy: Reconciling Equality, Deliberation, and Minority Protection. By Anthony McGann. Ann Arbor: University of Michigan Press, 2006. 256p. $65.00 cloth, $26.95 paper.

Deliberation, Social Choice, and Absolutist Democracy. By David van Mill. New York: Routledge, 2006. 200p. $110.00.

Social choice theory examines group decision making from axiomatic and mathematical perspectives. It often produces results that have troubling implications for democracy. Consider Kenneth Arrow's general possibility theorem (see Social Choice and Individual Values, [1951] 1963). It shows that no social welfare function can simultaneously satisfy several apparently reasonable postulates involving rationality and ethical norms. When this theorem is applied to the study of politics, it challenges the legitimacy of all collective decision-making procedures. No voting system can guarantee rational social preference orderings through ethical means when there are more than two voters and more than two alternatives in the choice set. Majority rule, for example, has been subject to criticism because it cannot ensure rational outcomes. Rationality, in this case, is defined in terms of transitivity. When majority rule fails to produce transitive collective preference orderings—a condition that is commonly called cycling—the outcomes may be interpreted as arbitrary or incoherent.