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.