Judgment aggregation: a survey

Judgment aggregation is the subject of a growing body of work in economics, political science, philosophy and related disciplines. Although the literature on judgment aggregation has been in‡uenced by earlier work in social choice theory, the recent interest in the problem was sparked by the so-called ‘doctrinal paradox’in law and economics (Kornhauser and Sager 1986). Suppose a three-member court has to reach a verdict in a breach-of-contract case. According to legal doctrine, the defendant is liable (the conclusion, here denoted c) if and only if he or she did a particular action and had a contractual obligation not to do it (the two premises, here denoted a and b). The doctrinal paradox consists in the fact that majority voting on the premises may support a di¤erent verdict from majority voting on the conclusion. As illustrated in Table 1, suppose the …rst judge holds both premises to be true; the second holds the …rst premise, but not the second, to be true; and the third holds the second premise, but not the …rst, to be true. Then a majority of judges holds each premise to be true, which seems to support a ‘liable’ verdict, and yet a majority of judges holds the conclusion to be false. Although the …rst discussions of this problem focused on the distinction between ‘premise-based’and ‘conclusion-based’methods of decision-making, the doctrinal paradox illustrates a more general point, which Pettit (2001) has called the ‘discursive dilemma’: Majority voting on multiple, interconnected propositions may lead to an inconsistent set of collective judgments. In the court example, majorities accept a, b, [c if and only if (a and b)], and the negation of c, an inconsistent set of propositions in the standard sense of logic (see also Brennan 2001). Naturally, the observation that majority voting may fail to produce consistent collective judgments raises several questions. In particular, how general is the problem? Is