Discursive Dilemma

The discursive dilemma (also called the doctrinal paradox) is a result in social choice theory and philosophy showing that a group of individually rational agents, each holding a consistent set of beliefs, can arrive at a collectively inconsistent set of beliefs through majority voting on individual propositions. The classic case: a three-judge panel must rule on a contract dispute where liability requires both (A) a valid contract and (B) a breach. Judge 1 holds A-yes, B-yes, liable. Judge 2 holds A-yes, B-no, not liable. Judge 3 holds A-no, B-yes, not liable. Majority vote on A: yes (2-1). Majority vote on B: yes (2-1). But majority vote on liability: no (2-1). The conclusion does not follow from the majority's premises. The dilemma was formalized by Philip Pettit and Christian List, who showed it as a generalization of the Condorcet Paradox from preferences to beliefs. The implication is troubling for deliberative theories of democracy: collective reasoning over propositions inherits the irrationality of preference aggregation, and no simple voting procedure can avoid it. The conditions for collective rationality are inconsistent with the conditions for adequate representation of individual views.