Collective choice for simple preferences

Abstract

Simple preferences with restricted structures, such as dichotomous or trichotomous orderings, circumvent the classic impossibility results of social choice theory. On these domains, majority rule and approval voting emerge as uniquely well-behaved mechanisms, satisfying axiomatic properties like transitivity, anonymity, and neutrality. Axiomatic characterizations demonstrate that majority rule is the only transitive social decision function under standard conditions when individuals have at most two indifference classes. Strategic analysis shows that approval voting is uniquely strategy-proof on the entire domain of dichotomous preferences when voters are not constrained in their ballot choices. In multi-issue environments with separable preferences, strategy-proofness leads to the characterization of voting-by-committees, although a tension remains between Pareto efficiency and non-dictatorial strategy-proofness. These theoretical developments extend to opinion aggregation and group identification problems, where collective decisions are represented by systems of individual powers regulated by social consent. By shifting the focus from universal to simple preference domains, it is possible to resolve specific conflicts between libertarian rights and Pareto efficiency, identifying conditions under which democratic aggregation remains robust, stable, and axiomatic. – AI-generated abstract.