The Perversity of Weighted Voting

Weighted voting involves weighting representatives’ votes by the populations that they represent. Such systems have been adopted in some legislative bodies as a remedy for malapportionment, and are sometimes used to elect candidates for the executive branch of government. But they receive little attention. This note observes the neglected vices of weighted voting systems: they violate intuitive conditions of monotonicity and participation. These vices count significantly against the use of weighted voting, and reflecting on why they arise improves our understanding of axioms in social choice theory.