Normative properties of four single-stage multi-winner electoral procedures

This article focuses on decision-making by voting in systems at the levels of the organization, the community, the society, and the international system. It examines the compatibility of four voting procedures (plurality, approval voting, Borda's count, and Hare's single transferable vote) with ten normative properties commonly used to evaluate the desirability of voting procedures by social choice theorists. The analysis alternately assumes that one candidate, as well as more than one candidate, must be elected under each of the procedures. It thus extends previous analyses of the same issues which were mainly restricted to situations where only a single candidate must be elected. We show that: (i) under all four procedures, if a property is violated when only a single candidate must be elected it is also violated when more than one candidate must be elected; (ii) all properties that are satisfied under the AV procedure when a single candidate must be elected are also satisfied when more than one candidate must be elected; (iii) at least one property that is satisfied under each of the remaining three procedures when only a single candidate must be elected, may be violated when the number of available slots is larger than one. Theoretical issues and practical implications of these findings are discussed.