Freedom and voting power

This paper proposes a method of evaluating elections in terms of freedom of choice. It evaluates voting institutions in terms of their allocation of control. Formally, the paper develops the symmetric power order, a measure of voting power for multicandidate elections. The measure generalizes standard pivotality-based voting power measures for binary elections, such as Banzhaf power. At the same time, the measure is not based on pivotality, but rather on a measure of freedom of choice in individual decisions. I show that pivotality only measures freedom-based voting power in monotonic elections, and is not a good measure in multicandidate elections. Pivotality only provides an upper bound on freedom-based voting power. This result establishes a relation between voting power and strategyproofness. I argue that my results are robust, and that pivotality should generally be expected to over-estimate other sensible measures of voting power in multicandidate elections.