Neutrality in arrow and other impossibility theorems

Summary.

Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.