Implementation of Majority Voting Rules∗

I study implementation by agenda, a straightforward voting mechanism that is widely used in practice. The main result resolves an open question which dates back to Black [1958] and Farquharson [1957/1969]. It establishes that any neutral majority voting rule which satisfies the two necessary conditions identified in prior work (McKelvey and Niemi [1978]; Moulin [1986]) as well as a significantly weakened version of Sen’s α can be implemented by sophisticated voting on an agenda. The characterization establishes that virtually all of the majority voting rules studied in the literature can be implemented by agenda. As an added benefit, it also clarifies what can be implemented via dominance solvable voting and backward induction, two solutions concepts which are broadly appealing though poorly understood. To establish the main result, I adopt a novel algebraic approach. As an intermediate step, I establish the pairwise conjecture of Srivastava and Trick [1996]. JEL Codes: C72, D71, D72, D78.