Soc Choice Welf (2017) 49:657–669 DOI 10.1007/s00355-017-1065-5 ORIGINAL PAPER A spatial analogue of May’s Theorem Richard Lee Brady 1 · Christopher P. Chambers 1 Published online: 17 November 2017 © Springer-Verlag GmbH Germany 2017 Abstract In a spatial model with Euclidean preferences, we establish that the geomet- ric median satisfies Maskin monotonicity, anonymity, and neutrality. For three agents, it is the unique such rule. 1 Introduction An early social-choice theoretic foundation for majority rule was provided by May (1952). In an environment with a group of agents who choose one of two alternatives based on strict preferences, he shows that majority rule is the unique rule satisfying three natural axioms. The first of these axioms, anonymity, requires that the names of the agents do not matter. The second, neutrality, requires that the names of the alternatives do not matter. The third, positive responsiveness, means that in any given This paper is a reprint of Brady, R. L. & Chambers, C. P., A spatial analogue of May’s Theorem, Soc Choice Welf (2016) 47(1) 127–139, doi:10.1007/s00355-016-0949-0. It was submitted to this Special Issue in honor of John Roemer and by mistake appeared in the aforementioned volume and issue. The Publisher apologizes for the mistake occurred and any inconvenience caused. We are grateful to Roy Allen, John Duggan, Bill Zwicker, the guest editor, and two anonymous referees for comments and suggestions. All errors are our own. The result in this manuscript was previously circulated under the title Spatial implementation. B Richard Lee Brady rlbrady@ucsd.edu Christopher P. Chambers cpchambers@ucsd.edu 1 Department of Economics, University of California, San Diego, USA 123