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Published May 2009 | Accepted Version
Journal Article Open

Supermodularity and preferences


We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation.

Additional Information

© 2008 Elsevier Inc. Received 6 May 2008; accepted 11 June 2008. Available online 21 June 2008. We are very grateful to John Quah and Eran Shmaya, who each independently suggested a different proof of our main theorem; the current proof follows their ideas. We also thank Françoise Forges, Paul J. Healy, Laurent Mathevet, Preston McAfee, Ed Schlee, Itai Sher, Yves Sprumont, Leeat Yariv, Bill Zame and seminar participants at various institutions. Finally, we are especially grateful to Chris Shannon for comments and suggestions on a previous draft. We acknowledge the support of the NSF through grant SES-0751980.

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