Supermodularity and preferences

@article{Chambers2009SupermodularityAP,
  title={Supermodularity and preferences},
  author={Christopher P. Chambers and Federico Echenique},
  journal={J. Economic Theory},
  year={2009},
  volume={144},
  pages={1004-1014}
}
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. 
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