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Single-Crossing Differences in Convex Environments

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  • Navin Kartik
  • SangMok Lee
  • Daniel Rappoport

Abstract

An agent's preferences depend on an ordered parameter or type. We characterize the set of utility functions with single-crossing differences (SCD) in convex environments. These include preferences over lotteries, both in expected utility and rank-dependent utility frameworks, and preferences over bundles of goods and over consumption streams. Our notion of SCD does not presume an order on the choice space. This unordered SCD is necessary and sufficient for ''interval choice'' comparative statics. We present applications to cheap talk, observational learning, and collective choice, showing how convex environments arise in these problems and how SCD/interval choice are useful. Methodologically, our main characterization stems from a result on linear aggregations of single-crossing functions.

Suggested Citation

  • Navin Kartik & SangMok Lee & Daniel Rappoport, 2022. "Single-Crossing Differences in Convex Environments," Papers 2212.12009, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2212.12009
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    References listed on IDEAS

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    1. Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of Rank-Dependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 281-298, November.
    2. Lones Smith, 2011. "Frictional Matching Models," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 319-338, September.
    3. Gorkem Celik, 2015. "Implementation by Gradual Revelation," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 271-296, June.
    4. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    5. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    7. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    8. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
    9. Seidmann, Daniel J., 1990. "Effective cheap talk with conflicting interests," Journal of Economic Theory, Elsevier, vol. 50(2), pages 445-458, April.
    10. Shepsle, Kenneth A., 1972. "The Strategy of Ambiguity: Uncertainty and Electoral Competition," American Political Science Review, Cambridge University Press, vol. 66(2), pages 555-568, June.
    11. Ali E. Abbas & David E. Bell, 2011. "One-Switch Independence for Multiattribute Utility Functions," Operations Research, INFORMS, vol. 59(3), pages 764-771, June.
    12. Andreas Kleiner, 2022. "Optimal Delegation in a Multidimensional World," Papers 2208.11835, arXiv.org.
    13. Navin Kartik & SangMok Lee & Tianhao Liu & Daniel Rappoport, 2021. "Beyond Unbounded Beliefs: How Preferences and Information Interplay in Social Learning," Papers 2103.02754, arXiv.org, revised Apr 2024.
    14. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    15. Richard Zeckhauser, 1969. "Majority Rule with Lotteries on Alternatives," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 83(4), pages 696-703.
    16. John Duggan, 2014. "Majority Voting Over Lotteries: Conditions for Existence of a Decisive Voter," Economics Bulletin, AccessEcon, vol. 34(1), pages 263-270.
    17. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    18. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    19. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    20. Manuel Amador & Kyle Bagwell, 2013. "The Theory of Optimal Delegation With an Application to Tariff Caps," Econometrica, Econometric Society, vol. 81(4), pages 1541-1599, July.
    21. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    22. Jeffrey Banks & John Duggan, 2006. "A Social Choice Lemma on Voting Over Lotteries with Applications to a Class of Dynamic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 285-304, April.
    23. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    24. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    25. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    26. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    27. Matthew O. Jackson & Leeat Yariv, 2015. "Collective Dynamic Choice: The Necessity of Time Inconsistency," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 150-178, November.
    28. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
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