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Representation of constitutions under incomplete information

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  • Bezalel Peleg
  • Shmuel Zamir

Abstract

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizen are private information. We investigate whether there exist decision schemes (i. e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties. When applied to n-person games in strategic form, a decision scheme d is a mapping from profiles of (dichotomous) preferences on the set of pure strategy vectors to probability distributions over outcomes (or equivalently, over pure strategy vectors). We prove that for any feasible and individually rational payoff vector of a strategic game, there exists a decision scheme that yields that payoff vector as a (pure) Nash equilibrium payoff in the game induced by the strategic game and the decision scheme. This can be viewed as a kind of purification result.

Suggested Citation

  • Bezalel Peleg & Shmuel Zamir, 2013. "Representation of constitutions under incomplete information," Discussion Paper Series dp634, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp634
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    References listed on IDEAS

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    1. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
    2. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
    3. Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 167-181, December.
    4. Bezalel Peleg & Hans Peters, 2010. "Strategic Social Choice," Studies in Choice and Welfare, Springer, number 978-3-642-13875-1, June.
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    Cited by:

    1. Bezalel Peleg & Ron Holzman, 2017. "Representations of Political Power Structures by Strategically Stable Game Forms: A Survey," Games, MDPI, vol. 8(4), pages 1-17, October.
    2. Hans Peters & Marc Schröder & Dries Vermeulen, 2015. "On existence of ex post Nash consistent representation for effectivity functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 287-307, September.
    3. Hans Gersbach & Stephan Imhof & Oriol Tejada, 2021. "Channeling the final say in politics: a simple mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 151-183, February.

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    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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