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 citizens 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.
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Notes
The Borda count is originally defined for strict orderings, however, it can be extended to weak preference orderings as follows: Given \(R\in W\) and \(x\in A\), the Borda count of \(x\) is the average of the Borda counts of the elements of its equivalence class (in \(R\)) in a strict preference ordering \(Q\) on \(A\) that preserves the strict preferences in \(R\), that is if \(x\) is strictly preferred to \(y\) according to \(R\) then \(xQy\) (it is easily verified that this is well defined that is, it is the same for any such \(Q\)).
A representation \(d\) of \(E\) satisfies the CC if for all \(R^N\in W^N\), if \(c\in A\) beats every \(b\in A\setminus \{c\}\) by simple majority rule, then \(d(c, R^N)=1.\)
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We are indebted to three anonymous referees for their helpful comments.
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Peleg, B., Zamir, S. Representation of constitutions under incomplete information. Econ Theory 57, 279–302 (2014). https://doi.org/10.1007/s00199-014-0816-0
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DOI: https://doi.org/10.1007/s00199-014-0816-0