A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems (original) (raw)
Abstract
A simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate\(\rho \in [1/2, 1]\) are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when _K_=_S_−1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents’ preferences and the distribution of agents’ types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1–23, 1991) bound of 0.64: they obtain for production plans whose span contains the ‘ideal securities’ of all K mean shareholders.
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Authors and Affiliations
- HEC School of Management, 78351, Jouy-en-Josas, France
Hervé Crès
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Correspondence toHervé Crès.
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Hervé Crès is a member of the GREGHEC, unité CNRS, UMR 2959.
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Crès, H. A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems.Soc Choice Welfare 27, 377–406 (2006). https://doi.org/10.1007/s00355-006-0138-7
- Received: 03 November 2004
- Accepted: 15 November 2005
- Published: 31 May 2006
- Issue date: October 2006
- DOI: https://doi.org/10.1007/s00355-006-0138-7