A geometric study of shareholders' voting in incomplete markets: Multivariate median and mean shareholder theorems

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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 ρ ∈ [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.

Original languageEnglish (US)
Pages (from-to)377-406
Number of pages30
JournalSocial Choice and Welfare
Volume27
Issue number2
DOIs
StatePublished - Oct 1 2006

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shareholder
voting
market
firm
majority rule
equilibrium model
guarantee
Incomplete markets
Median
Shareholder voting
Shareholders

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

Cite this

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title = "A geometric study of shareholders' voting in incomplete markets: Multivariate median and mean shareholder theorems",
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 ρ ∈ [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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