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Optimal majority threshold in a stochastic environment

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Abstract

Within the model of social dynamics determined by collective decisions in a stochastic environment (the ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents. We obtain analytical expressions for the optimal majority threshold as a function of the parameters of the environment, assuming that the proposals are generated by means of random variables. The cases of several specific distributions of these variables are considered in more detail.

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Notes

  1. \(\#X\) denotes the number of elements in the finite set X.

  2. \([\alpha n]\) is the integer part of \(\alpha n\).

  3. See Nitzan and Paroush (1982) and Azrieli and Kim (2014) on other approaches to optimizing the majority threshold and Rae (1969) and Sekiguchi and Ohtsuki (2015) for a discussion of the case of multiple voting in this context.

  4. This result can also be obtained by applying Theorem 1 in Barberà and Jackson (2006) if we consider each agent as a country with \(n_i = 1\) (population) and a simple voting behaviour of the representative. In this case, \(\alpha _0\)-majority maximizes social and individual welfare. In the proof of Theorem 2, we provide a simpler argument for the case under consideration. Theorem 1 in Azrieli and Kim (2014) can also be used for this proof if we consider environment proposals (in the ViSE model) as agent types in their model.

  5. Corollary 7 has been suggested by an anonymous referee.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vitaly Malyshev

  2. Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, Russia

    Vitaly Malyshev

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  1. Vitaly Malyshev
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Correspondence to Vitaly Malyshev.

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Malyshev, V. Optimal majority threshold in a stochastic environment. Group Decis Negot 30, 427–446 (2021). https://doi.org/10.1007/s10726-020-09717-8

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