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Social Choice and Welfare

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29-08-2020 | Original Paper

Representative Voting Games

Authors: John Duggan, Jean Guillaume Forand

Published in: Social Choice and Welfare | Issue 3/2021

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Abstract

We propose the stationary Markov perfect equilibria of representative voting games as a benchmark to evaluate the outcomes of dynamic elections, in which the evolution of voters’ political power is endogenous. We show that the equilibria of dynamic elections can achieve this benchmark if politicians are sufficiently office motivated. For arbitrary equilibria of the electoral model, we characterize the faithfulness of politicians’ choices to the policy objectives of representative voters through a delegated best-response property. Finally, we provide conditions under which general dynamic electoral environments admit representative voters in each state.

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With a single state, our model mimics the equilibrium outcomes of dynamic model of elections with adverse selection following Duggan (2000) and Bernhardt et al. (2004): while we assume that a politician’s type is observed after she takes office to avoid complex updating of voters’ beliefs across states, the ex post commitment that we allow proxies for these beliefs in the absence of a state variable.

Forand (2014) and Van Weelden (2013) establish related results in different models of dynamic elections with a fixed median voter and underlying collective decision problem.

We assume a type-independent discount factor to simplify notation. As can be verified from their proofs, this assumption is not needed for Theorems 1 or 2. On the other hand, the result of Theorem 3 does not hold when different voter types have different discount factors.

Theorem 2 is related to Proposition 4.2 in Duggan and Forand (2019), where we focus on ruling out the implementation of policy rules that are not solutions to the representative voter’s dynamic programming problem. There, the representative voter is fixed, and equilibrium coordination between representative voters is not an issue, so we can rely on a refinement of voting strategies which assumes only that, in all states, all politician types have available some policy which leads to reelection.

If we allowed for history-dependent persistence of policy choices in the representative voting game, it would be the case that the outcomes of any Markov electoral equilibrium satisfying the conditions of Theorem 2 could be replicated by a (nonstationary) subgame perfect equilibrium of the representative voting game.

This augmented game is a special case of the model from Duggan and Forand (2018), where we prove general existence of Markov electoral equilibria.

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Title: Representative Voting Games
Authors: John Duggan
Jean Guillaume Forand
Publication date: 29-08-2020
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 3/2021
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-020-01283-x

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