Online Appendix: Optimal Retrospective Voting
نویسندگان
چکیده
We begin by pointing out that, under this setup, it is without loss of generality to assume that the Voter ‘knows’ the Legislator’s random variable xl : Ω → R. To see this, let x∗v : Ω → R and xl : Ω → R be the actual random variables of the Voter and Legislator. Append to the game a set of mappings xl : Ω → R, viz. Xl, where Xl is a metric space. Also, append to the game a (transparent) prior ν ∈ ∆(Ω×Xl), where margΩ ν = μ. Take the state space to be Ω ×Xl. Construct the random variable x∗∗ v : Ω ×Xl → R so that x∗∗ v (ω, xl) = x∗v (ω) for all (ω, xl) ∈ Ω×Xl. Construct the random variable x∗∗ l : Ω×Xl → R so that x∗∗ l (ω, xl) = xl (ω) for all (ω, xl) ∈ Ω ×Xl. Extend the definitions of the payoff functions in the obvious way. A Bayesian Equilibrium in this expanded game remains a Bayesian Equilibrium in the original game.4 So, if the Voter can design an optimal retrospective voting rule in this expanded game, he can also select the associated equilibrium in the original game. Finally, notice that, if Ω and Xl are Polish, then we can also expand the state space to incorporate any uncertainty of the Legislator about the Voter’s uncertainty, and so on. (To expand the state space, follow the steps in Brandenburger and Dekel [10, 1993].) With this in mind, we stick to the original setup.
منابع مشابه
Optimal Retrospective Voting∗
We argue that optimal retrospective voting can be thought of as an equilibrium selection criterion—specifically, a criterion that selects so as to maximize voter welfare. Formalized this way, we go on to provide an informational rationale for retrospective voting. We show that a Voter can use retrospective voting to extract information from a Legislator with policy expertise. In particular, whe...
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