Supplementary Appendix for Informative Cheap Talk Elections

Setting. Assume the set of possible types for the policymaker is Θ ≡ {θ1, θ2, . . . , θT} ⊂ R, where T ≥ 2 (T ∈ N), θi > θi−1 for all i ∈ {2, . . . , T}, and 0 ∈ Θ. Denote the prior on a politician’s type by the vector p ≡ (p1, . . . , pT ) where pi is the probability of type θi. For convenience, we also write p[θ] for the probability that p assigns to type θ. For now we consider only the policymaking stage, assuming that the PM is drawn according to p; the campaign stage is discussed in Section 3. The PM chooses an action after observing the state of the world. The set of states is S ≡ R with cumulative distribution function (CDF) F (·). We ∗Department of Economics, Columbia University. Email: [email protected]. †Department of Economics, University of Chicago. Email: [email protected].