Persuading Strategic Voters

Abstract

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Persuading communicating voters

“…Receivers know the joint distribution of signals (vectors of messages), but only observe their own and their neighbors' private messages from the signal realization. If the network is empty, then our model reduces to the model of Kerman, Herings, and Karos (2020), which is used as a benchmark.…”

“…Equilibrium It is natural to ask whether the optimal communication strategies under sincere voting form an equilibrium. As per Kerman et al (2020), if in a network with n nodes and quota k a communication strategy achieves the optimal value as under the empty network, V n k , then the strategy does not form a Bayesian Nash equilibrium (BNE) under sincere voting. This is because in optimal strategies agents are never pivotal in state X and are pivotal with positive probability in state Y .…”

“…One remedy to the swing voter's curse is never making agents pivotal by having at least k + 1 agents vote for x in state Y (Kerman et al, 2020). A setting where an optimal communication strategy yields a BNE under sincere voting is given in g 3 in Example 5.7.…”

“…This section demonstrates how the information-sharing feature of our model produces a non-trivial change in the overall setup of multiple-receiver Bayesian persuasion as many of the common assumptions in standard models cease to hold in general. First, we briefly consider the model in Kerman et al (2020), which corresponds to the empty network case in our framework and is used as a benchmark. Second, we demonstrate that the network structure can affect the agents' posteriors and the (optimal) value.…”

“…In Kerman et al (2020), it is without loss of generality to restrict attention to straightforward (in the sense of Kamenica and Gentzkow (2011)) and anonymous communication strategies. Given a binary state space Ω = {X, Y }, it is optimal for the sender to send "recommendations", x or y, as messages.…”