Delegation in a Cheap-Talk Game: A Voting Example

Suppose an agent is contemplating an action with state-contingent payoffs, and has a prior belief about the probability of the states. She hires an expert to update her priors before the action. Experts may be both informed as well as uninformed, and are not necessarily truthful. The question asked in this paper is when, if at all, is it better for the agent to assign the task of playing with experts and deciding on the action to another agent with a different set of priors. In particular, can an agent increase her payoff in a cheap-talk game by delegating to others to play on her behalf? This paper shows that such profitable delegation is possible and characterizes the agents to whom a given agent may delegate the responsibility. While this generic problem can arise in many contexts, we have chosen to model it in a simple voting situation where the electoral issue is whether a certain policy with contingent outcomes should or should not be implemented. Voters have different priors about probable states of the world, and hence their expected pay-offs from the policy vary. The elected decision-maker can use the institution of an advisor before deciding whether to implement the policy. We show that unless the median voter has very sure beliefs about the probable states, she would be better off getting someone else elected than herself as the decision-maker. In particular, if the median is predisposed to (against) the policy action, she would be better off choosing a candidate more (less) pro-action than herself. The optimal choice of the decision-maker is shown to depend on the cost of misdirected policy, i.e. of implementing it when it is actually unwarranted.