This dissertation is not fake news : formal models of persuasion, manipulation, and collective choice
Keywords: Business.

When does fact-checking fake news make things worse? What does Donald Trump have in common with a rap artist? Is encouraging independent thought always a good thing? Chapter 1 presents a game-theoretic model of a manipulator who wants to control one or more agents. The agents receive a signal that may be "real news" about the expected utility of a specific choice, or may be "fake news" from the manipulator. The news may come with a fact-check from a trusted third party, which reveals whether the news was real or fake. I show that whether fact-checking may backfire depends on the objective of the fact-checker. If the fact-checker wants to maximize each agent's expected utility, as might a consumer platform eliminating fake reviews, then the answer is no. If the fact-checker wants to minimize the probability that the manipulator successfully dupes each agent, as might a political watchdog concerned with the legitimacy of an election, then the answer is yes. I characterize conditions under which fact-checking can backfire, and show that the risk can be eliminated if the fact-checker certifies real news as often as it labels fake news. I extend the model to include endogenous fact-checking, allowing agents to purchase a fact-check after seeing the news. Reducing the cost of a fact-check never poses a backfire risk, even though agents concentrate their fact-checks on messages most likely to be fake. Chapter 2 extends the model to a setting where agents have heterogeneous preferences. The same news may make some agents more likely and other agents less likely to take the manipulator's preferred action. I show that in this setting multiple equilibria exist. These equilibria exist due to the possibility of "lies not to be taken too seriously, " messages which would be bad for the manipulator if interpreted by receivers as certainly authentic or certainly fake, but which benefit the manipulator when interpreted ambiguously. The equilibria which make maximal use of these messages are sender-optimal. Substantive examples include tweets from former President Donald Trump and hip-hop artists who brag about alleged crimes. I use the model to propose and solve a puzzle concerning political dog whistles: how can a political dog whistle persist after it becomes well known? I argue that such messages are pseudo-dog whistles: when faced with a heterogeneous audience, it may be strategically advantageous to send ambiguous messages even when the ambiguity is understood the same way by the entire audience. Pseudo-dog whistles are distinguished from real dog whistles, which use coded language to send a message only a subset of the audience can "hear." Chapter 3 builds on the Condorcet jury model to study independence and deference in group decision-making. In groups with diverse levels of competence, it may be advantageous for some less-competent agents to defer to some more-competent agents. In groups of equal competence, full independence is optimal. We demonstrate a theory of the second best result: even under conditions where full independence would be best for a group, encouraging some independence may hurt the group