opinion | How do economists get people to do what they want them to do

“The judge understands the statistics, he understands how prevalent they are, but we make him rule against nearly twice as many actual officials,” Kamenica said.

The courtroom scene demonstrates the power of being able to control the information being transmitted. If a prosecutor were only throwing cheap talk, he would always claim his guilt, but such empty allegations would never give any information to a rational judge. “The ability to stick to the type of information that will be generated is a powerful tool,” Kamenica said.

Now for some other applications of Bayesian persuasion:

The paper on lying politicians released this month is written by Florian Ederer of the Yale School of Management and Weicheng Min of the Yale University Department of Economics. Politicians would have no incentive to lie if fact-checkers discovered 100 percent of their lies, the authors wrote, but if the probability of catching a lie was low enough, the politician would compensate for fact-checking by lying more. Eder said in an interview that the sender (in this case a politician) “makes noise in the information environment.” (You might think that lying doesn’t fit within the Bayesian persuasion framework, but Eder says it can be appropriate as long as the politician “commits to sending a truthful or untruthful message with a certain probability” which can depend on the state of the world.)

A working paper, Persuasion with Anecdotes, released in April 2021, says that it makes sense for non-experts to get their information from underinformed people but with similar preferences rather than from experts “whose preferences may differ” from their own. The research, which includes five authors, says two from Microsoft, one from the University of California, Berkeley, one from the University of Michigan and one from Princeton. This explains a lot of what you see on social media.

The triumph of a silly tale is what you get when talk is cheap. This is not Bayesian persuasion. In Bayes’ case, the authors found, the transmitter of information would not choose anecdotes, but “will choose an unbiased and informative communication scheme”. That’s reassuring. Unfortunately, Bayes’ case is rare.

Penelope Hernandez of the University of Valencia in Spain and Zvika Neiman of Tel Aviv University in Israel wrote a 2019 paper titled “How Bayesian Persuasion Can Help Reducing Unlawful Parking and Other Socially Undesirable Behaviour.” They assume that if the probability of getting a ticket is less than a certain limit, people will stop the car illegally. Assuming the parking rule enforcement budget is constant, they write that it makes sense to forego enforcing the rules at certain times and places and focus the budget on others. In an interview, Neiman said drivers can get a red light on their phones when a law enforcement agent is nearby and either a red or green light when the agent is away. Drivers will be told, in all honesty, that a red light may be a false alarm, but it still urges them to park legally.

Bayesian persuasion has not been widely adopted by policy makers. “In practice, people are probably less than fully Bayesian rationalists, and certainly not as Bayesian rationalists as assumed in this paper,” admits the paper by Hernandez and Neiman.