Tommy James & the Shondells sang “Crystal Blue Persuasion.” Economists have their own shade of persuasion — Bayesian.
Bayesian persuasion is an idea only a little more than a decade old that’s being used to study phenomena as varied as advertising, the law, bond ratings and parking enforcement. A working paper this month uses it to analyze political lies. The authors conclude that politicians will lie more when they know they’re being fact-checked. (Finding a real-life example of that behavior is left as an exercise for the reader.)
Thomas Bayes was an 18th-century English statistician, philosopher and Presbyterian minister. He developed a statistical model for how to update your predictions in light of old and new knowledge. Let’s say you test positive for a rare, fatal disease. If the false positive rate is only 1 percent, you might start putting your affairs in order. But a Bayesian would incorporate, among other things, the prior knowledge of the rarity of the disease — say, one in a million people get it — and conclude that the test result is probably wrong.
Bayesian persuasion is a technique that uses information rather than bribes or threats to get people to see the world differently and change their behavior in desired ways. It assumes all people have prior beliefs about the world that they update as new information, such as a diagnostic test result, comes in. There is a “sender” and a “receiver.” The goal for the sender is to share the information that will most effectively persuade the receiver to act in a certain way.
This week I spoke with Emir Kamenica, one of the two authors of “Bayesian Persuasion,” the 2009 paper that gave birth to the new field. When I got Kamenica on the phone, he had just finished teaching a class on the topic at the University of Chicago’s Booth School of Business. He gave me a hypothetical situation to illustrate the basic idea.
Imagine a wrongful death case where the judge wants to get the verdict right but the prosecutor just wants to win the case. It’s a civil case so the standard of proof is simply the preponderance of evidence.
Let’s say the judge and the prosecutor think there’s a 30 percent chance the defendant is responsible for the wrongful death. There’s blood evidence from the person who caused the death and a blood sample from the defendant. The prosecutor could order DNA tests on the blood samples that would establish beyond a doubt if the accused person is liable.
But the prosecutor can improve his chances of winning the case if instead he just orders tests for blood type. Why? Let’s say the blood at the scene is Type A. If the defendant is liable, his blood will also be Type A. But even if he didn’t do it, there’s still about a 40 percent probability that his blood will be Type A, given the prevalence of that blood type in the population. That’s a high rate of false positives.
Still, a rational judge who learns that the defendant is Type A would conclude that this piece of evidence from the prosecutor raises the likelihood of the defendant’s responsibility from 30 percent (before) to slightly more than 50 percent (after). The blood test isn’t conclusive by itself but it adds weight to the case against the defendant, who was already under some suspicion.
“The judge understands statistics, he understands prevalence, but we’re getting him to rule against nearly twice as many people as are actually responsible,” Kamenica said.
The courtroom scene shows the power of being able to control information that is conveyed. If the prosecutor were just spewing cheap talk, he would always simply claim guilt, but such empty claims would never provide any information to a rational judge. “The ability to commit to what type of information will be generated is a powerful tool,” Kamenica said.
Now for some other applications of Bayesian persuasion:
The paper about lying politicians that came out this month is by Florian Ederer of the Yale School of Management and Weicheng Min of Yale’s economics department. Politicians would have no incentive to lie if fact-checkers caught 100 percent of their lies, the authors write, but if the probability of catching a lie is sufficiently low, a politician will compensate for the fact-checking by lying even more. The sender (in this case, a politician) “noises up the information environment,” Ederer said in an interview. (You might think that lying doesn’t fit into a Bayesian persuasion framework, but Ederer says it can fit as long as the politician “commits to sending a truthful or an untruthful message with a certain probability” that can depend on the state of the world.)
“Persuading With Anecdotes,” a working paper issued in April 2021, says that it’s rational for nonexperts to obtain their information from people who are poorly informed but have similar preferences rather than from experts “whose preferences may differ” from their own. Experts have a vast stock of anecdotes and may choose ones that steer people toward their beliefs, says the paper, which has five authors, two from Microsoft, one from the University of California, Berkeley, one from the University of Michigan and one from Princeton. That explains a lot of what you see on social media.
The triumph of the silly anecdote is what you get when talk is cheap. That is not Bayesian persuasion. In the Bayesian case, the authors find, a sender of information won’t cherry-pick anecdotes but rather “will choose an unbiased and maximally informative communication scheme.” That’s reassuring. Unfortunately, the Bayesian situation is rare.
Penélope Hernández of the University of Valencia in Spain and Zvika Neeman of Tel Aviv University in Israel wrote a 2019 paper, “How Bayesian Persuasion Can Help Reduce Illegal Parking and Other Socially Undesirable Behavior.” They assume that if the likelihood of getting a ticket is below some threshold, people will park illegally. Assuming that the budget for enforcing parking rules is fixed, they write, it makes sense to give up on enforcing the rules at certain times and places and focus the budget on others. In an interview, Neeman said drivers could get a red signal on their phones when an enforcement agent is close and either a red or a green signal when the agent is far away. Drivers would be told, in all honesty, that the red signal might be a false alarm, but it would still induce them to park legally.
Bayesian persuasion hasn’t been widely embraced by policymakers. “In practice, people are probably less than fully Bayesian rational, and certainly, probably not as Bayesian rational as assumed in this paper,” the paper by Hernández and Neeman concedes.
Nonetheless, Hernández and Neeman write, “A local government who wants to exploit the power of using messages to help regulate behavior would probably not do badly by ensuring that the messages it uses are Bayesian optimal as described in this paper.”
One appealing aspect of the Bayesian persuasion literature is that Bayesian persuasion doesn’t depend on trickery. The strategic disclosure of information exerts a strong influence even with everyone’s eyes wide open. It’s the most revolutionary result of the 2009 paper by Gentzkow and Kamenica. “That crystallized something that had been building up in the literature for a while,” said Brendan Lucier of Microsoft Research, an author of the “Persuading With Anecdotes” paper. “A lot of work has built on that.”
Mexico is by far the main source for fresh vegetables imported into the United States, according to the U.S. Department of Agriculture. Mexico doubled its exports of fresh vegetables to the United States to 12 billion pounds in 2020 from about six billion pounds in 2008. Mexico’s share of U.S. imports of fresh vegetables rose to 77 percent from 69 percent over the period. Imports are extending the lengths of seasons in which fresh vegetables are available — a phenomenon that the Department of Agriculture calls “market window creep.”
Quote of the day
“On the walls of the city hall of Gouda in the Netherlands is written the Latin motto: ‘Audite et alteram partem’ (Listen even to the other side). This is the attitude you should have in debating economic issues.”
— Ha-Joon Chang, “Economics: The User’s Guide” (2014)
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