Bayesian Persuasion: Information as a Lever of Soft Paternalism

The subtlest mathematical storyline of paternalism: to influence without forbidding and without deceiving — through the structure of information alone.

Intuition: to persuade without deceiving

In the Kamenica and Gentzkow model, the sender commits to some information-disclosure policy — a signal structure — before observing the state of the world; the receiver updates in Bayesian fashion and chooses an action (Bayesian Persuasion, AER).

Formalism: the design of posterior beliefs

The sender chooses not a single message but a distribution of the receiver's posterior beliefs — with the sole constraint of Bayesian consistency: the average of the posterior beliefs equals the prior. This is precisely "information design."

Concavification

The tool of solution is concavification: persuasion benefits the sender if and only if the concave hull of their value function over the distribution of beliefs lies, at the prior, above the function itself (NBER). The paradox is that even under complete honesty the sender can gain by dosing the precision of the signal.

Applications

The authors' own examples are a prosecutor, a lobbyist, a salesperson. But more broadly this is the language of ratings, disclosures, warning labels, and recommender systems: everywhere someone decides what information, and at what precision, you receive.

Conclusions

For this site's storyline this is pure soft paternalism: power influences not through a ban or a tax but through what information a person receives — while preserving formal freedom of choice. Hence the ethical question: disclosure of information may serve a person's good, or it may serve the sender's interests, and from the outward appearance of the signal the two are not always distinguishable.