Emir Kamenica and Matthew Gentzkow (2011), American Economic Review 101(6), 2590–2615 — DOI-10.1257/aer.101.6.2590
Key takeaways
Read in full; see NOTE-717. The online Appendix was not read.
- Bayes plausibility is the only constraint. Any distribution of posteriors whose mean is the prior is induced by some signal (Proposition 1). The sender’s optimal value is V(μ₀), the concave closure of its posterior-value function at the prior, and it gains iff V(μ₀) > v̂(μ₀) (Corollary 2).
- Overt design still works. In the judge example the judge “is fully aware that the investigation was designed to maximize the probability of conviction”, and convicts with probability 0.6 instead of 0.
- The optimum’s signature. When the receiver takes the sender’s worst action she is certain of the state; at an interior belief she is indifferent between two actions (Propositions 4 and 5).
- Alignment is not monotone. More aligned preferences can make the optimal signal less informative (Section IV).
- Persuasion against incentives. Incentives change marginal utility, coercion included; persuasion is “anything which changes beliefs”. Systematic harm to receivers is read as a sign of limited rationality.
Standing in the record
Filed for QUESTION-070 and QUESTION-071, on manipulation by an organized whole and manipulation invisible in present structure, and beside CLAIM-050. The reading answered the three checks the entry set:
- QUESTION-071: the case is not one of invisibility. This entry said that what shows the steering is who chose the information structure and why, a fact about history. In the paper that fact is not hidden: the receiver observes the signal and knows its purpose. The optimum also leaves a trace in present belief, a posterior exactly on a decision boundary. The case the paper gives the question is a different one: influence that is fully visible and still effective because each step of the receiver’s inference is sound.
- QUESTION-070: the paper does not say it is manipulation. It uses the word once, for the sender’s aim, and its taxonomy has only incentives and persuasion. The design is overt, so definitions that require covertness (LIT-1002, as summarised in the question) would exclude it. The reading adds a point the question would need: in the judge and product examples the receiver does exactly as well as with no information and loses all the value full information would have given her, so a harm criterion depends on its baseline. That arithmetic is the record’s. The paper’s sender is any optimiser of a payoff, and several of its examples are institutional procedures; that a selected rather than intended procedure would act the same is the record’s inference.
- CLAIM-050: related only through an unnamed garbling. The paper never cites Blackwell. It redefines the state as “the realization of the most informative signal Sender can generate”, so that every signal is a garbling of that. This entry’s earlier phrase “preferring a garbling of full information” is therefore true of every signal and says nothing. What bears on the claim is that the chooser of the experiment can strictly prefer a less informative one, which Blackwell’s theorem, a ranking for the decider, does not forbid.
game-theory comes first, as the paper’s subject. information-theory is
for signals and garbling, and epistemology for Bayes plausibility and
belief. No anthology topic holds it.
Note of 2026-10-21: applied to reflexive control and media capture
A20 and A21 of the exchange of 2026-10-20 applied this work to reflexive control and media capture (“A regulator might update its beliefs correctly on every signal it receives, yet its decisions can still be systematically influenced by who determines which signals are generated”). The entry’s history already records that the Mathematics of Meaning record “frames reflexive control as information design”. Both replies called this entry the record’s “reading”, but the reading is NOTE-717 and THEORY-404. Thomas (2004), named and not filed in the curation of 2026-10-13, is now registered as LIT-1339, Unavailable when sought on 2026-10-21, and the institutional route is filed as CLAIM-404.
Two readings of the same day bear on this work. Bergemann and Morris’s survey (LIT-1313, NOTE-1034) is its many-player generalization: an omniscient designer can attain exactly the Bayes correlated equilibria, and a receiver with information of its own bounds what can be induced (THEORY-844). Hayek’s prices (LIT-1337, NOTE-1036) are the undesigned signals beside this work’s designed one; Thomas’s reflexive control, which would join them, was not reached.