Bayesian Persuasion¶

Model how a sender who cannot lie — committed to a public, truthful signal structure faced by a Bayes-rational receiver — still shifts the receiver's action by choosing how informative the signal is, solved geometrically as the concave closure of the sender's value over posteriors.

Core Idea¶

Bayesian persuasion (Kamenica and Gentzkow, 2011) is the strategic situation in which a sender commits in advance to an information experiment — a signal whose distribution over realizations is a known, publicly binding function of the underlying state — and a receiver observes the realized signal, updates by Bayes' rule, and takes an action. The sender's payoff depends on the receiver's action; the receiver optimizes given their posterior. The question is: given commitment to a signal structure, what experiment maximizes the sender's expected payoff?

The result that defines the concept is that even when the sender cannot lie — the signal structure is publicly known and binding, and the receiver is fully Bayesian — the sender can profitably influence the receiver's action by choosing how informative the experiment is, often by committing to a less than fully revealing signal. The key constraint is Bayes-plausibility: the posteriors induced by the experiment must average back to the prior, because the signal distribution is derived from the actual state distribution. Given this constraint, the sender's problem reduces to choosing a distribution over the receiver's posterior beliefs whose average is the prior, and then optimizing the sender's expected payoff over that distribution. The geometric characterization is the concavification of the sender's value function over the simplex of posteriors: the highest achievable expected value is the concave closure of the value function evaluated at the prior, and the optimal experiment is the distribution over posteriors that achieves this concave hull.

Commitment is load-bearing: without it, the sender cannot credibly commit to the signal structure and the problem collapses to cheap talk, in which the receiver discounts messages and persuasion is limited by alignment of preferences. With commitment — implemented in practice by institutional design, regulatory disclosure rules, or credentialing — the sender can exploit the gap between full disclosure and optimal partial disclosure to shift the receiver's expected action in the sender's direction, not by falsifying information but by designing the coarseness of the signal. Applications within the domain include prosecutor evidence design, credit-rating scale choice, regulatory stress-test disclosure levels, and platform recommendation structures — each a case of a sender choosing informativeness, not content.

Structural Signature¶

Sig role-phrases:

the sender — a party whose payoff depends on the receiver's action, choosing how informative a public signal will be
the receiver — a fully Bayesian agent who observes the realized signal, updates, and takes an action
the committed information experiment — a signal structure (conditional distribution of signals on states) chosen in advance and publicly binding, so the sender cannot lie or renege
the receiver's belief-to-action map — how posteriors translate to actions, whose thresholds are where persuasion can have bite
the Bayes-plausibility constraint — the induced posteriors must average back to the prior, so the sender can only redistribute belief, not manufacture it
the posterior-mixture design — the sender's problem recast as choosing a distribution over the receiver's posteriors
the value-over-posteriors function — the sender's expected payoff as a function of the receiver's posterior over the belief simplex
the concavification — the geometric solution: the concave closure of that function evaluated at the prior gives the highest achievable value, and its chord gives the optimal experiment
the partial-disclosure result — committing to a strictly less-than-fully-revealing signal can beat full disclosure when the prior sits under a non-concavity
the commitment precondition — without a binding signal structure the problem collapses to cheap talk, capped by preference alignment

What It Is Not¶

Not deception or lying. The signal structure is publicly known, binding, and truthful, and the receiver is fully Bayesian. The sender's entire latitude is informativeness choice — how coarse a truthful signal to commit to — not misrepresentation. Persuasion here is posterior-mixture design, not falsification.
Not cheap talk. Cheap talk has no commitment: messages are costless and non-binding, the receiver discounts them, and informativeness is capped by how well sender and receiver preferences already align. Bayesian persuasion turns on a binding signal structure; remove the commitment and the whole result collapses to cheap talk.
Not Spencean signalling. In signalling, the sender's own type is the private information, revealed through a costly action. In persuasion, the state of the world is the load-bearing uncertainty, and the sender chooses the informativeness of a costless public signal. Different locus of private information, different mechanism.
Not free manipulation of beliefs. Bayes-plausibility binds: the induced posteriors must average back to the prior. The sender can only redistribute belief — make some posteriors likely at the cost of others — not manufacture it. The design problem is genuinely constrained, not a license to move beliefs at will.
Not always profitable, and not always "reveal less." Whether partial disclosure beats full disclosure depends on the geometry: it helps only when the prior sits under a non-concavity of the sender's value-over-posteriors function. Where that function is already concave at the prior, full disclosure is optimal and coarsening gains nothing. "Commit to a less informative signal" is the optimum in some cases, not a universal rule.
Not a substrate-portable mechanism under its own name. Its machinery — concavification, the Bayes-plausible posterior mixture, simplex geometry, the commitment device — is bound to committed sender-receiver games. The travelling lesson (information-structure choice is consequential even under truthfulness) is carried by gatekeeping, framing, information_asymmetry, and commitment; invoking "Bayesian persuasion" for an institution that merely shapes what its audience learns, without a binding signal structure, borrows the coarsen-the-signal idea while dropping the concavification-under-commitment that is the concept's content.

Scope of Application¶

Bayesian persuasion lives within a single home discipline — the information-design field it founded within economic theory — restaged across its application domains; its reach is bounded to committed sender-receiver games with a Bayes-rational receiver and a binding public signal structure, and the travelling lesson (information-structure choice is consequential even under strict truthfulness) is carried by the parents gatekeeping, framing, information_asymmetry, and commitment, not by the concavification-under-commitment machinery.

Information design in markets — prosecutor evidence design, credit-rating granularity, and exam-certification thresholds, each a sender choosing the informativeness of a truthful signal.
Regulatory disclosure — stress tests, drug labels, and calorie counts, where the regulator chooses how informative a public signal will be, knowing the audience Bayes-updates on it.
Advertising and recommendation systems — which reviews to surface or products to feature, shaping posteriors without saying anything false.
Political communication — which polls or endorsements to commission, knowing voters will rationally update on the outcome.

Clarity¶

Bayesian persuasion makes legible a lever that the lying-versus-truth dichotomy renders invisible: a sender who cannot say anything false, facing a fully rational receiver, still holds enormous strategic latitude through the design of the experiment — the choice of how informative the public signal will be. The folk model of influence locates a communicator's power in the content of the message and asks whether it is honest; this concept relocates the power to the structure of disclosure and shows that even at full honesty the structure is a decision variable. The crisp separation it draws is between deception, which the framework forbids, and informativeness choice, which is the entire game — and the surprising content is that committing to a less than fully revealing signal can strictly beat full disclosure, because coarsening the signal pools states in a way that pushes the receiver's posterior across an action threshold it would not otherwise cross. Persuasion is thereby reframed as posterior-mixture design rather than misrepresentation.

The concept also makes commitment a load-bearing object the practitioner must check for rather than assume. The whole result hinges on the signal structure being public and binding: if the sender could secretly re-choose the experiment after observing the state, the receiver would discount every message and the situation would collapse to cheap talk, where influence is capped by how well sender and receiver preferences already align. Naming the equilibrium this way sharpens the operative question from "what should I say?" to "what experiment should I commit to, and what institution makes that commitment credible?" — directing attention to the disclosure rule, the credentialing body, or the regulatory mandate that does the binding. It also keeps Bayes-plausibility in view: because the induced posteriors must average back to the prior, the sender cannot manufacture belief freely but only redistribute it, so the design problem is the genuinely constrained one of choosing which posteriors to make likely, not a license to move beliefs at will.

Manages Complexity¶

The sprawl Bayesian persuasion compresses is the continuum of disclosure strategies a sender could adopt. An information experiment is any conditional distribution of signals on states, so the strategy space is enormous — every degree of informativeness from full revelation to silence, every way of pooling and partitioning states into messages — and it recurs anew in each application: which evidence a prosecutor presents, how granular a rating agency's grades are, how much a stress test reveals, which reviews a platform surfaces. Confronted naively, the sender would have to search that whole space of experiments separately for every case. The concept collapses the search to a single geometric operation. Because what the receiver does depends only on the posterior they hold, and an experiment is exactly a Bayes-plausible distribution over posteriors (a distribution that must average back to the prior), the sender's problem reduces to: take the sender's value as a function of the receiver's posterior over the belief simplex, form its concave closure, and evaluate that closure at the prior. The entire continuum of experiments is replaced by one curve and one geometric construction on it.

What the analyst then tracks shrinks to a small, fixed set: the receiver's belief-to-action map (which determines the value-over-posteriors function and, in particular, its non-concavities — the action thresholds), and the prior (the point at which the concave hull is read). From these the qualitative outcome falls out directly. The decisive branch is whether the value function is already concave at the prior or not: where it is, full disclosure is optimal and the sender has nothing to gain by coarsening; where it is not — where the prior sits under a non-concavity — committing to a strictly partial experiment beats full disclosure, and the optimal coarsening is read off as the chord of the concave hull, the specific mixture of posteriors (one pushed across an action threshold, one held below) that the sender should make likely. So instead of evaluating message after message, the analyst inspects one function for its non-concave regions, locates the prior relative to them, and reads off both whether persuasion has any bite and exactly how coarse the optimal signal is — the high-dimensional strategy problem reduced to a concavification with a single read-off point and a clean binary at its center.

Abstract Reasoning¶

Bayesian persuasion licenses inferences that reframe influence as the design of an information experiment and reduce the optimization to a single geometric operation.

Start from the receiver's belief-to-action map, not from the message. The foundational move is to reason backward from how the receiver acts: because the receiver's action depends only on the posterior they hold, the analyst first specifies the belief-to-action map and reads off its thresholds — the posteriors at which the receiver switches action. The inference is that persuasion has bite only where moving a posterior across such a threshold changes the receiver's choice in the sender's favor, so the analyst reasons about which posterior regions are worth inducing before considering any signal. This inverts the folk model, which would start from message content.

Concavify the value function over posteriors. The signature technical move is to express the sender's payoff as a function of the receiver's posterior over the belief simplex, form its concave closure, and evaluate that closure at the prior. The analyst infers the highest achievable sender value directly from this construction, and reads the optimal experiment off the chord of the concave hull at the prior — the specific Bayes-plausible mixture of posteriors that achieves the hull. The entire continuum of possible experiments is thereby replaced by one curve and one geometric operation, so the analyst reasons about a single function's shape rather than searching the space of signal structures.

The decisive binary — is the value function concave at the prior? A central diagnostic move follows immediately: inspect whether the value function is already concave at the prior. If it is, the analyst infers that full disclosure is optimal and coarsening gains nothing; if the prior sits under a non-concavity, the analyst infers that a strictly partial experiment beats full disclosure, and the optimal coarsening pools states so as to push one posterior across an action threshold while holding another below it. So from the location of the prior relative to the function's non-concave regions, the analyst predicts both whether persuasion is profitable at all and how coarse the optimal signal should be — the surprising content being that committing to a less revealing signal can strictly dominate full disclosure.

Bayes-plausibility as the binding constraint. A guarding inference is that the sender cannot manufacture belief freely but only redistribute it: the induced posteriors must average back to the prior. The analyst reasons that the design problem is the constrained one of choosing which posteriors to make likely (subject to that averaging constraint), not a license to move beliefs at will — so any proposed mixture of posteriors is checked for Bayes-plausibility before it is admitted as a feasible experiment.

Commitment as a precondition to check, not assume. A boundary move is to verify that the signal structure is public and binding before applying the whole apparatus. The analyst infers that if the sender could secretly re-choose the experiment after observing the state, the receiver would discount every message and the situation would collapse to cheap talk, where influence is capped by sender-receiver preference alignment. So the operative question shifts from "what should I say?" to "what experiment should I commit to, and what institution (disclosure rule, credentialing body, regulatory mandate) makes that commitment credible?" — and absent a commitment device, the analyst predicts the persuasion result does not hold.

Deception-versus-informativeness boundary. Finally, the concept licenses a sharp separation the lying-versus-truth dichotomy hides: the analyst reasons that the sender's strategic latitude lives entirely in informativeness choice (the coarseness of a truthful signal), not in misrepresentation, and so analyzes a fully honest sender as still holding a consequential decision variable — relocating the power of a communicator from message content to disclosure structure.

Knowledge Transfer¶

Within economic theory and the information-design field it founded, Bayesian persuasion transfers as mechanism: the backward-from-the-receiver reasoning (specify the belief-to-action map and locate its thresholds before considering any signal), the signature concavification technique (express the sender's value over posteriors, take its concave closure, evaluate at the prior, and read the optimal experiment off the chord), the decisive binary (is the value function concave at the prior? if not, partial disclosure strictly beats full disclosure), and the two preconditions to verify (Bayes-plausibility as the binding constraint; commitment as the institutional precondition) all carry intact wherever a sender commits to a public signal structure faced by a Bayes-rational receiver. So the same apparatus and the same concavification operation apply across information design in markets (prosecutor evidence design, credit-rating granularity, exam certification thresholds), regulatory disclosure (stress tests, drug labels, calorie counts), advertising and recommendation systems (which reviews to surface), and political communication (which polls or endorsements to commission). These are application domains of one model — all sender-receiver games with commitment — not structurally distinct substrates, so this is reach within a domain; the concavification technique itself exports cleanly to the neighbouring mechanism-design, contract-theory, and platform literatures because those share the substrate.

Beyond sender-receiver games with commitment the honest characterisation is a shared abstract insight carried by component primes, not the Bayesian-persuasion model itself. The model's load-bearing commitments — Bayes-plausibility, concavification, sender-side commitment to a binding signal structure, a fully Bayesian receiver — are formal game-theoretic constructs, and outside game-theoretic and mechanism-design substrates they do not transfer with structural fidelity. What does carry broadly is the deeper lesson the model sharpens: the choice of information structure is strategically consequential even under strict truthfulness — the power of a communicator can live in the coarseness of disclosure rather than in the content of the message. That insight genuinely recurs across domains, but it is housed in primes the catalog already holds: gatekeeping and a selective-disclosure pattern (what is allowed through, at what granularity), framing (how a truthful signal is structured shapes the response), information_asymmetry (the gap the sender exploits), signal_extraction (the receiver's inference problem), and commitment (the precondition that separates persuasion from cheap talk). When a cross-domain analyst needs the lesson — that an honest communicator still wields a consequential design variable in how informative they choose to be — it should be carried by those parents, of which Bayesian persuasion is one specific formalisation in one substrate. The home-bound cargo is the model's machinery: the concavification of the value function, the Bayes-plausible posterior mixture, the simplex geometry, and the commitment-device apparatus (disclosure rules, credentialing, regulatory mandates). So the honest move is to attribute the cross-domain reach to the disclosure-and-framing primes, and to treat an invocation of "Bayesian persuasion" outside a committed sender-receiver game — say, for an institution that merely shapes what its audience learns without a binding signal structure — as analogy that borrows the coarsen-the-signal idea while dropping the concavification-under-commitment that is the concept's actual content (see Structural Core vs. Domain Accent).

Examples¶

Canonical¶

Kamenica and Gentzkow's 2011 prosecutor-and-judge example is the defining worked case. A defendant is guilty with prior probability 0.3; a Bayes-rational judge convicts only if her posterior probability of guilt is at least 0.5, and the prosecutor wants to maximize the conviction rate but cannot lie. Under full disclosure the judge convicts only the guilty — 30% of the time. Instead the prosecutor publicly commits to an investigation that emits just two verdicts, "convict" and "acquit," calibrated so that every "convict" carries posterior guilt of exactly 0.5. Sending all guilty defendants (0.3) plus a fraction of innocents to "convict" such that 0.3 / (0.3 + innocent share) = 0.5 requires an innocent share of 0.3, so "convict" fires with total probability 0.6. The judge, rationally trusting the committed signal, convicts 60% of the time — double the full-disclosure rate — without a single false statement, because the coarsened signal pools some innocents with the guilty right at her threshold.

Mapped back: The prosecutor is the sender and the judge the receiver, whose "convict if posterior ≥ 0.5" rule is the receiver's belief-to-action map. The publicly calibrated two-verdict investigation is the committed information experiment. That the two messages' posteriors average back to the prior (0.6 × 0.5 + 0.4 × 0 = 0.3) is the Bayes-plausibility constraint, and beating full disclosure by coarsening is the partial-disclosure result.

Applied / In Practice¶

Post-2008 bank stress tests are analyzed as Bayesian persuasion in practice. A regulator (for example the Federal Reserve) learns each bank's true condition and must decide how much of that information to disclose to markets. Full disclosure risks triggering a run on a weak bank; total opacity leaves investors unable to trust any bank. The regulator instead commits in advance to a public testing-and-disclosure methodology — the scenarios, the pass thresholds, and what results are released — and markets Bayes-update on the published outcomes. By choosing the coarseness of what is revealed (a pass/fail grade rather than a full balance-sheet dump), the regulator can shift market beliefs enough to preserve confidence and recapitalize the system while disclosing nothing false, exactly the informativeness-design lever the model formalizes (Goldstein and Leitner and related work).

Mapped back: The regulator is the sender and the market the receiver. Publicly fixing the stress-test methodology before results are known is the commitment precondition — without a binding rule, banks could re-choose disclosures and markets would discount them (cheap talk). Choosing pass/fail granularity rather than raw data is the posterior-mixture design operating on the value-over-posteriors function: the regulator picks how informative a truthful signal to release, not what to falsify.

Structural Tensions¶

T1: Truthfulness as constraint versus truthfulness as cover (honest influence that is harder to resist). The model's defining and normatively reassuring feature is that the sender cannot lie: the signal structure is public, binding, and truthful, and the receiver is fully Bayesian. But the same truthfulness is what makes the influence hard to contest. A receiver confronting a coarsened-but-honest signal has no falsehood to catch and no misrepresentation to flag, yet is being maneuvered — via the choice of informativeness — toward the action the sender prefers and away from what full disclosure would have prompted. The prosecutor's 60% conviction rate is achieved without a single false statement. The tension is that "cannot lie" reads as a protection for the receiver while functioning as a more effective, less detectable mode of influence than lying would be. Diagnostic: Is the sender's truthfulness protecting the receiver, or licensing a manipulation the receiver cannot flag precisely because nothing said is false?

T2: Commitment as enabler versus commitment as binding and institution-dependent (the device that empowers also constrains). Commitment is load-bearing: without a binding signal structure the game collapses to cheap talk, and it is exactly the power to commit that lets the sender profit. Yet commitment is double-edged. It binds the sender ex post — once the experiment is fixed, the sender must honor the realized signal even when the true state is unfavorable and they would dearly like to renege — which is precisely why it works ex ante, but also why it is not free. And it exists only when some external institution (a disclosure rule, a credentialing body, a regulatory mandate) makes it credible; where no such device exists, the whole apparatus does not apply and influence reverts to preference-alignment. The tension is that the sender's power flows entirely from a constraint they must accept and an institution they may not have. Diagnostic: Is the commitment genuinely binding through an enforcing institution, or merely assumed — and would the sender honor the signal ex post when the realized state cuts against them?

T3: Bayes-rational receiver versus real audiences (an idealization the predictions depend on). The concavification result presumes a receiver who knows the committed signal structure and inverts it by exact Bayes updating. That idealization is what delivers the crisp predictions — the 60% conviction, the preserved market confidence. Real receivers are boundedly rational: they may not know the experiment, may over- or under-react, may naively trust or reflexively discount. Departures cut both ways — a credulous receiver can be moved further than the model allows, a suspicious one refuses to update as required and the optimal experiment misfires — so the prediction is fragile in either direction. The tension is that the model's elegance and its exact action forecasts rest on a receiver whose real-world counterpart rarely updates as assumed. Diagnostic: Does the receiver actually know and correctly invert the committed signal structure, or does bounded rationality break the concavification's exact prediction (in either direction)?

T4: The memorable "reveal less" result versus its geometric conditionality (not a universal rule). The concept is famous for the counter-intuitive finding that committing to a less than fully revealing signal can strictly beat full disclosure — and this is the lesson most often carried away. But it holds only where the prior sits under a non-concavity of the sender's value-over-posteriors function; where that function is already concave at the prior, full disclosure is optimal and coarsening gains nothing. Treating "reveal less" as the general prescription inverts the actual result, which is that the optimal informativeness is whatever the concave hull dictates at the prior, sometimes full and sometimes partial. The tension is that the concept's most quotable takeaway is a special case its own geometry frequently contradicts. Diagnostic: Does the prior sit under a non-concavity so that coarsening genuinely helps, or is full disclosure in fact optimal here and "reveal less" a misapplied slogan?

T5: Autonomy versus reduction (a game-theoretic model or the disclosure-and-framing primes it formalizes). Bayesian persuasion is a named, precisely specified model with heavy proprietary machinery — Bayes-plausibility, the concavification of the value function over the simplex, sender-side commitment to a binding experiment, a fully Bayesian receiver — and within information design it travels as full mechanism across evidence design, ratings, stress tests, and recommendation systems. But the deeper lesson it sharpens — that the choice of information structure is strategically consequential even under strict truthfulness, so a communicator's power can live in the coarseness of disclosure rather than the content of the message — is housed in parents the catalog already holds: gatekeeping, framing, information_asymmetry, and commitment. Invoking "Bayesian persuasion" for an institution that merely shapes what its audience learns, without a binding signal structure, borrows the coarsen-the-signal idea while dropping the concavification-under-commitment that is the concept's actual content. Diagnostic: Resolve toward gatekeeping/framing/information_asymmetry/commitment when carrying the lesson outside a committed sender-receiver game; toward Bayesian persuasion only where a binding public experiment faces a Bayes-rational receiver.

Structural–Framed Character¶

Bayesian persuasion sits toward the structural side — best read as mixed-structural, at the domain-bound edge of that band and a shade more framed than Bayesian Nash equilibrium, because it is a neutral formal model whose commitment precondition ties it to institutional substrates. The five criteria lean structural with two framed pulls. On evaluative weight it reads mostly structural: the concept is an optimization over information experiments — a geometric result (concavification) — that renders no verdict, though its subject is "persuasion" and its T1 flags that honest influence can be a manipulation the receiver cannot flag, giving it a faint valence a pure mechanism lacks. On human-practice-bound it reads framed-leaning: the model requires a sender, a fully Bayes-rational receiver, and a binding commitment device that "exists only when some external institution (a disclosure rule, a credentialing body, a regulatory mandate) makes it credible" — so it is bound not just to strategic agents but to an institution that does the binding, and collapses to cheap talk without one. On institutional origin it reads structural: "Bayesian persuasion" is a named theoretical model (Kamenica and Gentzkow 2011), a defined construct of information-design theory, not an artifact of a survey or agency. On vocab-travels it is mixed: the operative machinery — concavification, Bayes-plausibility, the posterior-mixture, simplex geometry, the commitment device — travels intact across evidence design, ratings, stress tests, and recommendation systems, but the entry stresses these are "application domains of one model," and the machinery does not transfer with fidelity beyond committed sender-receiver games. On import-vs-recognize the profile is within-substrate recognition: genuinely the same mechanism across information-design applications, but beyond committed games only the disclosure-and-framing lesson travels through the parents, and any further invocation is "analogy that borrows the coarsen-the-signal idea."

Here the portable structural skeleton is a composition the entry demonstrably needs: the choice of information structure is strategically consequential even under strict truthfulness — a communicator's power can live in the coarseness of disclosure, not the content of the message — housed in gatekeeping and selective disclosure (what passes, at what granularity), framing (how a truthful signal is structured shapes response), information_asymmetry (the gap exploited), signal_extraction (the receiver's inference), and commitment (the precondition separating persuasion from cheap talk). That insight is genuinely substrate-spanning, but it is exactly what Bayesian persuasion instantiates from those umbrella primes, not a force the named model carries beyond its substrate — the entry is explicit that "when a cross-domain analyst needs the lesson... it should be carried by those parents, of which Bayesian persuasion is one specific formalisation in one substrate." So the cross-domain reach belongs to the disclosure-and-framing primes, while the domain-accented machinery — the concavification of the value function, the Bayes-plausible posterior mixture, the simplex geometry, the commitment-device apparatus — stays bound to committed sender-receiver games. Its character: an evaluatively near-neutral formal information-design model recognised as the same construct across its applications, structural in skeleton yet a named composition of disclosure-and-framing primes whose concavification-under-commitment machinery is bound to institutional commitment devices — mixed-structural, at the domain-bound edge, and short of a prime because its portable lesson already lives in its parents.

Structural Core vs. Domain Accent¶

This section settles why Bayesian persuasion is a domain-specific abstraction and not a prime — the case for its domain-specificity, kept separate from the mixed-structural placement above.

What is skeletal (could lift toward a cross-domain prime). Strip away the game theory and a thin relational structure survives: a party who cannot misrepresent still shifts a second party's choice by choosing how informative a truthful signal will be — the power lives in the coarseness of disclosure, not in the content of the message. The portable pieces are abstract: a target audience whose action depends only on its own belief, a truthful channel whose granularity is a decision variable, a redistribution of belief that cannot be manufactured from nothing but only reallocated, and a binding of the signaller that makes the whole thing credible. That skeleton is genuinely substrate-portable, which is exactly why the entry names it as a composition it demonstrably needs — gatekeeping (what passes, at what granularity), framing (how a truthful signal is structured shapes response), information_asymmetry (the gap the sender exploits), signal_extraction (the receiver's inference problem), and commitment (the precondition separating persuasion from cheap talk). But this is the core Bayesian persuasion shares with those parents, not what makes it distinctive.

What is domain-bound. Almost all of the content is information-design furniture, and none of it survives extraction intact: the concavification of the sender's value function over the belief simplex; the Bayes-plausibility constraint that induced posteriors average back to the prior; the posterior-mixture design that recasts an experiment as a distribution over the receiver's posteriors; the simplex geometry whose non-concavities are the action thresholds; the fully-Bayesian receiver who inverts the committed structure by exact updating; the memorable "reveal less under a non-concavity" result; and the commitment-device apparatus — disclosure rules, credentialing bodies, regulatory mandates — that makes the binding real. These are the worked vocabulary, the instruments, and the empirical cases (prosecutor evidence design, credit-rating granularity, stress-test disclosure) the field actually studies, all specific to committed sender-receiver games. The decisive test: remove the binding public signal structure and the whole apparatus collapses to cheap talk, capped by preference alignment — it is no longer Bayesian persuasion but a looser, discountable communication problem, because the concavification-under-commitment that is the concept's content has nothing left to grip.

Why this does not clear the prime bar. A prime is a relational structure whose vocabulary travels and whose cross-domain transfer is recognition of the same mechanism, not analogy. Bayesian persuasion's transfer is bimodal. Within the information-design field it founded, the mechanism travels intact across information design in markets, regulatory disclosure, advertising and recommendation systems, and political communication — the same concavification operation, the same backward-from-the-receiver reasoning, the same Bayes-plausibility and commitment checks — because these are application domains of one model, not distinct substrates. Beyond committed sender-receiver games it travels only by analogy: invoking "Bayesian persuasion" for an institution that merely shapes what its audience learns, without a binding signal structure, borrows the coarsen-the-signal idea while dropping the machinery. And when the bare structural lesson is wanted cross-domain — that an honest communicator still wields a consequential design variable in how informative they choose to be — it is already carried, in more general form, by the parents Bayesian persuasion instantiates. The cross-domain reach belongs to gatekeeping, framing, information_asymmetry, signal_extraction, and commitment; "Bayesian persuasion," as named, carries game-theoretic baggage that should stay home in the committed sender-receiver substrate.

Relationships to Other Abstractions¶

Current abstraction Bayesian Persuasion Domain-specific

Parents (5) — more general patterns this builds on

Bayesian Persuasion is part of Bayesian Updating Prime

Bayesian Persuasion contains the receiver's prior-to-posterior update on each realized signal, which is the belief-to-action link the sender designs around.
Bayesian Persuasion presupposes Credible Commitment Prime

Bayesian Persuasion presupposes a publicly believable ex-ante commitment to honor the chosen signal structure after the state is realized.
Bayesian Persuasion presupposes Information Asymmetry Prime

Persuasion presupposes that the receiver lacks payoff-relevant state information that the committed experiment can selectively reveal.
Bayesian Persuasion is a decomposition of Framing Prime

Removing the game-theoretic frame leaves truthful presentation structure altering evaluation and action even though no underlying fact is falsified.
Bayesian Persuasion is a decomposition of Gatekeeping Prime

Stripping the posterior-simplex apparatus leaves selective passage control: the sender chooses which distinctions reach the receiver and at what granularity.

Hierarchy paths (10) — routes to 8 parentless roots

Bayesian Persuasion → Credible Commitment → Commitment → Constraint

Not to Be Confused With¶

Mechanism design. The sibling design problem within game theory: given a target outcome, choose the rules, payoffs, and allocations — the incentive structure — that implement it. Bayesian persuasion holds the payoffs and allocation fixed and designs only the information the receiver gets. The two are complementary levers on a strategic situation, not the same one. Tell: is the designer choosing who gets what and how much they pay (mechanism design), or choosing how informative a truthful public signal about the state will be while leaving the payoff rules untouched (Bayesian persuasion)?
Information design (the general field). The broader theory of which Bayesian persuasion is the canonical single-sender, single-receiver case; the field also covers multiple senders competing to inform, multiple receivers, private/discriminatory signals, and dynamic information provision. Part-versus-whole: results like sender competition eroding the persuasion advantage belong to the wider field, not to the one-sender model. Tell: is there exactly one committed sender facing one Bayes-rational receiver (Bayesian persuasion), or a richer configuration of competing senders or many receivers (general information design)?
Verifiable-disclosure / unravelling games (Grossman–Milgrom). Disclosure games where a sender holds hard, verifiable evidence and chooses what to reveal; the classic result is that a rational receiver's skepticism drives unravelling toward full disclosure. This looks like persuasion but runs the opposite way: the sender cannot commit to a signal structure in advance and can only selectively withhold provable facts, so silence is interpreted adversely. Bayesian persuasion's sender commits ex ante to a possibly-coarse experiment and can profitably reveal less. Tell: does the sender selectively disclose verifiable facts with no prior commitment (unravelling toward full disclosure), or commit up front to an informativeness level that a skeptical receiver still trusts because it is binding (Bayesian persuasion)?
Rational inattention. The mirror-image problem: the receiver chooses how much costly attention to pay and thus how informative their own signal is, given a fixed information environment. Bayesian persuasion puts the informativeness choice on the sender's side and treats the receiver as a costless, exact Bayesian updater. Tell: who controls the coarseness of what is learned — the audience deciding how hard to look (rational inattention), or the communicator committing to how much to reveal (Bayesian persuasion)?
Nudging / choice architecture. Behavioral influence that steers a decision through presentation, defaults, and salience, typically exploiting a boundedly rational audience and requiring no commitment device or Bayesian receiver. Bayesian persuasion's entire result depends on a fully Bayes-rational receiver who correctly inverts a committed signal structure (T3), so its influence is achieved through the informativeness of honest signals, not through cognitive biases. Tell: does the influence work by exploiting the audience's psychology and framing effects on a non-Bayesian agent (nudging), or by optimally coarsening a truthful signal a rational agent will correctly update on (Bayesian persuasion)?
The parent primes it instantiates (gatekeeping, framing, information_asymmetry, signal_extraction, commitment). The substrate-neutral pieces whose composition Bayesian persuasion formalizes — selective disclosure at chosen granularity, structure-shaped response, the exploited information gap, the receiver's inference, and the binding precondition — not confusable peers. Outside committed sender-receiver games it is these parents that carry the lesson that information-structure choice matters even under truthfulness. Tell: strip the binding public experiment and Bayes-rational receiver and what remains is gatekeeping/framing/commitment, not "Bayesian persuasion." The parents — treated fully in the sections above — hold the cross-domain reach; the named model holds only where a committed experiment faces a Bayesian receiver.

Neighborhood in Abstraction Space¶

Bayesian Persuasion sits in a crowded region of the domain-specific corpus (28^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Unclustered & Miscellaneous (309 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12