Persuasion Duality: Structural Asymmetries

• Persuasion Duality is a framework capturing two-sided asymmetries, contrasting message production with verification and linking latent cognition to observable dialogue.
• It spans diverse fields—Bayesian persuasion, computational complexity, and multi-agent systems—each highlighting a unique duality between design and evaluation.
• The concept underpins key insights in mechanism design, efficiency trade-offs, and safety protocols, offering actionable guidance for theory and practical applications.

Persuasion Duality is a label used in several research traditions to denote a structured asymmetry within persuasion rather than a single doctrine. In Bayesian persuasion and information design, it commonly refers to a primal–dual relation between signal design and a price- or value-based dual problem, or to a gap between feasible persuasion schemes and their supporting hyperplanes (Dworczak et al., 2019). In computational work, it denotes the asymmetry between the difficulty of producing persuasive messages and the relative ease of verifying or adopting them once supplied (Wojtowicz, 2024). In dialogue and multi-agent systems, it denotes paired oppositions such as hidden mental states versus observable language, or internal reasoning that simultaneously increases resistance to persuasion and, when exposed, increases persuasive efficacy (Zhang et al., 28 Feb 2025, Zhao et al., 25 Sep 2025). Across these uses, the term consistently marks a two-sided structure in which the same mechanism supports opposed roles, constraints, or forms of leverage.

1. Conceptual scope

The literature uses the expression for multiple formal asymmetries rather than a single canonical definition.

Research area	Core duality	Representative papers
Bayesian persuasion	Primal signal design vs dual price/supergradient characterization	(Dworczak et al., 2019, Dughmi et al., 2019)
Computational complexity	Hard message production vs easy verification/adoption	(Wojtowicz, 2024)
Non-linear and geometric persuasion	Contact-set structure, pairwise pooling, productive transport	(Kolotilin et al., 2022, Kolotilin et al., 2023, Anunrojwong et al., 2022)
Dynamic and network persuasion	Static–dynamic equivalence or breakdown; gains and losses from communication	(Kobayashi, 17 Aug 2025, Aïd et al., 2024, Kerman et al., 11 Sep 2025)
Dialogue modeling	Hidden mental states vs observable dialogue under “Double Blind” conditions	(Zhang et al., 28 Feb 2025, Zhang et al., 18 May 2026)
Multi-agent LLM systems	Resistance from internal reasoning vs influence from exposed reasoning	(Zhao et al., 25 Sep 2025)
Argumentation dynamics	Local persuasion acts vs global temporal properties	(Arisaka et al., 2017)

A recurring pattern is that persuasion is modeled as a coupling between two levels: search and verification, latent cognition and public explanation, or signal design and its dual certificate. This suggests that “Persuasion Duality” functions less as a unitary theory than as a family of structurally related asymmetries.

2. Price-based and mechanism-design dualities

In Bayesian persuasion, the standard duality is formulated over distributions of posteriors. With prior belief $\mu_0 \in \Delta(\Omega)$ and sender payoff $V:\Delta(\Omega)\to\mathbb{R}$, the primal problem is

$$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$

where

$$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$

The dual problem introduces a Lipschitz price function $p\in \Lip(\Omega)$ and minimizes

$$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$

over

$\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$

The optimal dual variable is interpreted as a price function on the state space and is a supergradient of the concave closure of the objective function at the prior belief. Weak duality gives $\widehat V(\mu_0)\le \widetilde V(\mu_0)$, and the no-gap result yields $\widehat V(\mu_0)=\widetilde V(\mu_0)$. When $V$ is Lipschitz on $V:\Delta(\Omega)\to\mathbb{R}$0, strong duality holds and the dual is attained (Dworczak et al., 2019).

The same paper extends this logic to moment persuasion. When the objective depends on the posterior through a set of moments, the state price function induces prices on posterior moments. In that setting, the dual object becomes a convex majorant $V:\Delta(\Omega)\to\mathbb{R}$1 on the moment space, together with moment prices $V:\Delta(\Omega)\to\mathbb{R}$2 that appear as tangent hyperplanes. This yields necessary and sufficient conditions for convex-partitional signals and explicit structure in the two-dimensional quadratic case.

A related tradition imports Lagrangian duality from mechanism design. In single-receiver Bayesian persuasion with payments, the primal linear program includes persuasiveness constraints

$V:\Delta(\Omega)\to\mathbb{R}$3

and dual multipliers $V:\Delta(\Omega)\to\mathbb{R}$4 attached to those constraints generate a dual-adjusted receiver payoff

$V:\Delta(\Omega)\to\mathbb{R}$5

Optimal signaling then recommends, in each state, an action maximizing $V:\Delta(\Omega)\to\mathbb{R}$6. With arbitrary payments and symmetric $V:\Delta(\Omega)\to\mathbb{R}$7 actions, the optimal scheme recommends the action maximizing $V:\Delta(\Omega)\to\mathbb{R}$8; in the two-action case the canonical rule becomes $V:\Delta(\Omega)\to\mathbb{R}$9 (Dughmi et al., 2019). In this formulation, persuasion duality is the analogue of revenue duality in auction theory: persuasiveness constraints play the role of incentive compatibility, and dual variables act as shadow prices or virtual utilities.

3. Geometry, contact sets, and non-linear preferences

A second major meaning of Persuasion Duality appears when the receiver’s action is one-dimensional and preferences are single-peaked but non-linear. In that setting, the receiver’s best response is characterized by a first-order condition rather than by posterior means alone. The persuasion problem can be written as an outcome-based linear program over joint distributions $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$0 on $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$1, with the state marginal fixed and obedience encoded by

$$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$2

for measurable action sets. The dual introduces a state price function $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$3 and an obedience multiplier $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$4 satisfying

$$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$5

The associated contact set is

$$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$6

An implementable outcome is optimal if and only if its support is contained in $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$7 (Kolotilin et al., 2022).

Complementary slackness yields a sender-side first-order condition on the contact set,

$$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$8

and this drives the geometry of optimal signals. In both the non-linear persuasion formulation and its “optimal productive transport” extension, pairwise signals are always without loss: every signal can be replaced by one in which each realization pools at most two states. Under a twist condition, expressed as a non-vanishing determinant involving $$\widehat V(\mu_0):=\sup_{\tau\in T(\mu_0)} \int_{\Delta(\Omega)} V(\mu)\, d\tau(\mu),$$9, $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$0, and $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$1 across triples of states, pairwise signals are the only optimal solutions (Kolotilin et al., 2022, Kolotilin et al., 2023).

This dual geometry also distinguishes full disclosure from negative assortative disclosure. Full disclosure is optimal if and only if, for all two-point posteriors $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$2,

$$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$3

When the sender strictly prefers pooling and the contact set is strictly single-dipped or single-peaked, optimal disclosure becomes negative assortative: the support at each action is a pair $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$4 with one branch decreasing and the other increasing in the action, and the optimal pairing is characterized by a pair of ordinary differential equations, one from obedience and one from the dual first-order condition (Kolotilin et al., 2022, Kolotilin et al., 2023).

A related geometric formulation arises with risk-conscious receivers whose utility is nonlinear in belief. There the standard revelation principle fails, and the problem is rewritten in terms of belief regions

$$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$5

The sender then solves a convex program over joint probabilities $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$6 subject to

$$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$7

and $$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$8. Full persuasion is possible if and only if the target allocation

$$T(\mu_0) = \left\{\tau\in \Delta(\Delta(\Omega)):\, \int_{\Delta (\Omega)} \mu\, d \tau (\mu) = \mu_0 \right\}.$$9

is feasible. In binary persuasion under a convexity assumption, the problem reduces to a linear program, and the canonical signal set consists of pure states together with boundary beliefs in $p\in \Lip(\Omega)$0 (Anunrojwong et al., 2022).

4. Complexity, dynamics, and networks

In computational complexity theory, Persuasion Duality names a search–verification asymmetry. Informational persuasion is formalized as the decision problem: given a probability space $p\in \Lip(\Omega)$1, a focal event $p\in \Lip(\Omega)$2, a set of facts $p\in \Lip(\Omega)$3, and a threshold $p\in \Lip(\Omega)$4, is there a subset $p\in \Lip(\Omega)$5 such that

$p\in \Lip(\Omega)$6

The paper proves that informational persuasion is NP-Complete. Producing persuasion is NP-hard via reduction from exact cover, whereas verifying that a given subset $p\in \Lip(\Omega)$7 is persuasive is in NP because set intersection, function lookup, and arithmetic can be implemented in linear time by a deterministic Turing machine (Wojtowicz, 2024). In this usage, persuasion is hard to discover but easy to adopt or certify once supplied.

Dynamic work introduces a different duality: equivalence, or non-equivalence, between static and sequential information release. With a Bayesian sender and a non-Bayesian receiver, divisible updating rules imply

$p\in \Lip(\Omega)$8

so one-shot and two-step persuasion have the same feasible ex-ante payoff set. Under Grether’s $p\in \Lip(\Omega)$9–$$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$0 rule, this equivalence breaks. In the two-state judge–prosecutor environment with $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$1, two-step persuasion is strictly better when $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$2, strictly worse when $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$3, and equal when $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$4 (Kobayashi, 17 Aug 2025). Related work on dynamic competitive persuasion interprets the no-price case as a static–dynamic duality in which average subgame-perfect equilibrium payoffs coincide with the one-shot Cotton game, whereas with prices and sufficient patience a folk theorem yields the full feasible individually rational payoff set $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$5 (Whitmeyer, 2018).

Continuous-time persuasion by filtering embeds the sender in a Stackelberg partial-observation control problem. The sender chooses an observation device

$$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$6

while the receiver controls a hidden state process

$$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$7

Filtering converts the receiver’s partial-observation problem into an ergodic control problem on the estimate $$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$8, and the sender’s objective reduces to a static optimization over the stationary distribution induced by the chosen filter parameters (Aïd et al., 2024). This is a continuous-time version of the duality between information design and a value or distributional representation of the receiver’s response.

Network models introduce yet another asymmetry: more communication can help or harm the sender. In a Bayesian persuasion problem with binary states, binary actions, and a critical mass threshold, the sender’s network value satisfies

$$\widetilde V(\mu_0):=\inf_{p \in \mathcal P(V)} \int_{\Omega} p(\omega)\, d \mu_0(\omega),$$9

The empty network achieves the upper bound $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$0, while public signaling yields the lower bound $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$1. However, the value is not monotonic in network density: circle networks can attain $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$2, and suitable extensions of stellar, halo, galaxy, and cluster networks can strictly benefit the sender. Whenever these extensions raise the sender’s value, receivers are strictly worse off because the probability that the final outcome matches the true state decreases (Kerman et al., 11 Sep 2025).

A final dynamic use of the term appears in abstract argumentation. There, persuasion acts are local transition rules over visible arguments, but the resulting transition system is also analyzed globally via CTL formulas such as $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$3, $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$4, and $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$5. Persuasion is therefore both a local dynamics modifier and a global temporal property, tightly coupled to attack and defence relations (Arisaka et al., 2017).

5. Hidden mental states, observable dialogue, and meta-cognition

In persuasive dialogue modeling, Persuasion Duality is often the duality between latent mental states and observable language. The “Double Blind” formulation treats realistic persuasion as a setting in which the persuadee’s beliefs, desires, and intentions are not directly disclosed to the persuader, and the persuader’s strategy is not directly disclosed to the persuadee. Causal Theory of Mind operationalizes this by distinguishing preventive and generative behavior, each with associated belief and desire states, and by making persuasion a joint problem of inference and intervention (Zhang et al., 28 Feb 2025).

The ToMMA framework implements this structure with three agents: persuader, persuadee, and observer. A hidden annotation layer defines preventive and generative content together with belief and desire; the persuader sees only the scenario and dialogue history, the persuadee sees the scenario plus the true mental state, and the observer checks alignment between inferred and true states. The resulting CToMPersu dataset contains 6,275 dialogues, 6,257 unique scenarios, and 35 domains. On dataset-level evaluation, CToMPersu attains Context-Coherence $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$6, Logical-Coherence $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$7, Helpfulness $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$8, Direct Prompting $\mathcal P(V)=\left\{p\in \Lip(\Omega):\, V(\mu)\leq\int_\Omega p(\omega)\, d \mu(\omega) \text{ for all } \mu \in \Delta(\Omega)\right\}.$9, and Causal ToM Eval $\widehat V(\mu_0)\le \widetilde V(\mu_0)$0, whereas DailyPersuasion drops from Direct Prompting $\widehat V(\mu_0)\le \widetilde V(\mu_0)$1 to Causal ToM Eval $\widehat V(\mu_0)\le \widetilde V(\mu_0)$2 (Zhang et al., 28 Feb 2025). The key distinction is that surface persuasiveness and causal faithfulness are not identical; duality arises because high-quality dialogue must align both the hidden mental-state layer and the overt dialogue layer.

MA$\widehat V(\mu_0)\le \widetilde V(\mu_0)$3P makes this dual structure explicit through a meta-cognitive autonomous intelligent agent framework. It consists of three stages—Meta-level Judging, Task-level Persuading, and Knowledge Updating—and a multi-agent architecture with Perception, World Model, Persuader, Short-Term Memory, and Evaluator agents. The meta-cognitive configurator selects a meta-strategy by

$\widehat V(\mu_0)\le \widetilde V(\mu_0)$4

where the score is a case-layer success count for a domain-specific meta-strategy. At the task level, perception and strategy are separated by

$\widehat V(\mu_0)\le \widetilde V(\mu_0)$5

with

$\widehat V(\mu_0)\le \widetilde V(\mu_0)$6

The framework treats persuasion as a coupling between a meta-level “way of thinking” and a task-level turn-by-turn planning process (Zhang et al., 18 May 2026).

This architecture is evaluated on CToMPersu. For gpt-4o-mini, MA$\widehat V(\mu_0)\le \widetilde V(\mu_0)$7P raises Success from $\widehat V(\mu_0)\le \widetilde V(\mu_0)$8 to $\widehat V(\mu_0)\le \widetilde V(\mu_0)$9, Persuasive from $\widehat V(\mu_0)=\widetilde V(\mu_0)$0 to $\widehat V(\mu_0)=\widetilde V(\mu_0)$1, Logic from $\widehat V(\mu_0)=\widetilde V(\mu_0)$2 to $\widehat V(\mu_0)=\widetilde V(\mu_0)$3, Helpful from $\widehat V(\mu_0)=\widetilde V(\mu_0)$4 to $\widehat V(\mu_0)=\widetilde V(\mu_0)$5, and lowers Avg_Turn from $\widehat V(\mu_0)=\widetilde V(\mu_0)$6 to $\widehat V(\mu_0)=\widetilde V(\mu_0)$7. For deepseek-v3, Success rises from $\widehat V(\mu_0)=\widetilde V(\mu_0)$8 to $\widehat V(\mu_0)=\widetilde V(\mu_0)$9 and Avg_Turn falls from $V$0 to $V$1. The ablation without meta-cognitive augmentation (+Auto) improves success but can worsen cross-domain dispersion, whereas the full system reduces Range and SD by using a three-layer knowledge base organized around Cialdini-style meta-strategies, domains, and case counts (Zhang et al., 18 May 2026). In this line of work, Persuasion Duality is a separation between explicit language generation and latent meta-cognitive control.

6. Reasoning models, resistance, and safety

In multi-agent systems built from LLMs and large reasoning models, Persuasion Duality denotes a trade-off created by explicit reasoning. The basic claim is that the mechanisms that make an agent’s arguments more logically coherent and transparent simultaneously make that agent more resistant to being persuaded, yet when these reasoning traces are shared as “thinking content,” they make the same agent much more persuasive to others. The paper formalizes this with three metrics computed on instances where the persuadee was initially correct: Persuaded-Rate (PR), Remain-Rate (RR), and Other-Rate (OR). High RR indicates resistance or belief robustness; high PR indicates susceptibility when acting as a persuadee, or efficacy when evaluating a persuader’s impact (Zhao et al., 25 Sep 2025).

The empirical setting spans objective MMLU multiple-choice questions and subjective claims from PersuasionBench and Perspectrum, using 7 models and 10 modes, including o4-mini, Gemini-2.5-flash, DeepSeek-R1, Qwen3-32B, Hunyuan-7B-Instruct, Qwen2.5-7B-Instruct, and Llama-3-8B-Instruct. When LRMs act as persuadees, enabling thinking mode increases RR and decreases PR. On objective questions, enabling thinking mode reduces PR by about $V$2; when reasoning content from persuaders is also present, the PR reduction is about $V$3. When LRMs act as persuaders, adding thinking content brings an average PR increase of $V$4 on objective tasks.

The same study disentangles length, coherence, and misalignment through ablations. When LRMs persuade other agents, the baseline condition without thinking content yields PR $V$5. Adding native thinking content raises PR to $V$6. Replacing the reasoning with non-semantic padding of equivalent length still yields PR $V$7, showing a substantial length effect. Replacing the reasoning with mismatched thinking content from another LRM drops PR to $V$8, below baseline. This indicates that verbosity alone matters, but coherent and aligned reasoning matters more, while incorrect or mismatched reasoning is actively harmful.

The paper also extends the duality to networked influence. In multi-hop settings, persuasion can amplify when an intermediate agent reformulates an argument in a more effective way, or attenuate when additional hops dilute or distort reasoning. This suggests that Persuasion Duality is not only a property of isolated models but also a property of agent networks. The work explicitly connects these findings to the Elaboration Likelihood Model, distinguishing central routes from peripheral cues, and reports an attention bias in which models allocate high attention to short, confident statements and low attention to longer reasoning segments.

The safety implications are correspondingly two-sided. Transparent reasoning is not unconditionally benign: chain-of-thought sharing can increase persuasive power and can accelerate the spread of misinformation in multi-agent systems. The paper proposes a prompt-level mitigation, adversarial argument detection, which instructs the persuadee to examine logic and evidence, identify unsupported or rhetorical language, and avoid being swayed by confident language without substance. Across multiple models, this reduces PR and increases RR. The practical design guidance is therefore selective sharing of reasoning, a default critical stance for persuadees, explicit management of thinking modes and role assignments, and network-level controls in multi-hop environments.

Taken together, these strands show that Persuasion Duality is best understood as a family of formal asymmetries linking production and adoption, latent cognition and public discourse, and primal design with dual certificates. In economics it clarifies why optimal persuasion is often characterized by prices, supergradients, contact sets, and virtual utilities; in computation it explains why persuasive messages can be difficult to construct but easy to verify; in dialogue and multi-agent systems it highlights how hidden mental states, explicit reasoning, and communication structure can simultaneously strengthen robustness and expand influence.