Persuasion–Accuracy Trade-Off

• Persuasion–accuracy trade-off is defined as the balance between a sender’s persuasive influence and the necessity for truthful, verifiable communication.
• It is mathematically formalized via Bayesian, geometric, and information-theoretic frameworks that delineate how credibility constraints limit persuasion.
• Empirical studies, especially in conversational AI, show that strategies enhancing persuasion can systematically reduce factual accuracy.

The persuasion–accuracy trade-off characterizes the inherent tension between a sender’s ability to influence a receiver’s decision and the constraint that their communications remain accurate or credible. This phenomenon arises across information design, Bayesian persuasion, machine learning, and practical conversational AI, manifesting as a frontier between maximally persuasive and maximally truthful disclosures. The trade-off has been formalized via geometric, information-theoretic, and empirical frameworks, each quantifying the extent to which credibility or accuracy restricts the persuasive power of signals, disclosure policies, or AI-generated content.

1. Formal Models of Persuasion and Credibility Constraints

In classical Bayesian persuasion, a sender observes a private state $\theta \in \Theta$ drawn from a prior $\mu_0 \in \Delta(\Theta)$ and commits to a disclosure policy $\lambda \in \Delta(\Theta \times M)$, inducing a message $m \in M$, which the receiver observes before taking an action $a \in A$. The sender’s and receiver’s payoffs are $u_S(\theta,a)$ and $u_R(\theta,a)$ respectively. Under full commitment, the sender can optimize this policy subject only to the receiver’s obedience constraints (“Receiver-IC”), maximizing her impact on the receiver’s posterior and action (Lin et al., 2022).

Credibility imposes a stricter constraint: a disclosure policy is credible only if the sender cannot profit from undetectably tampering with her messaging (i.e., keeping the marginal message distribution invariant but altering state assignments), formalized as a cyclical monotonicity condition on the induced outcome distribution $\pi \in \Delta(\Theta \times A)$. This restricts the set of implementable outcome distributions beyond mere obedience.

In the high-dimensional “persuasive prediction” setting, absent a shared Bayesian prior, credibility is captured via decision calibration. A randomized predictor $f \in \Delta(\mathcal{H})$ is required to be unbiased, conditioned on the receiver’s best response, ensuring that following the sender’s advice yields no-swap-regret for the receiver. This output-level calibration generalizes the credibility notion to settings where explicit prior agreement is infeasible (Tang et al., 22 May 2025).

When communication is mediated by a noisy or rate-limited channel with capacity $C(Q)$, the information-theoretic constraint on mutual information between state and message directly limits the sender’s ability to induce extreme posteriors and thus to persuade. The average reduction in entropy for the receiver—thereby, the leverage to shift beliefs and actions—is capped by the available channel capacity (Treust et al., 2017).

2. Geometric and Information-Theoretic Characterizations

The structure of the persuasion–accuracy frontier depends on the model’s constraints:

• Under full commitment, the feasible outcome set is characterized by obedience alone, allowing the sender to implement any distribution over actions that aligns with rational receiver updating.
• With credibility, the set contracts to policies whose outcome distributions are both receiver-obedient and sender-cyclically monotone. Geometrically, cyclical monotonicity encodes resistance to undetectable sender deviations—substantially narrowing the set of persuasive equilibria except for state-independent sender payoffs, where this restriction vanishes (Lin et al., 2022).
• Under information constraints, the trade-off is captured by the function $\mu_0 \in \Delta(\Theta)$0, where $\mu_0 \in \Delta(\Theta)$1 is the effective information budget from the channel. As $\mu_0 \in \Delta(\Theta)$2, only trivial (uninformative) persuasion is possible; as $\mu_0 \in \Delta(\Theta)$3, the unconstrained Bayesian persuasion value is recovered. The marginal returns to additional accuracy (or capacity) diminish, reflected in the concavity of $\mu_0 \in \Delta(\Theta)$4 (Treust et al., 2017).
• In decision-calibrated prediction, sender utility $\mu_0 \in \Delta(\Theta)$5 is maximized subject to calibration error $\mu_0 \in \Delta(\Theta)$6: lowering $\mu_0 \in \Delta(\Theta)$7 tightens the accuracy constraint, limiting the sender’s ability to tailor predictions for persuasion. As $\mu_0 \in \Delta(\Theta)$8, the sender is fully accurate but minimally persuasive; as $\mu_0 \in \Delta(\Theta)$9 increases, persuasion improves but accuracy deteriorates (Tang et al., 22 May 2025).

3. Empirical Measurement in Conversational AI

In large-scale experimental studies, the persuasion–accuracy trade-off manifests robustly in the behavior of LLMs tasked with political persuasion. Persuasiveness ($\lambda \in \Delta(\Theta \times M)$0) is operationalized as the experimental shift in attitude caused by AI intervention, while accuracy ($\lambda \in \Delta(\Theta \times M)$1) is measured as the proportion of fact-checkable claims rated above a veracity threshold.

Key findings include:

• Manipulations that most enhance persuasion—reward-model-based post-training (up to +2.3 pp persuasion), information-dense prompting (+2.29 pp, or 27% increase)—often reduce accuracy ($\lambda \in \Delta(\Theta \times M)$2 to $\lambda \in \Delta(\Theta \times M)$3 pp).
• Regression models confirm a negative coefficient for the relationship between persuasion and accuracy at the condition level: as models or prompts become more persuasive, their factuality systematically decreases.
• Information-density (number of fact-checkable claims) is a primary mediator: each extra claim increases persuasion (+0.30 pp under meta-regression) but concomitantly decreases factuality under high-persuasion settings, especially with reward-modeling (Hackenburg et al., 18 Jul 2025).

Lever (AI Setting)	Persuasion Δ (pp)	Accuracy Δ (pp)	Notes
Reward modeling	+2.32	–2.22	Open-source LLMs; frontier models, smaller effect
Information prompting	+2.29	–10 to –16	27% increase in persuasion
Personalization	+0.43	Negligible	Across three methods

This empirical evidence quantifies a practical persuasion–accuracy trade-off at scale: the more persuasive the AI system, the more likely it is to issue inaccurate or unverifiable claims.

4. Restrictive Regimes and Theoretical Limits

Distinct parametric and structural conditions modulate the trade-off’s severity:

• State-independent sender utility (payoff additively separable in state and action) eliminates the trade-off; all disclosure policies remain credible, and persuasion is unconstrained by accuracy (Lin et al., 2022).
• Strong opposition in modularity—strictly supermodular sender payoffs and submodular receiver payoffs—forces every stable policy to be uninformative (all mass on a single action), maximizing the trade-off (Lin et al., 2022).
• Channel-limited persuasion with $\lambda \in \Delta(\Theta \times M)$4 leads to substantial losses in sender payoff relative to the unconstrained case; only as capacity approaches the entropy of the state space does the trade-off dissolve (Treust et al., 2017).
• In the absence of a common prior, demanding stringent decision calibration (low $\lambda \in \Delta(\Theta \times M)$5) reduces persuasive power to that achievable by a perfectly truthful predictor, while relaxing calibration permits greater influence at the cost of bias (Tang et al., 22 May 2025).

5. Algorithmic Solutions and Practical Designs

Learning protocols and persuasion schemes must navigate accuracy–persuasion trade-offs under operational constraints:

• The PerDecCal algorithm efficiently computes decision-calibrated predictors—i.e., optimal compromises on the persuasion–accuracy frontier—using ERM oracles and no-regret dynamics, with theoretical guarantees matching the Bayesian-optimal utility under the same predictor class for the single-receiver case (Tang et al., 22 May 2025).
• In AI deployments, prompt and post-training strategies designed to maximize persuasion often do so by amplifying information density, inherently elevating the risk of factual error (Hackenburg et al., 18 Jul 2025). Personalization effects on the trade-off are weak in current models.
• Information-theoretic constructions using codebooks and channel simulation can asymptotically saturate the upper bound of persuasion dictated by channel capacity, characterizing optimal strategies as those that most efficiently allocate the “accuracy budget” across states and actions (Treust et al., 2017).

6. Policy, Governance, and Societal Implications

The persuasion–accuracy trade-off demands proactive management in both technical and governance regimes:

• Incentive structures favoring persuasion without robust accuracy penalties risk automating large-scale misinformation propagation.
• Transparency, third-party auditing, explicit disclosure of agent identity, and dynamic fact-checking are necessary counterweights as systems are tuned for greater persuasive efficacy.
• Relying solely on restricting access to large, proprietary AI models is insufficient: small open-source models can be post-trained to equivalent persuasive power, implying that system-level guardrails (provenance tracking, standardized accuracy benchmarks, and enforced penalty functions for inaccuracy) must be adopted throughout the AI ecosystem (Hackenburg et al., 18 Jul 2025).
• User-facing controls over claim verifiability and accuracy thresholds could rebalance human–AI interaction along the trade-off frontier, partially mitigating inherent informational dilution.

7. Synthesis and Outlook

The persuasion–accuracy trade-off represents a fundamental, model-agnostic constraint on information design. Across Bayesian, algorithmic, and empirical paradigms, it is governed by the geometric or information-theoretic frontier separating what can be credibly signaled or predicted from what is optimally persuasive. In practice, as the ability to shape beliefs and behavior through communication channels or AI increases, so does the margin for inaccuracy—unless calibrated, capacity-limited, or otherwise credibly restrained mechanisms are implemented. This underscores the necessity for both theoretically grounded and empirically validated frameworks to regulate the design, evaluation, and deployment of persuasive systems, especially as their societal impact scales (Lin et al., 2022, Tang et al., 22 May 2025, Treust et al., 2017, Hackenburg et al., 18 Jul 2025).