Three-Party Persuasive Dialogue Dynamics

Updated 12 October 2025

Three-Party Persuasive Dialogue is an interactive paradigm where three agents engage in structured argumentation and dynamic opinion exchanges using formal models and adaptive strategies.
Formal models, such as the constrained voter model and argumentation frameworks, reveal critical thresholds, exponential consensus delays, and emergent coalition behaviors.
Empirical studies and simulation experiments demonstrate that AI agents and human participants exhibit social conformity and strategic adaptation, informing design improvements in persuasive systems.

Three-party persuasive dialogue refers to interactive scenarios in which three distinct agents engage in arguments, appeals, or opinion dynamics aimed at influencing one another’s beliefs, attitudes, or behaviors. Unlike two-party persuasive exchange, three-party structures introduce additional complexity through the interplay of multiple persuasive forces, the possibility of mediating or moderating roles, the amplification or suppression of social influences, and emergent coalition or opposition dynamics. This paradigm has been formally studied in statistical physics-inspired models, agent-based simulations, argumentation theory, cognitive architectures, and empirical behavioral studies, each providing complementary perspectives on the mechanisms and consequences of triadic persuasion.

1. Formal Models and Dynamics in Three-Party Persuasion

At the abstract modeling level, triadic persuasion has been deeply analyzed via the three-party constrained voter model (Mobilia, 2012). In this model, a finite population consists of agents in four possible states: radical voters for party A, radical voters for party B, susceptible centrists (C), and a fixed fraction ζ (zealotry) of committed centrist zealots (C_z), who cannot be converted.

The microscopic dynamics are as follows:

A susceptible centrist (C) converts to A with rate 1 + δ_A after interaction with A, or to B with rate 1 + δ_B after interaction with B (with δ_A ≥ δ_B > 0, encoding asymmetric persuasion strength).
An A or B agent may revert to a centrist (C) after interaction with any centrist at rate 1, but zealots (C_z) never change.
Key schematic reactions include:

$A + C \xrightarrow{1+\delta_A} A + A \qquad B + C \xrightarrow{1+\delta_B} B + B \qquad A + C \xrightarrow{1} C + C$

The population evolves according to the density-based mean-field equations:

$\frac{da}{dt} = a [\delta_A c - \zeta] \qquad \frac{db}{dt} = b [\delta_B c - \zeta]$

with centrist density $c = 1 - \zeta - (a + b)$ .

The resulting dynamics exhibit a critical threshold for zealotry

$\Delta_c = \frac{\delta_A}{1 + \delta_A}$

separating a coexistence phase ( $\zeta < \Delta_c$ ) with stable radical–centrist coexistence from a centrism-dominated regime ( $\zeta \geq \Delta_c$ ), where only centrists persist. The consensus time τ exhibits nontrivial scaling: for $\zeta < \Delta_c$ and small initial centrist density,

$\tau \sim N^{-1/2} \exp[N\gamma(\delta_A, \zeta)]$

with

$\gamma(\delta_A, \zeta) \approx \delta_A - \zeta (1 + \ln (\delta_A / \zeta)).$

For $\zeta \geq \Delta_c$ , τ grows logarithmically with system size, $\tau \sim \ln N$ , indicating rapid centrism consensus. Stochastic simulation (e.g., Gillespie algorithm) corroborates these dynamics quantitatively.

Significance: This formal approach exposes how three-party formations, especially when combining opposing radicals and intransigent moderates, yield complex metastable states, exponential consensus delays, and phase transitions fundamentally distinct from binary voter models.

2. Argument Representation: Trichotomy and Multi-Agent Structures

Theoretical models of argumentation have extended the representation of persuasive dialogue to trichotomic and multi-entity forms. The Trichotomic Argument Interchange Format (T-AIF) (Göttlinger et al., 2018) proposes a structure that encodes:

Logos: Argument map connecting illocutions (I-nodes) and argument schemes (S-nodes), implemented via logical graphs and fuzzy logic semantics.
Ethos: Explicit trust networks connecting actors (E-nodes) by weighted edges, representing the degree of credibility and relational trust—thus modeling the impact of speaker identity on argument acceptance.
Pathos: Weighted edges from actors to propositions indicating the degree of emotional commitment (commitment strength), essential for tuning perceived engagement and investment.

In three-party dialogues, each agent’s trust in others, their pattern of logical support and attack, and their displayed commitment are formally represented within a joint argumentation graph. Weighted, multi-dimensional labelling functions spanning $l: P \to [0,1]$ (truth values) and actor-specific agreement or rationality predicates (e.g., $\Ag(l,x)$) enable fine-grained semantic analysis of multi-party exchanges.

Significance: These argumentation frameworks provide substrates for mapping agent reasoning, cross-participant trust, and affective investment in scenarios involving complex triadic persuasion, as required for systematic computational profiling and dialogue system design.

Contemporary research demonstrates that three-party dialogues amplify group-level psychological effects, notably the conformity effect (Sasaki et al., 5 Oct 2025). In empirical studies involving a Persuader Agent, a human participant, and a Persuadee Agent, it was shown that:

When the AI Persuadee Agent explicitly accepted the persuasive argument mid-dialogue, human participants exhibited a statistically significant increase in both perceived persuasiveness and actual attitude change (Kruskal–Wallis H(3)=20.19, p<0.0005 for persuasiveness; H(3)=23.96, p<0.0001 for attitude change).
The conformity effect (as described in classical social psychology) manifested sharply as participants observed the agent's switch to acceptance, particularly when preceded by an icebreaker session. In the absence of agent acceptance, attitude change was significantly suppressed.
Turn-by-turn analyses and linguistic measurements (increased use of affirmative expressions) confirmed that the agent’s behavioral switch acts as a social cue, directly triggering participant acceptance.

Context and significance: This demonstrates that AI “peers” in a three-party environment can non-trivially elevate or dampen human compliance through social proof, with implications not only for persuasive system design but also for the modeling of complex peer effects in group settings.

Three-party persuasive dialogues in realistic settings must contend with partial observability and private mental states among participants. The ToMMA framework (Zhang et al., 28 Feb 2025) advances a multi-agent approach under double-blind conditions:

Each agent (persuader, persuadee, observer) retains private mental states (beliefs, desires, strategy choices), which are not exposed to the other agents.
The persuader deploys causal Theory of Mind reasoning to infer others’ hidden states based solely on dialogue cues and observed behavior, aligning persuasive strategies (S) with inferred target states, formalized as $S = f(\mathcal{B}_1, \mathcal{D}_1, ..., \mathcal{B}_n, \mathcal{D}_n)$ for n agents.
The CToMPersu dataset implements this protocol over 6,275 multi-turn, multi-domain dialogues, evaluated on context coherence, logical coherence, and effectiveness of causal ToM reasoning.

When extended to three-party scenarios, this model grants each participant their own epistemic boundary, necessitating more sophisticated inference and dynamic adaptation to partial and asymmetric information—mirroring negotiation and mediation dynamics found in naturalistic persuasion.

Interpretive note: This approach avoids unrealistic, fully-shared-information setups found in some earlier datasets, more faithfully capturing the epistemic structure of real-world triadic persuasion.

5. Strategies, Personalization, and Cognitive Control

Triadic persuasive dialogue systems benefit from adaptive strategic control and personalization. As shown in “Persuasion for Good” (Wang et al., 2019) and cognitive-strategy-enhanced agents (Chen et al., 7 Feb 2024):

Persuader agents can deploy multiple strategy types (logical, emotional, credibility appeals; personal stories; self-modeling), chosen dynamically considering personality traits and value profiles of participants—including possible mediators.
The CogAgent architecture formalizes multi-strategy generation in a modular pipeline:

$(\mathrm{Per}, \mathrm{Top}, \mathrm{Arg}) = \text{Str\_Pre}(Q_S, H)$

$P(A | Q_S, H, \mathrm{Per}, \mathrm{Top}, \mathrm{Arg}) = \prod_{t=1}^n p(a_t | Q_S, H, \mathrm{Per}, \mathrm{Top}, \mathrm{Arg}, a_{<t})$

where (Per, Top, Arg) index the persuasion, topic path, and argument structure strategies, respectively.

In three-party dialogue, the cognitive-strategy module can be extended to select, coordinate, or even negotiate strategies across diverse roles and cognitive profiles, optimizing not only for single-party conversion but for informed group deliberation or coalition-building.

Editor’s term: Persuasion agenda alignment—systems harmonizing strategies across multiple agents and perspectives to maximize group-level acceptance or consensus.

6. Evaluation, Metrics, and Systemic Performance

Evaluation of three-party persuasive dialogue draws on a range of metrics, including scaling of consensus time, group attitude change, argumentation coherence, and agent-specific measures:

Population models (e.g., (Mobilia, 2012)) quantify consensus time τ and metastability under parameter sweeps (δ_A, δ_B, ζ, N), with stochastic, agent-based variants capturing demographic fluctuations.
Dialogue systems are benchmarked on datasets reflecting triadic structures (e.g., CToMPersu), using contextual and logical coherence, helpfulness, and success at causal ToM inference.
Intervention studies track perceived persuasiveness, conformity effects, and order dependence in multi-agent debates, confirming that system behavior (e.g., sequence of agent persuasion) directly modulates collective outcomes (Stengel-Eskin et al., 18 Oct 2024, Sasaki et al., 5 Oct 2025).
Argumentation systems apply fuzzy labelling and graph-theoretic measures for assessing per-agent agreement, rationality, and justified trust, leveraging the trichotomic structures analyzed in (Göttlinger et al., 2018).

7. Implications, Challenges, and Future Research

The current state of research in three-party persuasive dialogue reveals both opportunities and challenges:

The addition of a third party introduces qualitative and quantitative changes, including new phase transitions, social proof effects, richer trust and commitment structures, and requirements for sophisticated Theory of Mind reasoning.
Practical deployment in systems demands modular, role-aware, and strategy-adaptive architectures (e.g., modular agenda-pushing, as in (Chen et al., 2022); graph/speaker-aware encodings, as in (Hu et al., 20 Jan 2025)).
Key open challenges include the integration of multimodal cues, generalizing across domains and scenarios, deepening psychological modeling, and balancing conflicting persuasive aims in dynamic group settings.
Ongoing development of benchmarks, transparent evaluation protocols, and explainable reasoning models (e.g., trichotomic/fuzzy-logic representation) is critical.
Extensions to more general n-party persuasion, and to longitudinal or real-time adaptation, are promising directions.

In sum, three-party persuasive dialogue research stands at the nexus of statistical physics, cognitive psychology, argumentation theory, and AI system engineering. Its findings elucidate both the micro-level dynamics of influence and the macro-level emergence of consensus, with broad implications for automated dialogue systems, social computing, opinion dynamics, and the design of AI-mediated group decision tools.