Opinion Dynamics¶

Sonality's belief system draws from formal opinion dynamics models — mathematical frameworks that describe how agents update their beliefs in response to social influence and evidence. This page explains the magnitude formula, Bayesian belief resistance, power-law decay, and structural disagreement detection, with research grounding from Friedkin-Johnsen, Hegselmann-Krause, Deffuant, and Oravecz et al.

The Magnitude Formula¶

When an interaction passes ESS quality gates, Sonality stages an opinion delta for delayed commit.

Primary path: LLM-based assess_belief_evidence() determines direction, evidence strength, and contraction signal per topic with provenance tracking.

Fallback path:

Bootstrap dampening maps to the Deffuant model's "initial uncertainty" concept.¹ Without it, the agent's personality would be disproportionately shaped by whoever talks to it first — "first-impression dominance" (Chameleon LLMs, EMNLP 2025).

Example magnitudes:

Cooling-Period Staging¶

Opinion deltas are not committed immediately. They are queued in staged_opinion_updates and committed after OPINION_COOLING_PERIOD interactions (default 3).

At commit time, due deltas for the same topic are netted:

This reduces short-burst social pressure effects while preserving accumulated evidence.

Bayesian Belief Resistance¶

Established beliefs resist change proportionally to their evidence base. Each belief's BeliefMeta tracks a confidence score that grows logarithmically:

Capped at 1.0. The effective magnitude is:

This implements sequential Bayesian updating (Oravecz et al., 2016)² — posterior distributions serve as priors for the next update. Hegselmann-Krause (2002)³: only sufficiently strong evidence should shift opinions.

Structural disagreement bonus: When the user argues against the agent's existing stance (position × direction < 0), the code adds abs(old_pos) to the confidence denominator, further resisting flip-flopping.

Opinion Vector Updates¶

• direction = +1.0 (supports), -1.0 (opposes), or 0.0 (neutral; no update)
• Clamping keeps opinions in [-1, 1]

LLM-Guided Belief Decay¶

During reflection, stale beliefs are assessed with BELIEF_DECAY_PROMPT and classified as RETAIN, DECAY, or FORGET.

Fallback behavior still uses conservative floor protection (min(0.6, max(0.0, (evidence_count - 1) × 0.04))) and minimum confidence pruning to avoid catastrophic forgetting.

Structural Disagreement Detection¶

Sonality detects disagreement with DISAGREEMENT_DETECTION_PROMPT (LLM-structured), with sign-based fallback:

# User argued against agent's existing stance
for topic in ess.topics:
    position = sponge.opinion_vectors.get(topic, 0.0)
    if abs(position) > 0.1 and position * ess_direction < 0:
        return True  # disagreement detected

Keyword approaches ("I disagree", "I don't think") miss nuanced, qualified, or reframing-based disagreements. The CARE framework (EMNLP 2025) documents "conceptual gap" and "reasoning gap" for keyword-based detection.

The disagreement rate is tracked as a running mean in behavioral_signature.disagreement_rate. Target: 20–35% (DEBATE benchmark human baselines). Below 15% suggests sycophancy; above 50% suggests contrarianism.

Connection to Friedkin-Johnsen Model¶

The Friedkin-Johnsen (FJ) model is the standard mathematical framework for opinion dynamics. In FJ, each agent has an innate opinion \( s_i \), a stubbornness parameter \( \lambda_i \in [0,1] \), and a trust matrix \( T \). The update rule:

Sonality maps onto this framework:

Research finding (arXiv:2410.22577): moderate stubbornness in neutral agents reduces polarization — counterintuitive but validated. Sonality's initial agent is neutral; Bayesian resistance provides moderate stubbornness that increases with evidence, naturally avoiding both excessive volatility and excessive rigidity.

The Diminishing Stubbornness Extension (arXiv:2409.12601) shows that stubbornness that decreases over time leads to eventual convergence. Sonality achieves this implicitly: bootstrap dampening adds extra stubbornness early (0.5× scaling), then relaxes. As the agent matures, novelty scores for established topics decrease, producing smaller updates — adaptive stubbornness without explicit scheduling.

Research Grounding¶

Next: Reflection — when and how belief decay runs. Personality Development — expected opinion dynamics at each interaction milestone.