In LLM‑agent opinion simulations, each agent reports a probability $p$ that a claim is true after observing its own previous probability and the probabilities reported by its neighbors; this number becomes its state in the next round. If the number reflects the agent’s stance rather than the exact sentence shown, rewriting the claim as its complement and replacing every $p$ with $1-p$ should yield complementary answers whose sum equals $1$.
We evaluated three small open‑source models—Qwen3‑4B, Llama‑3.2‑3B, and Gemma‑3‑4B. On 2,304 agent states extracted from a running network simulation, Qwen’s paired reports averaged $1.18$, and on 48 real fact‑checking claims from AVeriTeC they again exceeded one. A controlled benchmark of 24 worlds, each with exactly two possible outcomes, showed the same failure across all three models.
The discrepancy is two to ten times larger than the change caused by a same‑meaning paraphrase and persists under repeated sampling, across different peer‑group sizes, and report strengths. When the reports are fed back into two populations that start from complementary states, the populations do not remain mirror images: after five rounds the divergence is positive for every model.
Averaging each answer with the complement of its paired answer restores consistency by construction and reduces the Brier loss averaged over the two wordings, but at the final round it beats the better of the two original wordings for only one of the three models. A schedule‑by‑targeting experiment on the same model yields a small, stable interaction because such sweeps keep the claim wording fixed.
Consequently, re‑wording consistency requires its own test before simulated probabilities are interpreted as beliefs.
Review