Message capacity and claim wording set the transition points of collective truth-finding in language-model networks
Makoto Fukushima at Honda Research Institute Japan shows that the number of peer messages an agent reads, one parameter he calls message capacity, predicts where a language-model collective flips between converging on the truth and converging on a falsehood.
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One parameter generates the network. Message capacity sets how many of the others' messages each agent reads, and the communication graph is generated from it, so the reading bound alone becomes the independent variable.
The prediction was registered before the experiment. Coefficients were measured from a public dataset and a direct measurement of the experimental agent, and the collective experiment was run against a preregistered prediction.
The reduced map is accurate to a few percent. Against exact numerics over a three-decade parameter grid the map locates the transition to a median 2.7 percent, and 6.7 percent in fully closed form.
Correct majorities still lose. Majorities of 75 percent correct agents ended on the correct side in fewer than half of episodes at every capacity tested.
Wording drives the outcome, not content. A discrimination experiment across 31,824 randomized queries shows the drive is the assertion's wording rather than the claim's content, and a capacity-only surrogate predicts wrong consensus in 0.1 percent of episodes against 75 percent observed.
Abstract
Whether human or large language model (LLM), an agent in a discussion reads only a few of the others' contributions, bounded by cognition, context, or cost. LLM collectives can settle on a wrong consensus even when a majority starts out correct; we ask how far that reading bound alone decides the outcome. We model the bound with one number, the message capacity, which sets how many of the others' messages an agent reads, and generate the communication network from it. Over 31,824 randomized queries, we found that an 8-billion-parameter model's judgment of a claim effectively reduces to a logistic function of a weighted sum of its inbox, the update rule of a stochastic binary neuron with divisively normalized weights. From these weights and the network's degree statistics alone, the wrong consensus should become unreachable from any start once agents read, on average, fewer than 6.4 of their 31 sources. In 1,414 episodes with assigned starts the prediction failed: the correct side won in fewer than 50% of episodes from every start, and in only 28-45% when 75% of agents started correct. The failure traces to the field, the threshold that a claim's wording sets for the agent's answer before any message is read: the experimental claims' fields lay below the calibration mean, and with each claim's own field the same weights reproduce the outcomes. Reversing the wording showed that the threshold follows what a claim asserts, not whether it is true. On a second 8B model the pipeline predicts claim-dependent bistability; transition points appeared where computed, and an eight-claim calibration matched in 15 of 16 conditions. At 70B the assertion bias is not detected. Thus a collective's fate is largely set by two single-agent measurements: the threshold a claim's wording sets, and the message capacity that sets the transition point.