Consensus Too Soon, or Agreement From the Start? Shared Prior, Social Coupling and Pool Coverage in Decentralised LLM Collectives, and Why Prompted Diversity and Model Heterogeneity Act on Different Terms

@misc{mahendrakar2026consensus,
  author       = {Mahendrakar, Pranay},
  title        = {{Consensus Too Soon, or Agreement From the Start? Shared Prior, Social Coupling and Pool Coverage in Decentralised LLM Collectives, and Why Prompted Diversity and Model Heterogeneity Act on Different Terms}},
  year         = {2026},
  month        = sep,
  date         = {2026-09-27},
  publisher    = {Life of Research},
  doi          = {10.5281/zenodo.22997961},
  url          = {https://lifeofresearch.com/articles/57},
  abstract     = {(c) 2026 Pranay Mahendrakar. Licensed under CC BY 4.0. Groups of language-model agents that exchange answers and settle on a common one are now a standard way to build decentralised decision systems. A common worry is that they agree too soon: agents copy each other, diversity collapses, and the group loses the independent errors that make collective judgement work. This paper examines that worry against the published record and argues that it runs together two different mechanisms. An observed consensus can be produced by social coupling (agents moving toward what peers say) or by a shared prior (agents that would have agreed without ever hearing each other). The literature contains clean evidence for both. In one 2026 study, agents that never saw each other ended in nearly the same place as agents that debated; in another, a lattice of identical agents aligned through a shared label preference that outweighed neighbour influence in every model tested, by nearly an order of magnitude even in the most social one; elsewhere, conformity to peers turns correct answers into wrong ones in 57 to 77 percent of strict-conformity cases. The paper separates three quantities that "diversity" is used to name: whether a correct answer is in the pool at all, whether agents' errors are independent, and how strongly agents are coupled to one another. It argues that prompting mostly moves the first, model heterogeneity partly moves the second at a measurable cost in quality, and neither sets the third, which is a property of the interaction protocol. It states which control would tell a reader which mechanism produced a given consensus, and names the experiments that would settle what remains open. The literature search, drafting and citation verification for this paper were carried out with AI assistance under the author's direction. Every arXiv citation was machine-verified against its live arXiv Atom API record, and every other citation against its Crossref or DOI record, during drafting (title and author list checked against the record returned). Every quantitative claim is taken from the abstract, full text or a table of the source credited with it; full-text numbers were read from the sources' own HTML or PDF renderings rather than from summaries. No experiment was run and no number in this paper was measured by its author. Table 1 re-presents numbers published by the cited papers, each named on its row; Figure 1 plots published values from four cited papers with no transformation. The three-term decomposition, Algorithm 1 and the reporting protocol in Section 11 are original conceptual synthesis by the author, not empirical results, and are presented as such. Four social-science references (Zollman 2010, Ladha 1992, Stasser and Titus 1985, Kameda et al. 2022) were verified as records but their full texts were not available to the verification step; they are cited only for what their titles or deposited abstracts state.},
  keywords     = {multi-agent debate, LLM collectives, conformity, collective intelligence, model heterogeneity, persona prompting, wisdom of crowds, correlated errors},
  language     = {en},
  copyright    = {Creative Commons Attribution 4.0}
}