Collective intelligence through aggregation

When the same question is asked of multiple AI advisers, as in self-consistency and LLM-as-a-judge panels, Condorcet's jury theorem predicts that adding independent, competent advisers makes the majority more reliable. The theorem, however, has a latent dimension when viewed from the user's vantage: adding advisers also makes disagreement more visible. A binomial model reveals that this ``visible dissent'' becomes nearly inevitable as the number of advisers grows, and that reliability and disagreement approach certainty at rates that cross at an adviser accuracy of 4/5 (0.8); below it, visible dissent eventually becomes more likely than a correct majority. Even ideal panels of independent and competent advisers can be correct in aggregate but appear divided; such disagreement does not by itself indicate aggregation failure. The way advisers split also provides a common basis for predictive multiplicity, reconciliation load, and reliance miscalibration. These results separate aggregation from disclosure and turn the latter into testable questions about how disagreement should be presented and interpreted.

Groups of individuals can solve collective problems more accurately than any single member, by aggregating their opinions. Recent theoretical work has identified individual-level reward schemes that allow uninformed individuals to evolve collective intelligence from the bottom up, through social learning. Yet these results are restricted to linear prediction problems and simple averaging, while the decision tasks that real groups confront are often non-linear, and the institutions that aggregate opinions are seldom single-layer averages: districts elect representatives who in turn vote on policy, referees advise editors who decide on publication. Here we develop a framework for the evolution of collective intelligence in multi-layer voting populations, where individuals observe limited information and groups recursively aggregate their opinions by majority rule. We prove that single-layer voting cannot solve non-linear classification problems under any individual reward scheme. We then identify a "marginal feedback" payoff structure, which rewards individuals only when their opinion is pivotal in their group, and at every layer above them. This reward scheme induces a layered population to evolve accurate collective solutions to complex, non-linear decision tasks through individual-level peer imitation alone. The collective behavior that emerges is equivalent to a multi-layer perceptron in machine learning. Our results provide a naturalistic account of hierarchical institutions, in which the outsize importance of swing voters is the incentive that sustains collective accuracy; and they identify the credit-assignment rule in machine learning as not just an engineered solution but a natural evolutionary outcome.

More capable agents do not necessarily form a more capable collective. A multi-agent system may jointly possess sufficient information yet fail because evidence is poorly routed, unreliable reports enter public belief, correlated claims masquerade as independent support, shared state becomes stale or strategically distorted, or useful evidence is exposed through an ineffective action interface. We ask when additional resources should improve the reasoner and when they should instead change the institutional structure through which the collective forms and acts on public information. Drawing on functional distinctions from research on group decision making and distributed cognition, we construct controlled artificial ecologies around four loci of collective failure: access and routing, admission and dependence, state maintenance and incentives, and representation and action. Across these ecologies, we separately vary model capability and institutional structure, pairing positive interventions with matched reasoning baselines and mechanism-breaking controls. The experiments reveal a consistent boundary: institutions help when they repair failures in how a collective constructs usable public state, but lose their advantage when their signals are uninformative or uncheckable, when stronger intelligence can perform the same transformation directly, or when the resulting state cannot support reliable action. Our results recast the choice between intelligence and institutions as a diagnosis of where collective reasoning fails.