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This paper extends previous work on the evolution of collective intelligence by introducing a framework for multi-layer voting populations where opinions are recursively aggregated via majority rule. It proves that single-layer voting is insufficient for non-linear classification and identifies a "marginal feedback" payoff structure that incentivizes individuals to become pivotal, enabling layered populations to solve complex, non-linear tasks through social learning. The emergent collective behavior mirrors that of a multi-layer perceptron, offering a naturalistic explanation for hierarchical institutions and linking credit assignment in machine learning to evolutionary principles.
A "marginal feedback" payoff structure, rewarding pivotal opinions, enables layered populations to evolve collective intelligence for complex non-linear tasks, mirroring multi-layer perceptrons.
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.