Wisdom-of-crowds conjecture for robust nonlinear aggregation on large symmetric networks

Prove that for undirected Erdős–Rényi graphs on [n] with edge probability p(n) ≫ log(n), and for robust aggregation operators T : ℝ^n → ℝ^n defined by symmetric local functions τ_d with uniformly bounded derivatives (so that T_i(x) = τ((x_j)_{j ∈ N(i)})), the long-run output T^∞ depends negligibly on any small set of entries as n grows—i.e., establish an analogue of “wisdom of crowds” in this nonlinear setting.

Background

The paper generalizes DeGroot’s linear model to robust nonlinear operators T exhibiting entrywise monotonicity and translation properties, citing convergence theory for such operators.

Motivated by symmetry in large random networks, the author conjectures that no small set of agents becomes globally prominent. While Cerreia-Vioglio, Corrao, and Lanzani (2024) make progress under technical assumptions on the second-largest eigenvalue, these assumptions fail in important network models (sparse Erdős–Rényi, block models, lattices), leaving the conjecture open in those regimes.