Rademacher Complexity and Models of Group Competition (www.symmetrybroken.com)

This piece argues that disputes between kin selection (Hamilton’s rB > C) and group selection (Nowak, Tarnita & Wilson 2010) can be reframed using tools from statistical learning and physics: mean‑field approximations and Rademacher complexity. NTW’s group‑selection model is presented as a mean‑field theory that replaces detailed, worker‑level interactions with averaged demographic parameters (queen reproductive rate b_i and death rate d_i as functions of colony size i). By treating workers as phenotype extensions or “robots” of the queen and ignoring localized genetic correlations (relatedness r), the model captures macroscopic colony fitness while sacrificing microscopic detail central to kin‑selection analyses. The significance for AI/ML and evolutionary modeling is twofold. First, it shows both kin and group selection are valid but different modeling regimes: kin selection is more granular and expressive, while mean‑field group models are lower‑variance, tractable approximations useful in strongly interacting, large systems. Second, invoking Rademacher complexity suggests a formal way to quantify model capacity and expected generalization: high‑complexity, worker‑level models may overfit local noise and be intractable, whereas lower‑complexity mean‑field models may generalize better for population‑level predictions. Practically, this frames cooperation versus competition as a modeling choice—pick kin‑level detail when relatedness and local strategy fluctuations matter, or a mean‑field group model when macroscopic demographics dominate.