An Amplifier of Position, Not Competence: Why Hierarchy Emerges, What We Pay for It to Hold, and Why Its Cost Cannot Be Settled

Kristian Sestak

No fxzj5_v1, SocArXiv from Center for Open Science

Abstract: A prior trilogy established that individual outcomes are dominated by the dispersion of the environment rather than of capability, formally Var(ln ρ_eff) ≫ Var(ln k) at a global dominance ratio R ∈ [27,134], but not where that dispersion comes from. We supply the mechanism: hierarchy as an amplifier, a multiplicative cascade that turns tiny, often capability-irrelevant initial differences into the large positional dispersion the trilogy measured, so that R becomes an output of structure rather than a fact about people. We microfound the feedback f(S) in Gould's deference model (linear at the bottom, saturating at the top) and identify the Kesten reset that creates the heavy tail with Boehm's reverse-dominance insurance, pinning the tail index in closed form, α = 1 + [δ + √(δ² + 2σ²p)]/σ², confirmed by a Clauset MLE. The calibrated amplifier reproduces R at all four aggregation levels and requires a near-random-walk between-environment process. On the raw ICIJ Offshore Leaks officer network the predicted heavy tail holds (global α ≈ 2.25), but no concentration metric tracks recording opacity across jurisdictions: that negative result vindicates the demarcation paper, since the quantity that would test the lever is hidden by construction. We then turn to a domain where position is logged, GitHub pull requests. On 113,895 closed pull requests, position multiplies the merge odds 3–7× at fixed diff size; a within-author design bounds the position premium at 12.6 pp (p = 2×10⁻¹⁸); and the cleanest design, a promotion holding author and project fixed, still finds acceptance rising +4.1 pp in the same repository at unchanged proposal size (p = 2×10⁻⁷), though even it cannot fully separate the badge from the competence that travels with it. The amplifier's gains are continuous and visible while its costs are rare, delayed and hidden, so hierarchy always appears beneficial and its net cost cannot be honestly settled.

Date: 2026-06-19
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Persistent link: https://EconPapers.repec.org/RePEc:osf:socarx:fxzj5_v1

DOI: 10.31219/osf.io/fxzj5_v1

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