Breaking Symmetry, Not Choosing Direction: A Model of Hierarchy as a Position Amplifier, and What It Can and Cannot Recover

Kristian Sestak

No axvmp_v1, SocArXiv from Center for Open Science

Abstract: Status hierarchies form even among people of near-equal ability. Their inequality is usually read as meritocracy (sorting by ability), as coordination (a group's need for someone to decide), or as cumulative advantage (small early leads compounding). This paper formalises a fourth possibility, often conflated with the third: hierarchy as a symmetry-breaking amplifier of position, a process that turns tiny, ability-irrelevant initial differences into large and durable gaps in standing. A population of near-equals sits at a symmetric state with no natural ranking; because that state is unstable, any noise, once amplified, breaks the symmetry and fixes an order by chance rather than by merit. The mechanism is not new; the contribution is to make it precise and to tell it apart from its rivals, in three results. First, amplification is not just one route to inequality but a precondition for any durable, self-generated order: without the self-reinforcing feedback, early leads wash out. Second, the process is self-limiting, so concentration first rises and then falls with the strength of amplification, unlike ordinary cumulative advantage. Third, the model yields signatures that separate positional amplification from meritocracy, coordination, and cumulative advantage without measuring ability, using only how early the final order is fixed and whether an early lead survives when position can be contested and revoked. As amplification grows the winner decouples from genuine quality, the group advances while its typical member stalls, and a symmetric lower threshold makes an early loss as unrecoverable as an early lead is self-reinforcing. Illustrative evidence from an online cultural market, Wikipedia adminship, GitHub, and startup funding is reported as suggestive rather than confirmatory, and all results are reproducible from seeded simulations and public data.

Date: 2026-07-10
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Persistent link: https://EconPapers.repec.org/RePEc:osf:socarx:axvmp_v1

DOI: 10.31219/osf.io/axvmp_v1

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