Power as Harm Capacity: A Unified Mathematical Framework for Understanding Social Domination

This paper proposes a unified theory of power grounded in a single, operationally precise concept: harm capacity. The central argument is not that power always causes harm, but that what defines power — across every domain of social life — is the latent, measurable capacity to impose irreversible consequences upon others, whether or not that capacity is ever exercised. A mother nurtures and loves her child; yet her authority rests on an asymmetry that is difficult to deny — she could, if she chose, cause the child irreparable harm. A prime minister governs with the best of intentions; yet his power is measurable precisely because he could, in principle, dismantle the very nation he leads. A commoner, however virtuous, possesses no such reach. This distinction — between the exercise of power and the mere possession of its latent form — is the conceptual heart of this framework.
By making this distinction explicit from the outset, the framework avoids the reductionism of equating power with harm. Harm capacity is a structural feature of social relationships, not a behavioral tendency. It can and does coexist with benevolence, care, cooperation, and love. What it cannot coexist with is powerlessness — because where the capacity to impose consequences is absent, so is power, whatever else remains.
The paper formalizes this insight mathematically through information-theoretic domain weighting and probabilistic harm capacity modeling, generating six testable hypotheses about institutional behavior, consciousness development, and social evolution. The implications challenge comfortable assumptions about democratic governance, benevolent authority, and the nature of liberation itself — not to provoke, but to provide a more honest foundation for understanding how social structures actually function.

Power theory, harm capacity, mathematical sociology, latent coercive capacity

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