Threshold dynamics of corrective action in a population model of structural discrimination

Structural discrimination can sustain underrepresentation even when no actor explicitly excludes a group. We develop a simple population model in which current representation changes each type’s per-capita effective rate of maintaining or expanding its presence, while corrective action responds to the gap from a reference-population share. The model yields three main results. First, an exclusionary state can remain stable when corrective action is present but weak relative to representation-dependent structural feedback. Second, the corrective strength required to destabilize exclusion is greater for a focal type that is rarer in the reference population. Third, avoiding complete exclusion is not the same as attaining proportional representation: with finite corrective strength, the stable long-run share can remain below the reference share. These results connect qualitative accounts of cumulative structural disadvantage to explicit conditions for long-run stability. They also suggest that corrective policies should be evaluated by their effective dynamic strength relative to the structural feedback they are intended to change, rather than by their formal presence alone.Author summary: We study how underrepresentation can persist even when explicit exclusion is absent. In many social systems, current representation affects what happens next: people may have better access to information, support, role models, and networks when people like them are already present. We use a simple population model in which these mechanisms change the per-person rate at which each group maintains or expands its representation. The model shows that a corrective measure can exist yet remain too weak to prevent exclusion. A lasting nonzero share appears only when corrective action exceeds a threshold relative to the structural feedback. That threshold is higher when the focal group is rarer in a broader reference population. Even above the threshold, the long-run share in the target population can remain below the reference share. Thus, preventing exclusion and approaching proportional representation are distinct policy goals, and both the strength of corrective action and the strength of the underlying structural feedback matter.