Correction Freeze Problem

Abstract

This paper proves four independent conditions under which a system’s perceived state can become detached from its true state, and shows what follows when that detachment coincides with self-reinforcing dynamics that make an eventual correction harder to reverse than it was to prevent. A sequence of individually imperceptible changes can accumulate to arbitrary cumulative drift without any single step ever being flagged. Two independent, fully rational reasons can lead a corrective judgment to be legitimately suspended: genuine uncertainty about the reliability of one’s own instrument, and a collapse of verification incentive below a sharp cost threshold. Even a fully active, fully resourced, fully self-trusting corrector faces a hard information-theoretic ceiling on accuracy once the signal distinguishing genuine change from ordinary variation grows statistically indistinguishable. A population state governed by a bandwagon-reinforced dynamic exhibits a trichotomy of long-run outcomes separated by a hysteresis gap, so reversing an already-shifted state requires strictly more than what triggered the shift. Together, these results suggest a precise reading of familiar worries about smartphone habits, synthetic media, and self-reinforcing online communities, not as vague metaphors, but as specific, checkable conditions under which an unnoticed and hard-to-reverse drift becomes possible.

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