Theoretical analysis reveals an exhaustive six-stage judgment chain in decision systems, highlighting how self-referential loops drive irreversible error ratchets regardless of scale.
The standard treatment of cognitive error is a list: overconfidence, anchoring, confirmation bias, survivorship bias. Such lists can be long, and they have no way of checking themselves for omissions, because their entries do not lie on one axis. Some name the direction of a belief, some the manner of sampling, some the handling of a signal after it arrives; set side by side, any counterexample can be reassigned to one of the others. This paper argues that a judgement travels a chain from data to bet, and that the identifiable positions on that chain are exactly six. The first three are an existing three-layer decomposition — sampling, operator, absorbing wall; the fourth is position size; the fifth is updating; the sixth is ownership of distinguishability, which is peculiar to the cognitive layer and has no counterpart in the material one. Each position has an exhaustible set of ways to fail, and their product is the complete space of misjudgement. Entries on the standard lists each land somewhere definite in it, and the familiar two-by-two of belief direction against action is a two-dimensional projection of this six-dimensional space whose vertical axis is the sign of a sum of three differently sourced biases. The additive and multiplicative rays are not a seventh component but the background in which the six sit: the same error is averaged away on the additive side and amplified to ruin on the multiplicative one. Four separately computable consequences of misreading the ray are given. The core is Section 5. The six components close into a self-referential loop: the internal model sets the allocation tilt, the tilt sets the tail index, the tail index sets distinguishability, distinguishability sets the recognition delay, the delay derates the corrective branch, and the net self-referential coupling rises — while the critical coupling falls as the tail index falls. The two curves approach each other, so the ignition point precedes the failure of any external constraint, and past it, halting the growth of the coupling does not restore stability. That is a ratchet, and it is the exact form of "large errors are irreversible", requiring no assumption about will or character. The sixth component sits on the corrective branch itself: a taboo removes that branch entirely, and the loop becomes unconditionally unstable. Hence the shortest conclusion of this paper: the first five components make the estimate deviate; the sixth makes it unable to return. The first five are error; the sixth is irreversibility. On the applied side the paper gives a criterion for strategy versus tactics that looks at structure rather than at amounts: three binary questions land on eight cells, only the all-yes cell is genuinely strategic, and the middle six each carry a different remedy. Three falsifiable predictions follow with their falsification standards, the principal one being that the tail index of the loss distribution separates by cell, accompanied by a sample-exclusion protocol against artificial truncation.
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Qinfu Li (2026) studied this question.
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