Thinking, Fast and Slow · chapter 1 · id thinking-fast-and-slow-c1-03-system-2-has-limited-capacity-

“System 2 has limited capacity and requires effort -- engaging it for one task depletes resources available for other tasks.”

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Receipts

Baumeister et al. (1998), JPSP 74(5)DOI registry: valid
An act of self-control depleted a limited resource, causing poorer performance on a subsequent self-control task.
Hagger et al. (2016), Perspectives on Psychological Science 11(6)DOI registry: valid
A pre-registered multi-lab replication of the ego depletion effect found no significant effect across 23 laboratories (d = 0.04).
Evans & Stanovich (2013), Perspectives on Psychological Science 8(3)DOI registry: valid
Type 2 processing requires working memory capacity, which is demonstrably limited. However, the resource metaphor of 'depletion' is distinct from the capacity limitation claim.

This claim is a stable, citable object. If you can falsify a verdict, tell us — corrections are loud here.