The Imitation Game We Never Agreed to Play

Quan-Hoang Vuong

No 26-011, Working Papers CEB from ULB -- Universite Libre de Bruxelles

Abstract: As language models converge on the statistical distribution of human-written text, a human’s ability to tell machine output from human output is governed by information-theoretic quantities that no judge’s skill or vigilance can override. This note shows that the best possible accuracy of any test for human-vs-machine origin is fixed exactly by the total variation distance between the two source distributions, then bounds that same ceiling in terms of Kullback–Leibler divergence: as a model’s output converges to the human one, no test can beat chance. A separate result shows that a fixed attention budget independently limits how many such judgments can even be attempted, and a fourth result proves this independence formally. Together, human discernment faces two distinct, additive limits: a ceiling on accuracy and a coverage limit on volume. None of this is offered as a major contribution; it is a personal thought experiment, worked through mostly for the author’s own understanding.

Keywords: artificial intelligence; discrimination; entropy; Kullback–Leibler divergence; total variation distance; Turing test; attention economics (search for similar items in EconPapers)
Date: 2026-08-27
References: Add references at CitEc
Citations:

Published by:

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/412828/3/wp26011.pdf Œuvre complète ou partie de l'œuvre (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sol:wpaper:2013/412828

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/412828

Access Statistics for this paper

More papers in Working Papers CEB from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().