R. Duncan Luce (1956), Econometrica 24(2):178–191 — DOI-10.2307/1905751
Key takeaways
Registered, not read. What follows is from the abstract only.
- Intransitive indifference is admitted. “In this paper intransitive indifference relations are admitted and a class of them are axiomatized.” The title gives the motivation as discrimination. The usual gloss, which is the record’s and was not checked against the paper, is that options whose utilities differ by less than a just-noticeable amount are not told apart, while a chain of such small differences can add up to one that is.
- The representation is by thresholds. “This class is shown to be substantially equivalent to a utility theory in which there are just noticeable difference functions which state for any value of utility the change in utility so that the change is just noticeable.” The paper’s own axioms and the exact form of its representation were not seen.
Standing in the record
Filed on 2026-10-23 for the correction to CLAIM-436, part 3a. That part shows that a threshold override set on the level of a cost, alarm on above c*, still has a numerical representation. An override that fires on a difference in cost larger than a discrimination threshold is a different structure. Its indifference is not transitive, so it is not a weak order, and part 1’s construction does not apply to it even on a finite set. Luce’s semiorder is that structure in one dimension, and Tversky’s lexicographic semiorder (LIT-1472) puts it in front of a second dimension. The bearing is set out in LIT-1472.
No instruction for machine-learning practice; nothing here belongs in the anthology.