| paper | d4-journals-geb-2018-0139 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | yes |
other→NP-hard discrete result → its continuous mirror
Answer: The threshold decision problem is \(\mathrm{NP}\)-complete, even for fixed \(q=1/3\); exact computation of \(\operatorname{OPT}\) is \(\mathrm{NP}\)-hard. · discrete side: other · adjudication: proved_with_minor_gaps
full proof & adversarial review →
Proposition 2
statement extracted from the paper’s text layer
Given a standardized finite experiment battery and a society represented by a finite support of response-record types \(r\), each with rational mass \(\mu_r\), compute the maximum mass \(\sum_{r\in S}\mu_r\) of types \(S\) for which there exist strictly increasing values \(\phi_m\) and strictly decreasing values \(\varphi_t\) satisfying \(\phi_m+\varphi_t\geq\phi_n+\varphi_s\) for every revealed comparison \((m,t)R^*(n,s)\) in that type’s record.
Each type is a complete record of one participant’s choices across the battery. Test each support type using Proposition 2’s linear-feasibility system, then sum the masses of the types that pass; the cohort may use a different rationalizer for each type.
The paper studies one consumer’s choices, so cohort prevalence adds an empirical estimand and no cross-type computational structure; its fit depends on whether the authors would recognize that extension as their experimental question.
fatal: False
The mirror covers discounted-utility rationalizability via Proposition 2; it leaves aside the paper’s narrower weakly present-biased, quasi-hyperbolic, and exponential characterizations and its discount-factor identification results.
The strongest positive case is narrow, and it rests on one borderline anchor: Proposition 2, proved in this paper. It says that an individual’s observed choices are rationalizable by discounted utility exactly when there are strictly increasing values \(\phi_m\) for observed payments and strictly decreasing values \(\varphi_t\) for observed delays such that every revealed comparison \((m,t)R^*(n,s)\) satisfies \(\phi_m+\varphi_t\geq\phi_n+\varphi_s\). That is a finite linear-feasibility characterization. The paper presents it as a convenient way to check rationalizability, but does not state a complexity bound or analyze an algorithm. So I would use Proposition 2 only if the brief’s LP-formulation exception is read broadly; it is not a printed “in P” result.
A plausible population mirror would take a standardized experiment battery and a cohort of many participants. A type is a complete record of one participant’s choices across that battery; \(\mu_r\) is the fraction of participants with record \(r\). The continuous problem, Maximum Discounted-Utility-Explained Mass, is: choose a set \(S\) of response types and, for each \(r\in S\), a discounted-utility rationalizer for that record, maximizing \(\sum_{r\in S}\mu_r\). The solution is the largest population share whose observed records the model can explain, with utility witnesses for those records. This is plausible for a large online experiment with many participants but relatively few distinct response records. Each record can be checked using the linear-feasibility characterization, so the proposed problem is tractable by checking types and summing their masses—assuming exact rational input data.
That is a genuine population lift, but it is a lift of the paper’s individual rationalizability test into a question about the share of a cohort it explains. The paper does not ask that prevalence question, and the per-type checks are independent, so the continuous model adds little computational structure. Its stronger results—Theorem 1 on discounted-utility rationalization, Theorem 2 on weakly present-biased rationalization, and Propositions 5 and 6 on quasi-hyperbolic and exponential rationalization—are characterizations by testable conditions, not complexity results. They could motivate analogous population-share questions, but I would not present them as computational anchors.
My weakest point is decisive under a strict reading of the anchor requirement: the paper contains no named result establishing a complexity class or analyzing an algorithm’s complexity. The cohort problem is a plausible extension, not a computational mirror of a problem the paper itself studies.
The strongest negative is that the paper’s object is one decision maker observed across repeated trials. The index \(K\) counts trials, not people. Its named results—Theorems 1 and 2 and Propositions 5 and 6—characterize when that person’s choices admit particular utility representations. Proposition 2 gives a finite linear-feasibility test, which makes this a borderline case: it points toward an algorithm, but it establishes no runtime bound or complexity classification for a population problem.
The best population version would use a standardized experiment and define each type as a participant’s complete response record. A large cohort with repeated records is plausible, and its mass could measure the share rationalizable by each discounting model. But the calculation separates by type: test each record, then sum the masses of those that pass. For the proposed “maximum explained mass,” every passing type is included; no population-level optimization remains. The continuous distribution supplies a weighted prevalence statistic, while the paper’s individual feasibility test does all the computational work. Requiring one common discount function across participants would add a cross-person hypothesis the paper does not study.
The same limitation applies to Theorem 1, Theorem 2, and Propositions 5 and 6: their population-share versions reuse the individual test. Such a prevalence measure could be useful empirically, so I cannot rule out every worthwhile application. The negative case is strongest under ChoCo’s stated target: the paper offers no named complexity result with a continuous-population counterpart. If a weighted prevalence extension counts as a mirror on its own, that boundary is genuinely debatable.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.