| paper | d4-journals-mss-2003-0010 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Theorem 1 is an axiomatic impossibility result, and Theorem 2 is an axiomatic characterization; neither states an algorithm, complexity bound, hardness result, or computation-used formulation. The opponent's weighted-majority and alignment-recognition suggestions are possible extensions, but they do not supply the missing computational result from this paper.
fails bit a — no named computational result to mirror
Theorem 1, Theorem 2, Proposition 1, and Proposition 2 concern axiomatic possibility, characterization, or outcome coherence; none gives a computational guarantee or complexity result.
This paper contains no named computational result in the sense required for a continuous-mirror case. Theorem 1, attributed to List and Pettit (2002a), is an axiomatic impossibility theorem: on the unrestricted domain, no aggregation function producing complete, consistent, deductively closed collective judgments can satisfy unrestricted domain, anonymity, and systematicity. Theorem 2, proved here, characterizes propositionwise majority on the unidimensional-alignment domain as the unique rule satisfying the stated axioms and producing almost complete, consistent, deductively closed outcomes. Neither classifies a computational problem as tractable or hard.
A continuous population of judgment types is imaginable, but computing propositionwise majority from rational type masses would not turn Theorem 2 into a computational anchor. I would not claim a positive computational mirror for this paper.
The strongest case against a mirror is that the paper’s central results are axiomatic, not computational. Theorem 1 rules out an aggregation function under one domain condition; Theorem 2 characterizes the unique function under another. Replacing a finite profile with a rational distribution over judgment types gives weighted majority, but neither theorem classifies the complexity of computing a rule or solving an intervention problem.
There is a credible high-multiplicity setting: a large population judging the same interconnected propositions. Identity is irrelevant to the model, and fractions of that population are meaningful. But the direct computation is just summing the masses that accept each proposition. For an explicitly supported distribution, that takes \(O(\tau |X|)\) rational additions and comparisons. It makes the aggregation input continuous without uncovering a computational question in the paper’s results.
The strongest attempted mirror would ask whether weighted majority produces consistent judgments, or whether the distribution satisfies unidimensional alignment. Those are possible research questions, but they require choices the paper does not make. Coherence checking depends on how the agenda is encoded; alignment recognition asks for a new procedure to find a structuring order. Supplying the latent order makes the median argument immediate, while omitting it turns recognition into a separate problem. A minimum-mass repair to alignment adds yet another ingredient: an intervention cost the paper never defines. These could motivate independent work, but the paper does not single out any as its own computational problem.
So the negative case is not that no population scenario makes sense. It does. It is that the plausible continuization preserves the paper’s aggregation theorem while adding no computational result, and the computational variants require inventing a new problem around it. I would call the case strong against a *mirror of this paper*, but not airtight against every worthwhile project one could build from its ideas.
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.