| paper | d4-conf-atal-2015-0063 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The numbered theorems establish existence and incompatibility of participation and efficiency properties for social decision schemes, but assert no algorithm, runtime, or complexity classification. The paper cites the #P-completeness of computing RSD as prior work; the proposed continuous RSD computation is an adjacent follow-up, not a continuous analogue of a computational result established here. Bit (a) fails.
fails bit a — no named computational result to mirror
No result is covered by a qualifying computational mirror. The numbered results concern participation and efficiency axioms; the RSD complexity statement is cited prior work.
This paper has no qualifying computational anchor, so I can’t make a positive case that meets your criteria. Theorem 1, Theorems 3 and 6, and Theorem 8 prove incompatibilities among participation, efficiency, and classes of social decision schemes. Theorems 2, 4, 5, and 7 establish existence or properties of particular schemes. None asserts a computational complexity result.
The closest candidate is the statement in Section 5.1 that computing RSD is #P-complete, cited to [2]. It is an external result, not a numbered result of this paper. The paper’s lottery over alternatives is also outcome-space randomization; it does not itself make the voter population continuous.
A plausible *new* question would represent ranking types by masses and ask how an SDS changes when mass abstains. But that would need its own precise formulation and computational result to anchor it. In particular, an individual has zero mass in a continuum, so the paper’s individual-participation theorems do not automatically transfer to that setting. I would not present this as a mirror of one of the paper’s named computational results.
This is a strong negative case on programme fit: the paper’s numbered theorems establish existence and incompatibility of axioms for social decision schemes. None gives an algorithm, runtime bound, or complexity classification. The closest computational statement is that computing RSD is #P-complete, but the paper reports it as an external result. That makes it a weak anchor for a computational mirror of this paper.
The best candidate is Theorem 4: take a distribution \(\mu\) over preference types, define RSD as the limit of finite electorates whose type proportions approach \(\mu\), and ask for the complexity of computing the resulting lottery. One could also ask whether abstaining mass of a type improves its outcome. These are coherent high-multiplicity questions, and I would not dismiss them because a single agent has zero mass: positive-mass abstention supplies a natural version. But the first imports a complexity result the paper only cites; the second turns its participation property into group abstention, which the paper already studies axiomatically. Neither mirrors a computational result established here.
So the proponent’s diagnosis holds, though the universal claim goes too far if read as “no worthwhile question could be posed.” A continuous RSD computation could be worthwhile as a separate project. The case against is that it is an adjacent computationalization of an axiomatic paper, not a continuization of one of its computational results.
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.