| paper | d4-conf-ijcai-2021-0267 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named theorems give worst-case bounds on power indices, not algorithms, complexity classifications, or computational formulations. The high-multiplicity setting is plausible, but this paper supplies no computational result to continuize.
fails bit a — no named computational result to mirror
No result is covered by a computational mirror: Theorems 3.1, 4.1, 5.1, and 6.1 state mathematical bounds, while the false-name conjecture and experiments provide no named computational guarantee.
A plausible continuous-population regime is a weighted voting body with many interchangeable unit-weight members and a few weight classes of larger voters. With \(N\) large and the number of weight types \(\tau\) small, that is a natural high-multiplicity setting. The paper itself points to oceanic games with finitely many significant players and a continuum of small ones, though it distinguishes its own results as non-asymptotic.
But the paper has no named computational result to anchor the required mirror. Theorem 3.1 proves \(\bar R_\phi=2\); Theorem 4.1 proves the absolute and normalized Banzhaf ratios are unbounded; Theorem 5.1 gives \(\bar R_\rho\leq 3\); and Theorem 6.1 bounds aggregate post-split power for the Shapley–Shubik and Deegan–Packel indices. These are mathematical bounds, not complexity classifications or algorithmic results. The false-name conjecture and its experiments do not supply one either.
So I can’t honestly give a prover-ready continuous problem per eligible anchor: there are none. A continuum version of the power-versus-proportion analysis is a plausible research direction, but presenting it as a computational mirror of this paper’s results would overstate the case.
The proponent raises no qualifying anchor. Theorem 3.1 bounds the Shapley–Shubik ratio by \(2\); Theorem 4.1 shows the Banzhaf ratio is unbounded; Theorem 5.1 bounds the Deegan–Packel ratio by \(3\); and Theorem 6.1 bounds aggregate power after splitting. Each is an inequality about power indices, with no algorithm or complexity claim. The false-name conjecture and exhaustive experiments add no such result. The NP-hardness and PP-completeness claims in the introduction are attributed to earlier papers.
A plausible regime does exist: finitely many large weighted players alongside a high-multiplicity population of unit-weight members. The paper itself cites oceanic games, so this regime is sensible. Its natural continuous questions would ask whether the power-to-proportion bounds persist for a continuum population. Those are analytic questions about limiting power indices. The indices here are defined through finite random permutations, subsets, or minimal winning coalitions; taking limits may be interesting, but it does not supply a computational result for this paper to mirror.
The strongest computational rescue would be to ask how to compute power indices or find an optimal false-name split in a continuous model. The paper establishes no computational result about either task. Theorem 6.1 gives a bound for every strategy profile without computing a best response or equilibrium. Replacing integer partitions with continuous split allocations would pose a new optimization problem, not extend a result the paper proves.
So the negative case is strong under ChoCo’s anchored-mirror standard: there is no named computational result here to continuize. The universal claim is weaker. The high-multiplicity scenario is plausible, and a separate computational study of continuous power-index evaluation could be worthwhile; the paper simply does not provide the anchor for calling it a mirror.
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.