| paper | d4-conf-atal-2017-0182 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The numbered Theorems 1–6 establish structural properties and examples of Nash equilibria; none states an algorithm, complexity bound, or hardness result. The cited equilibrium-existence hardness is from earlier work, so it cannot supply the required result-of-this-paper anchor. In the nearest atomless population limit, an individual ballot change has no effect on the outcome, so truthful reporting is optimal and the distance-based distinctions collapse.
fails bit a — no named computational result to mirror
No result is anchored. Theorems 1–6 concern equilibrium sets and ballot structure; the cited hardness results are prior work.
The positive case stops at the anchor requirement: this paper contains no named computational-complexity result. Its Theorems 1–6 prove structural facts about Nash equilibria, not that a problem is in P, NP-hard, FPT, or similar. For instance, Theorem 1 proves that equilibria under swap, footrule, or maximum-displacement bias are also equilibria under binary bias; Theorem 2 shows that the equilibrium sets for each pair of those three distance measures can differ. Both are proved here, but neither is a computational-complexity anchor.
The paper does mention that deciding equilibrium existence for plurality and veto with binary truth bias is NP-hard, citing [19, 17]. That is prior work, not a numbered result of this paper, so it cannot honestly serve as the required anchor.
A large election with many voters and relatively few shared rankings is a plausible high-multiplicity regime. But carrying over the paper’s strategic question is difficult: in a nonatomic population, one voter’s ballot change has zero effect on the outcome. With a positive truth bias, each infinitesimal voter therefore prefers to report truthfully. Making a positive mass of voters act together could restore strategic effects, but would change the paper’s individual-deviation model.
So there is a natural continuous population setting, but no qualifying named result on which to base a prover-ready continuous computational question. The cited hardness result may motivate a separate mirror, but presenting it as this paper’s anchor would overstate the case.
The proponent names no result of this paper as an anchor, and the reason is sound: Theorems 1–6 describe equilibrium structure, but none gives a complexity classification for a computational problem. The paper cites equilibrium-existence hardness from earlier work; that could motivate a separate question, but it is not a result of this paper to mirror.
The deeper obstacle is that the paper’s results depend on an individual voter being able to change the winner. In an atomless society, one voter has zero mass, so changing their ballot leaves the outcome unchanged. With any of the paper’s distance costs, a nontruthful ballot then loses utility without improving the outcome. Truthful reporting is the unique equilibrium, and the distinctions among the distance metrics disappear: Theorem 2’s strict differences vanish, while the later structural results become vacuous.
Keeping individual pivotality requires retaining finite voters of mass \(1/n\). That gives a compressed high-multiplicity discrete game, not the continuous-population limit: a voter can still swing an election at a close score margin, and that effect disappears as mass tends to zero. Alternatively, letting a whole positive-mass type coordinate its ballot change preserves strategic impact, but replaces unilateral Nash deviations with coalition behavior. That may be a worthwhile new model, but it is not a mirror of these results.
So the plausible large-election regime does not rescue the mirror. The negative case is strongest for this paper’s equilibrium results; it cannot rule out a useful future model with coalition or dynamic behavior, but such a model would change the question the paper studies.
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.