| paper | d4-conf-ecai-2020-0066 |
| 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 classify whether axiomatic social choice functions exist; none states a computational result for a named problem. Some proofs describe witness rules, but the proposed case offers no computational anchor or precise continuous question. In the suggested mass model, fake identities have zero mass, so preserving their effect would require changing the manipulation model.
fails bit a — no named computational result to mirror
No named computational result is mirrored; the paper's existence and impossibility classifications for trees, cycles, and hypergrids remain uncovered.
This paper has no named computational result that qualifies as an anchor under the requested standard. Its numbered theorems classify whether deterministic Pareto-efficient, false-name-proof social choice functions exist—for example, Theorem 3 proves existence on single-peaked cycles \(C_k\) for \(3\le k\le5\), while Theorem 4 proves nonexistence for \(k\ge6\). Those are axiomatic existence results, not complexity or algorithmic results about a named computational problem.
A possible population model would put mass \(\mu_v\) on each graph vertex and ask a mechanism to choose a facility location. But the paper’s Theorem 1 shows that eligible mechanisms can be replaced by outcome-equivalent ones that ignore duplicate ballots. That makes the support, rather than the population shares, decisive; in a nonatomic version, an individual’s fake identities also have no effect unless the model changes what counts as a manipulation. This is a weak basis for a continuous-population mirror of the paper’s results, and it does not supply the required anchor.
The strongest case against starts before choosing a continuous model: none of the paper’s named results is a computational result in the programme’s sense. Theorem 3 and Theorem 4 classify when a Pareto-efficient, false-name-proof social choice function exists on a cycle. The hypergrid and single-dipped theorems make similar existence claims. They do not give the complexity of a named problem or an algorithm for it. One could recast “does such a function exist for this graph?” as a decision problem, but that would be a new computational target, not a result this paper establishes.
The most charitable population model would put mass \(\mu_v\) at each vertex and choose a facility location. That is a plausible high-multiplicity scenario. The problem is specific to these results, not to high multiplicity generally: Theorem 1 shows that whenever an eligible rule exists, there is an outcome-equivalent eligible rule that ignores duplicate ballots. For that witness, the decisive population information is which vertices have positive mass, not the amounts \(\mu_v\). The proposed mirror therefore remains an axiomatic existence question over supports; the continuous range of population shares supplies no computational problem for the paper’s theorems to answer.
False-name-proofness makes a mass interpretation harder still. If a fake identity has zero mass, its report cannot affect an ordinary mass-based rule. If any positive mass at a new vertex counts, manipulation turns on a support change, which is discontinuous at zero and recovers the support-based formulation. One could instead let an agent fabricate a positive mass of fake voters, but with the paper’s unrestricted, cost-free fake identities that gives a different strategic model; adding a cost or asking for the minimum mass needed to change the outcome would create a new robustness problem.
A study of those new problems could be worthwhile. But it would add an algorithmic objective or a quantitative manipulation model absent from the paper, rather than continuize one of its named computational results. The negative case is strong under ChoCo’s stated scope test; its limit is that no modelling argument can rule out every useful follow-on question.
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.