| paper | d4-conf-atal-2015-0382 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper has no numbered result asserting an algorithm, complexity bound, or hardness result for a computational problem; its theorems and proposition establish analytic or axiomatic properties. The proposed mass bribery problem is a plausible follow-on, and the paper itself points to studying bribery under its tiebreaking schemes, but it is not a continuous analogue of a computational result proved here. The missing anchor makes the mirror fail.
fails bit a — no named computational result to mirror
No result is mirrored: Theorems 1–4 and Proposition 1 establish analytic or axiomatic claims, while the paper's computational hardness statements refer to prior work.
I can’t make a case that meets your anchor rule: the paper has no numbered theorem, lemma, corollary, or proposition asserting a computational complexity result. Theorems 1 and 2 establish that PUT is independent of the computation tree under stated conditions, and is the unique continuous, non-singular extension agreeing with the rule on non-tied profiles. Theorem 3 establishes stability under sufficiently small perturbations, and Proposition 1 gives a perturbation radius for plurality. Theorem 4—proved here, with a proof sketch—characterizes NIVP as the unique symmetric perturbation scheme satisfying the paper’s four properties. These are analytic or axiomatic claims, not complexity classifications. The paper does mention that computing PUT winners can be NP-hard for STV and ranked pairs, but that is an unnumbered claim pointing to prior work, so it cannot serve as a required anchor.
The strongest positive lead I can see is a *new* continuous bribery question motivated by the paper’s closing suggestion to study bribery under its tiebreaking schemes. Consider a large election with standardized rankings, represented by a rational distribution \(\mu\) over the \(\tau\) rankings present. Types are complete rankings, and mass is each ranking’s population share. Given a target \(c^\star\), swap costs \(\gamma(r,r')\), a budget \(B\), and a probability threshold \(q\), ask whether there is a mass transfer \(x_{r,r'}\ge 0\), with \(\sum_{r'}x_{r,r'}\le\mu_r\) and total cost at most \(B\), that makes \(c^\star\)’s NIVP winning probability at least \(q\). The transferred mass defines the new society \(\mu'\); its NIVP probability is the probability that \(c^\star\) wins after an infinitesimal perturbation with independent \(Z_r\sim N(0,\mu'_r)\). A solution is such a transfer.
This has a credible high-multiplicity regime: millions of voters using relatively few ballot types, with bribery measured as a share of the electorate. It also keeps the population distribution as the object being changed; the perturbation is part of the tie-breaking rule. I would treat this as a research question whose complexity is open, not predict a class without further analysis.
The weakness is substantial: the paper already extends NIVP to real-weight profiles, and it gives no numbered computational result about bribery or its complexity. So this is a plausible follow-on to the authors’ work, but it is not an anchored mirror of a computational result in this paper.
The strongest case against a *mirror* is that the paper supplies no named computational result to mirror. Theorems 1 and 2 concern PUT’s definition and axiomatic properties; Theorem 3 and Proposition 1 concern perturbation stability; Theorem 4 characterizes NIVP. None classifies the complexity of an algorithmic problem. The paper’s claim that computing PUT winners can be NP-hard is presented as prior work, and its closing paragraph proposes studying bribery, control, and manipulation as future work.
The proposed NIVP bribery question is the strongest follow-on, but it is not anchored to a result in this paper. Its model is sensible: a large electorate with few ranking types, mass transfers between types, and costs attached to those types fits the high-multiplicity setting. Neither fractional transfers nor the probability objective makes it inherently ill-posed. But the computational question comes from adding an intervention problem that the paper does not analyze. A sharper variant—such as minimum-cost mass transfer to make a target a PUT winner—has the same problem: it is a new project, not a continuous version of a result here.
There is also little left to continuize in the paper’s existing formal results: it already extends homogeneous rules to real-valued profile vectors and extends NIVP to fractional profiles. That settles the relevant continuous definitions, though it does not settle the complexity of new intervention problems.
So the negative case is strong only under the assignment’s anchoring requirement: there is no continuous *mirror of a computational result* in this paper. It cannot honestly establish the broader claim that no worthwhile continuous question exists. The authors themselves point toward computational follow-ups, and the proposed mass-bribery problem could be worth studying on its own. If that counts as an anchor, the case against it is weak.
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.