| paper | d4-conf-ijcai-2017-0802 |
| 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 reports computational work and says OPRA computes margin of victory, but contains no numbered theorem, lemma, corollary, or proposition asserting a computational result to anchor this mirror. The continuous margin-of-victory question is recognizable, but the required computational-result bit fails for this paper.
fails bit a — no named computational result to mirror
This candidate mirror covers the margin-of-victory computation mentioned for OPRA; it leaves the paper's learning, manipulation, combinatorial voting, and resource-allocation results aside.
The strongest positive lead is margin of victory, which the paper says OPRA computes to measure consensus and attributes to Xia’s 2012 work. It has a natural population mirror. Let \(R\) be a fixed scoring rule, and let a society be a rational distribution \(\mu\) over the \(\tau\) reported ranking types. If \(w\) is the current unique winner, define continuous margin of victory as the minimum mass of ballots that must change type so that some \(c\ne w\) ties or defeats \(w\), under a specified tie convention.
A solution is a transfer matrix \(x_{t,t'}\ge 0\), with \(\sum_{t'\ne t}x_{t,t'}\le\mu_t\). It induces
\[
\mu'_t=\mu_t-\sum_{t'\ne t}x_{t,t'}+\sum_{s\ne t}x_{s,t},
\]
and minimizes \(\sum_{t\ne t'}x_{t,t'}\) subject to the winner-change condition under \(R\). The setting is plausible for a large election with many voters but relatively few distinct rankings: a type is a complete ranking, and mass is the fraction of voters with that ranking. For a fixed scoring rule, the winner conditions are linear, so this version can be solved with a polynomial-size LP in the supplied support.
The paper gives no qualifying anchor for that problem, though. It contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a complexity result. It mentions margin of victory as something OPRA computes, but does not state a numbered result or a complexity claim for it. The survey’s general statement that the author established NP-hardness of manipulation also lacks a specific voting scheme and numbered result. I therefore can’t present either as the required anchor or give a result-specific prognosis. The margin-of-victory formulation is a credible positive mirror candidate; this paper does not supply the named result needed to make it an anchored case.
The margin-of-victory proposal is not a result-level anchor from this paper. The paper says OPRA computes the margin of victory and cites Xia (2012), but it gives no formal problem variant or complexity result for it. Its statement that manipulation is NP-hard in “many common voting schemes” is also too general to anchor a specific mirror. So the proposed mass-transfer LP is a new question inspired by the paper, not a continuization of a named computational result in it.
The LP claim also needs a qualification: if a changed ballot may become any ranking, the destination types include rankings outside the society’s support. Restricting destinations to the \(\tau\) supported rankings changes the problem; allowing all rankings creates an exponential-variable formulation whose tractability depends on pricing.
That is the strongest honest negative case, and it is about the paper’s fit to this assignment, not a fundamental flaw in the mirror. Large elections with repeated rankings make continuous margin of victory a plausible population question. I cannot honestly argue that no worthwhile mirror exists in any scenario; the margin-of-victory mirror may be worth studying when anchored to the cited work.
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.