| paper | d4-conf-ecai-2014-0174 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The type-level MOOC model is a plausible extension, but Proposition 1 only characterizes the fixed point as an eigenvector. The paper gives no computational guarantee, hardness result, or computational formulation used to compute, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed model covers basic PeerRank's fixed-point grades; it leaves the axiomatic properties in Propositions 2–7 and the synthetic accuracy experiments aside. The generalized rule's grading-error reward would require additional type-level error information.
The best positive lead is a type-level PeerRank model for a very large MOOC. Let each type describe a student’s work class and grading profile, and let \(\mu_t\) be that type’s share of the cohort. Let \(a(s,t)\) be the expected grade a type-\(t\) grader gives type-\(s\) work. The output is a grade \(x(s)\in[0,1]\) for each type, satisfying
\[ x(s)=(1-\alpha)x(s)+ \frac{\alpha}{M}\sum_t \mu_t x(t)a(s,t), \qquad M=\sum_t\mu_t x(t). \]
This is the mass-weighted version of PeerRank’s fixed-point equation. With a small number \(\tau\) of types and a grading pattern determined by type, the cohort can be enormous while the computation depends on \(\tau\). A finite-support instance reduces to an eigenvector problem, so the natural expectation is tractability. The mirror would cover computation of the basic PeerRank grades; further questions include uniqueness and convergence, and how the generalized rule’s accuracy-reward term behaves in a type-level model.
I can’t present that as an anchored case under your criteria. The closest named result is Proposition 1 (Fixed point), proved in this paper: the PeerRank fixed-point grades are an eigenvector of the grade matrix \(A\). Propositions 2–7 establish domain and axiomatic properties. None asserts a complexity result such as polynomial-time solvability or hardness, and the synthetic experiments are not numbered computational results. Proposition 1 makes the eigenvector mirror plausible, but it does not establish its complexity or a continuous-population result.
The proposed model’s weakest point is whether students can genuinely be grouped by type: PeerRank is sensitive to who grades whom, and the paper explicitly says it is not anonymous. If reproducing those individual relationships requires a distinct type for each student, the support-size advantage disappears. So there is a credible continuous-population direction here, grounded in the paper’s MOOC setting, but no eligible named anchor—and therefore no defensible per-anchor complexity verdict.
Proposition 1 is the only plausible anchor, and it is not a computational result. It says that a PeerRank fixed point satisfies \(AX=\lambda X\), where \(\lambda=\sum_i X_i\). The paper gives no complexity claim about finding that fixed point, no input-output problem with a stated precision or selection rule, and no algorithmic or hardness theorem. Propositions 2–7 are properties of the rule; the experiments measure prediction error. So “compute PeerRank grades for a continuous society” is a new study of the proposed method, not a continuous counterpart to a computational result in this paper. Under the stated criteria, that is the decisive objection.
The proponent’s best repair is a large MOOC with finitely many student and grading types. If every type-\(s\) student receives the same grade from every type-\(t\) grader, the mass-weighted equation
\[
x(s)=\frac{\sum_t \mu_t x(t)a(s,t)}{\sum_t \mu_t x(t)}
\]
is a coherent aggregate model. It is also a plausible high-multiplicity setting: the paper itself motivates PeerRank with MOOCs, so denying that such a regime makes sense would be a weak argument.
But the equation is an exact quotient only under strong symmetry: students within each type must remain interchangeable in the grading relationships the rule uses. The paper explicitly makes identity matter. With arbitrary individual assignments, students in the same proposed type can receive different grades; averaging the grade matrix does not generally preserve its fixed-point grades. The generalized rule needs still more information: its absolute-error term depends on the distribution of individual grading errors, which an average grade does not determine. Richer type descriptions can preserve those details, but may erase the support-size advantage; a stochastic or graph-based model can restore aggregation, at the cost of posing a further modeling question.
That leaves a credible MOOC extension, but not a surviving anchored mirror. The negative case is strongest on this distinction, not on the claim that a continuous population is implausible. If the standard is broadened to include new algorithmic questions about any rule a paper defines, the mirror may be worthwhile. On the requested standard—continuous mirrors of named computational results—this paper supplies no eligible anchor.
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.