| paper | d4-conf-ijcai-2018-0775 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The only named results raised are an axiomatic characterization and a structural transitivity condition; neither asserts an algorithm, complexity bound, hardness result, or computational formulation. Mass CP-majority is a recognizable extension with a straightforward weighted tally, but it has no computational result in this paper to mirror, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed extension reweights the CP-majority pairwise rule over context types. It does not mirror Theorem 1's axiomatic characterization or Theorem 2's result for socially single-peaked power relations.
There is a plausible population mirror here, but the paper supplies no named computational anchor of the kind your brief requires. Theorem 1, proved in the paper, characterizes CP-majority on two alternatives as exactly the solution satisfying Equality of Coalitions, Neutrality, and Positive Responsiveness. Theorem 2, also proved here, says that a socially single-peaked power relation yields no strict three-item cycle under CP-majority. Both are axiomatic or structural results: neither states a complexity bound, an algorithm, or a hardness result. Theorem 2 is the strongest basis for a positive case, but it cannot honestly serve as the required anchor.
The most credible extension is to treat the paper’s virtual electorate of coalitions as the population. Keep the ranked items \(C\) finite. A voter type \(t\) records which item pairs its coalition context can compare, and the context’s strict comparison or indifference on each such pair. An instance is a finite support of these types with rational masses \(\mu_t\) summing to \(1\). The named extension would be Mass CP-Majority: compute the pairwise relation
\[
xR_\mu y
\quad\Longleftrightarrow\quad
\sum_{t:\,x\succ_t y}\mu_t
\;\geq\;
\sum_{t:\,y\succ_t x}\mu_t .
\]
Its solution is that relation, including any ties or cycles; imposing a transitive ranking afterward would change the paper’s rule. There is no optimization objective—the task is to compute the social comparison.
This has a direct population story: many recurring teams or evaluation contexts compare a fixed pool of people or objects, and relatively few comparison patterns recur across those contexts. Each type is a context’s complete comparison pattern for this task; its mass is the fraction of contexts with that pattern. For a finite power relation, assigning each coalition context its induced pattern and its frequency recovers the paper’s CP-majority counts after normalization. That makes the proposed question recognizable from the paper’s explicit “coalitions as voters” interpretation, and it continuizes the electorate rather than the items being ranked.
The direct Mass CP-Majority problem is tractable when its type distribution is explicit: tallying each pair takes polynomial time in the support size, \(|C|\), and the mass bit length. A mass version of the transitivity question is also natural: under a common single-peaked order for the context preferences, does the pairwise relation avoid cycles? Theorem 2 provides the structural motivation, though not a computational result for this new input model. Further work could ask which mass profiles can actually arise from one coherent power relation, and what happens when that relation is given succinctly.
The mirror’s weakest point is that teams are derived subsets, not independent people, and the paper counts all coalitions equally. A real organization’s team contexts may have very different frequencies, while giving them empirical masses changes the paper’s input model. More fundamentally, an arbitrary distribution over comparison-pattern types may discard constraints that make those patterns come from a single power relation. So this is a defensible, narrowly scoped extension of the CP-majority rule and its transitivity analysis—not a continuous mirror anchored in a named computational result of this paper.
The strongest case against a continuous mirror is that the paper has no named computational result to mirror. Theorem 1 characterizes CP-majority through axioms; Theorem 2 gives a sufficient condition for transitivity. Neither states a complexity bound, algorithm, or hardness result. The other main results are also axiomatic or structural. That is a decisive mismatch with a programme about the computational complexity of problems posed over continuous societies.
The best rescue is the proposed Mass CP-Majority: treat recurring coalition contexts as a population, group them by their comparison patterns, and use rational masses to tally pairwise support. That is a plausible extension, and the paper itself mentions probabilities of coalition formation as a possible way to weight information. But it changes the input from one power relation over all subsets of \(N\) to a distribution over contexts or institutions. The contexts in the paper are overlapping subsets whose comparisons come from one shared power relation; a distribution over their patterns either drops that coherence or requires extra structure to preserve it. Either way, the resulting question is a new weighted aggregation problem, not the continuous counterpart of a computational result in this paper.
Theorem 1 does not supply a computational anchor: its characterization is about which solution satisfies the axioms, and changing equal coalition counts to masses changes the rule’s input and axiomatic setting. Theorem 2 likewise motivates a weighted transitivity question, but it is a structural condition, not an algorithmic claim. One could study those extensions, but the proponent’s own account concedes that they are extensions rather than mirrors of the paper’s results. On the programme’s stated terms, that is not enough to justify a continuous mirror.
This negative case has a real limit: the virtual-electorate interpretation and the paper’s mention of probabilistic coalition weights make a continuous extension credible. I would not claim that no sensible scenario exists. I would claim that the paper offers no computational result for that scenario to mirror.
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.