| paper | d4-conf-aaai-2013-0230 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
A population-weighted Kemeny objective is a coherent continuous question. But the paper has no numbered theorem, lemma, corollary, or proposition asserting an algorithm, complexity bound, or hardness result; it cites Kemeny hardness from earlier work, and its empirical performance findings do not meet the named-result test. Bit (a) therefore fails, regardless of the mirror’s plausibility.
fails bit a — no named computational result to mirror
The candidate mirror covers the paper’s Kemeny–Young aggregation objective; it leaves the PRBR agent, human learning, repeated-round adaptation, and experimental performance findings unmirrored.
The paper has no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. Its reported findings are empirical. It says computing Kemeny–Young is NP-hard, citing Dwork et al. (2001), and cites Dokow and Holzman for claims about manipulation; neither is a numbered result proved in this paper. So I cannot honestly supply the required named anchor.
The strongest nearby mirror is the computation underlying the paper’s social welfare rule. Given candidates \(C\) and a support of rankings \(T\), each with rational mass \(\mu_t>0\) summing to \(1\), find a ranking \(\pi\) minimizing
\[
\sum_{t\in T}\mu_t\,d(t,\pi),
\]
using the paper’s lexicographic tie-break. A type is a complete ranking; its mass is its share of a large electorate, such as participants ranking a recurring set of proposals. The output is the collective ranking, and the objective is expected disagreement. The question is its complexity in \(m\), \(\tau\), and the input bit length.
This is a credible population mirror of the Kemeny aggregation problem, though not an eligible anchor-based case. A finite profile with \(n_t\) votes of type \(t\) maps directly to \(\mu_t=n_t/n\), preserving the minimizing rankings. Thus the Kemeny hardness cited in the paper suggests hardness transfers. That addresses the aggregation rule, not the paper’s main agent-design contribution.
My weakest point is that the paper’s experiments use committees of three people and four candidates. The PRBR agent’s best response depends on being a pivotal individual; in a nonatomic population, one person’s vote has zero effect. Making that strategic question continuous would require an additional assumption, such as a positive-mass bloc, and would change the paper’s studied setting.
The strongest case against a mirror starts with the paper’s contribution: it proves no numbered theorem, lemma, or corollary about computational complexity. Its new results are empirical findings from a fixed game with three players and four candidates. The complexity claims about Kemeny computation and manipulation are cited from earlier work. PRBR is a strategy evaluated in the experiment, not an efficient algorithm whose complexity the paper establishes. On the requested anchor test, the case for supplies no named result to mirror.
The weighted Kemeny problem it proposes is nevertheless a coherent candidate: minimize \(\sum_{t\in T}\mu_t d(t,\pi)\) over rankings \(\pi\). It has a plausible large-electorate interpretation, and it would be a mistake to reject it just because the answer may be known or hardness may persist. For rational \(\mu_t\), clearing denominators gives an equivalent finite profile with integer multiplicities. That makes the bridge to high-multiplicity Kemeny exact, but it also shows that this candidate studies the complexity of the paper’s aggregation rule—not its main contribution, which is how a best-response agent performs against people over repeated rounds. It abstracts away the human behavior and agent-design findings that distinguish this paper.
A stronger attempt to mirror PRBR runs into a different problem. In a nonatomic population, one person’s vote has measure zero, so the individual best response defined in the paper cannot affect the outcome. Giving an entire type positive mass and letting it change its vote together avoids that degeneracy, but turns individual strategy into coordinated bloc behavior. Adding types for behavioral patterns and previous-round votes could support a continuum model of adaptation, but that would be a new dynamic computational question, not a computational result of this paper.
So the negative case is persuasive about the absence of an eligible anchor and the distance between the proposed Kemeny mirror and the paper’s main contribution. It cannot honestly establish the universal claim that no worthwhile mirror exists: the weighted Kemeny problem remains a credible mirror of the formal aggregation component, and high multiplicity makes its population regime sensible. The case against is therefore limited, not airtight.
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.