| paper | d4-conf-ijcai-2019-0524 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper presents an algorithm and numerical experiments, but no qualifying numbered result with a computational guarantee, so the required computational-result gate fails. The cohort proposal is concrete, but it turns sequential elicitation from one Decision Maker into population-level repeated measurement, and is not a continuous analogue of a qualifying result in the paper.
fails bit a — no named computational result to mirror
The proposed cohort version concerns Algorithm 1 for OWA and at-most-2-additive Choquet elicitation; it leaves static parameter fitting and larger-capacity models aside, and the paper proves no computational guarantee for it.
The paper has no qualifying theorem, lemma, corollary, or proposition asserting a computational result. Its closest numbered computational object is Algorithm 1, “Incremental decision making”: given alternatives, a regret threshold, and a prior over weights, it iteratively chooses a minimax expected-regret recommendation and an adversarial alternative, asks the DM to compare them, updates the posterior, and stops when the regret is below the threshold. The paper evaluates this procedure numerically, but proves no complexity classification. So there is no eligible named-result anchor here; I would not present the algorithm or its numerical tests as a hardness or tractability theorem.
The strongest positive extension I can make is a population version of Algorithm 1. Take a large, homogeneous user cohort choosing one option from a finite set \(A\subseteq[0,1]^p\). A type is a shared OWA weight vector, or a parameter vector for a 2-additive Choquet integral; mass is the fraction of residents of that type. In the simplest regime there is one type of mass \(1\), shared by millions of residents, with individual response noise following the paper’s probit model. For the relevant feature map \(g\), a member answers a query comparing \(a\) and \(b\) according to the sign of \(w^\top(g(a)-g(b))+\varepsilon\). Querying the cohort yields a fraction of “yes” responses. At a specified rational reporting precision, that fraction gives a likelihood for the shared \(w\) and updates its posterior.
The resulting problem is: given \(A\), the OWA or 2-additive Choquet feature map, a truncated Gaussian prior over \(w\), rationally reported cohort response fractions, a regret threshold \(\delta\), and an accuracy tolerance \(\epsilon\), compute an \(\epsilon\)-accurate minimax expected-regret recommendation and its adversarial comparison query. Return a recommendation once its max expected regret is at most \(\delta\). The regret objective retains the paper’s form, with \(f_w(a)=w^\top g(a)\) and \(PER(a,b)=\int [f_w(b)-f_w(a)]_+p(w)\,dw\). This mirrors Algorithm 1’s OWA and at-most-2-additive Choquet elicitation; it does not cover static fitting or higher-additivity capacities.
I would tentatively expect an approximation version to be tractable through sampling and regret estimation, but the paper establishes no such result, and exact computation could be harder. There is no hardness result here to transfer. The weakest point is also the main plausibility risk: the paper elicits preferences from one DM, while this model elicits a shared preference from a cohort. Aggregated noisy answers may also provide more information than the paper’s individual binary answers. The authors could recognize it as a natural group extension of their response-error-tolerant elicitation method, but it is not a continuous mirror of a proven result in this paper.
The decisive problem is that there is no named computational result here to mirror. The paper defines Algorithm 1 and reports numerical experiments, but proves no complexity or algorithmic guarantee about a computational problem. Its Gaussian prior is uncertainty about one Decision Maker’s preferences; it is not a distribution over a population. The paper’s continuous parameter space therefore does not make its society continuous.
The proponent’s cohort version is the strongest plausible extension of Algorithm 1, but it changes what the algorithm learns. For a cohort sharing one weight vector \(w\), a query with feature difference \(d\) would produce a response fraction. Under independent probit errors, observing \(k\) “yes” answers among \(N\) people contributes likelihood proportional to \(\Phi(w^\top d)^k(1-\Phi(w^\top d))^{N-k}\). That is repeated measurement of one preference, with cohort size controlling statistical information. In the continuum limit, the fraction can reveal the response probability exactly. This may be a useful group-elicitation protocol, but the paper studies one person’s sequential answers and gives no computational result about either protocol to extend.
Allowing heterogeneous preferences creates a more fundamental mismatch. A cohort’s response fraction is then an aggregate over different \(w\)’s, and Algorithm 1’s posterior over one DM’s \(w\) no longer describes it. If each person or type gets a personalized recommendation, the task separates into individual elicitation problems and mass has no role in the decision objective. A common recommendation would require specifying a new collective objective—such as average utility or population regret—and a query strategy for that objective. Those could be worthwhile research questions, but they would be newly formulated group decision problems, not continuous mirrors of a result in this paper.
So the negative case is strong for this paper: its central contribution is a procedure for eliciting one person’s preferences, and its computational claims are empirical. I cannot rule out every useful population-level extension of Bayesian preference elicitation. The point is narrower: the proponent’s extension does not supply a computational result from this paper whose population continuization the programme could study.
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.