| paper | d4-journals-geb-2005-0049 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Results 1–5 report experimental behavior; none states an algorithm, complexity claim, or computational formulation used to compute a result. The proposed population optimization is a plausible extension of the expected-income analysis, but it cannot supply the missing computational anchor, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed extension captures the expected-income optimization discussed alongside Result 4; it does not computationally mirror the paper’s experimental findings about offers, rejection, exclusion, or efficiency losses.
The eligible anchor set is empty. The paper’s numbered Results 1–5 report experimental findings; none classifies a computational problem as tractable, hard, or parameterized. The strongest is Result 5, established from this paper’s experiments: proposers’ self-interest, together with anticipated negative reciprocity, leads to social exclusion and inefficient allocations. Responders reject unfair offers, and proposers choose the smaller coalition when they expect it to yield more money. That is a behavioral result, not a complexity result, so it cannot support the required anchor-based case.
There is a plausible continuous extension, though it is unanchored under your criteria. Imagine a large bargaining platform that repeatedly forms three-person groups. For each responder role, let a type be a complete response rule giving that person’s acceptance probability for every offer and relevant history. Let \(\mu_1\) and \(\mu_2\) be rational distributions over the two roles’ finite sets of types, with many participants and relatively few types. A proposer faces responders drawn from those distributions.
Call the resulting problem Population Response Best-Offer. Its instance consists of the coalition values \(V_2<V_3\), the finite offer grid, and \(\mu_1,\mu_2\) with their types’ complete response rules. The task is to choose the coalition and legal offer allocation that maximizes the proposer’s expected monetary payoff under the paper’s acceptance and rejection rules. A solution gives that choice, its expected payoff, and the resulting probability of a two-person coalition. From that probability one can calculate the excluded population share and the potential efficiency loss. For fixed response rules, direct enumeration of offers and pairs of responder types solves this in polynomial time in the grid size and support sizes.
This extension has a connection to Result 4: the paper compares proposers’ actual choices with income-maximizing offers computed from observed responder behavior, finding that the high-value small coalition has the higher expected proposer income, while the intermediate condition is close. That connection makes the extension recognizable, but Result 4 still is not a computational classification and cannot count as an anchor.
The weakest point is substantial: this problem formalizes an optimization step used to interpret the experiment, rather than a computational problem the paper itself studies. The finite response-type support would also need empirical justification; if each participant has a distinct response rule, the high-multiplicity regime disappears. So there is a sensible population scenario and a precise candidate problem, but the paper supplies no qualifying named computational result to anchor the positive case.
The paper’s numbered Results 1–5 report experimental behavior, not the complexity of a computational problem. Result 5 is the strongest finding, but it says that self-interest and anticipated negative reciprocity lead to exclusion and inefficiency. Result 4 compares observed choices with income-maximizing offers calculated from estimated response behavior. Neither gives an algorithmic problem to classify. That leaves the proponent’s proposed extension without a qualifying anchor.
The proposed Population Response Best-Offer problem is the strongest version of that extension: give a proposer distributions over responder types and ask which coalition and offer maximize expected payoff. But it turns a finding about behavior in a fixed three-person game into a new optimization task for one proposer. The population distribution supplies probabilities for the proposer’s two opponents; it does not create a collective decision over the population. Repeating the experiment across many groups would aggregate the results, but each game would still involve one proposer and two responders. Making the problem more population-wide would require adding new structure, such as competition for partners or constraints on how agents can be grouped. The paper does not study those issues.
One could also ask a designer to choose coalition rules or offers for a large population of proposer and responder types. That might be a worthwhile problem in its own right, but its central question would be institutional design, not the computational counterpart of a result in this paper. The paper neither formulates such a design problem nor reports an algorithmic finding that could anchor it.
The negative case is strongest against this paper as a ChoCo anchor: its results are empirical claims about strategic behavior in a small, fixed game, and the proposed optimization formalizes a step in interpreting those claims rather than the paper’s own computational problem. It is weaker as a claim that no useful continuous coalition-formation problem could ever be built from this setting. A larger model with population-wide matching or group formation might be valuable, but that would be a new research direction, not a continuous mirror established by this paper.
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.