| paper | d4-journals-geb-2007-0052 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper's numbered results report experimental outcomes and subject behavior; none asserts that a computational problem can be solved or is hard. A population-level equilibrium comparison can be formulated, but it extends the theory the paper tests rather than mirroring a computational result of this paper.
fails bit a — no named computational result to mirror
The proposed equilibrium comparison covers only the bottom-up and top-down budget outcomes; it leaves the paper's experimental findings on proposals, votes, prediction accuracy, and decision time without a mirror.
This paper has no qualifying computational anchor. Its numbered findings are “Result 1” through “Result 8,” and they report experimental outcomes and subject behavior, not that a computational problem is in P, NP-hard, FPT, or similar. For example, Result 1 says that bottom-up and top-down outcomes significantly differ in most cases, in the direction predicted by Ferejohn and Krehbiel. That is a named empirical finding, but it is not the kind of named computational result required for an anchor. The paper’s account of the Ferejohn–Krehbiel equilibrium result is theoretical and attributed to their earlier work; it is not a numbered computational result of this paper.
There is a plausible, but weaker, population-continuum analogue of the paper’s equilibrium comparison. Let a type \(t\) have ideal budget \(x^*(t)\in\mathbb{R}_{\ge 0}^m\) and utility \(u_t(x)=K_t-\|x-x^*(t)\|_2^2\). Give each type rational mass \(\mu_t\), with \(\sum_t\mu_t=1\). In a regime with many residents represented by a small set of preference types, a budget choice could be decided by majority mass at each stage. The mirror question would be to compute the budget induced by bottom-up and top-down voting and compare their total spending. A solution would return the equilibrium budget for each process; the paper’s theoretical prediction is that their totals need not have a fixed ordering.
That is a recognizable extension of the paper’s equilibrium comparison, but it is not an anchor-based case for this programme. The paper studies five deliberating subjects, endogenous proposals, and experimental agreement with equilibrium predictions; a mass-voting model of many residents would not preserve all of that strategic procedure without additional choices. And the median-based equilibrium calculation does not by itself pose the computational complexity question the programme is designed to study. So the honest conclusion is: a possible continuous analogue of the theory is available, but this paper supplies no named computational result to mirror.
The strongest case against a mirror is the one the proponent already identifies: this paper reports no computational result. Results 1–8 are findings about 128 experiments with five subjects per group. They give no complexity classification, algorithmic task, or family of instances whose size varies. Result 5’s observation that every trial ended within 65 moves is a sample finding, not a bound for the voting procedure. The structural equilibrium theory is attributed to Ferejohn and Krehbiel; this paper tests its predictions experimentally.
The best rescue is a large electorate voting on budgets under bottom-up and top-down procedures. Let \(\mu\) distribute mass over ideal-budget types, and ask for the equilibrium budgets under each process. That is a plausible population story. But it does not preserve what this paper tests: subjects propose amendments and can propose ending deliberations, while the paper measures how their proposals and votes produce outcomes near the predicted equilibrium. Giving every member of a continuum those rights leaves no individual with positive voting mass; introducing a finite set of agenda setters or representatives restores the small, individuated decision-making group. The weighted-median equilibrium calculation is a legitimate question about a continuum electorate, but it is a question about the cited theory, not a computational result of this experimental paper.
One could go further and ask which budget process or agenda order best serves a given distribution of ideal points. That might be a worthwhile new computational social-choice problem. It is not what any numbered result establishes: the paper compares two specified processes and reports their experimental outcomes. Likewise, turning proposal rates, vote rates, or move counts into type-level population statistics would study behavioral distributions, not the computational questions the paper answers.
So the proponent’s Result 1 analogue is the strongest possibility, but it does not supply the missing computational anchor. The negative case is strongest on that criterion; it is weaker as a universal claim that no useful continuous model can be built. A direct-democracy budget model is plausible. If the programme accepts new computational questions inspired by empirical findings, that model could merit attention—though it would be a new problem, rather than a mirror of this paper’s results.
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.