| paper | d4-journals-jet-2011-0112 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named propositions characterize cascade formation and persistence in a sequential Bayesian model, but assert no algorithm, complexity bound, hardness, or computational formulation. A new algorithmic task over a continuous population would not supply the missing computational anchor.
fails bit a — no named computational result to mirror
Proposition 1, Proposition 2, Corollary 1, and Results 1 and 2 make analytic claims about cascades, probabilities, and welfare; the paper states no computational result.
There is no qualifying computational anchor in this paper, so I can’t give an honest per-anchor continuous computational problem under your rules.
The closest named results are Proposition 1 and Proposition 2, proved in this paper. Proposition 1 says that with observable actions and payoffs, a cascade starts almost surely; mistaken cascades occur with positive probability; a mistaken cascade has positive probability of lasting forever; and, with nondegenerate transient payoff shocks, a given cascade has a positive but less than one probability of lasting forever. Proposition 2 gives the corresponding claims for noisy payoff communication: the probability that a cascade eventually starts and lasts forever approaches one as the sequence grows, incorrect cascades occur with positive probability, and a given cascade has a positive but less than one probability of lasting forever. These are results about learning and cascade probabilities, not results about complexity or algorithms. Corollary 1 and Results 1 and 2 are likewise analytic claims, not computational anchors.
There is some positive plausibility at the level of setting: many investors or adopters could share the same signal structure and payoffs, and the paper itself discusses continuum-agent models of word-of-mouth learning. But the paper’s conclusions depend on the sequence of decisions and the evolving public history. Replacing that sequence with a static distribution over types would need to preserve those features, and the resulting question would still not be anchored by a named computational result here.
So I would not name a lead mirror or predict its complexity class. That is a limit of the paper’s eligible anchors, not evidence that no continuous-population computational question could be posed.
Proposition 1 and Proposition 2 are the strongest candidates the other analyst raised, but neither gives a computational result to mirror. They establish probability statements about equilibrium paths in an ordered sequence of Bayesian decision makers: when cascades form, when they can be mistaken, and whether they last forever. Corollary 1 and Results 1 and 2 are likewise analytic claims. None defines an algorithmic problem or studies its complexity.
The best population mirror would group investors or adopters who share a signal technology and payoff environment. A static distribution over their signal types, however, discards the order that drives the results: an action can reveal a private signal to the next decision maker, while an observed payoff informs beliefs only about a project that was tried. To preserve that mechanism, the model would need a continuum of arrival times or cohorts, along with evolving histories and beliefs. The paper itself notes continuum-agent word-of-mouth models, so that setting is plausible; their existence supports the regime rather than counting against it. But the resulting question would be about continuous-time social learning, not a computational result from this paper or a standard collective-choice problem. Asking for an algorithm to calculate cascade probabilities or optimize communication delays could be worthwhile, but it would require adding a computational task and its inputs and objectives. That would be a new research question attached to the paper, not a mirror of one of its results.
So the negative case is strongest on fit and anchoring, not on the claim that no continuous model could sensibly be built. A continuum learning model may be valuable in its own right; this paper gives little basis for treating it as a continuization-programme problem.
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.