Pairwise net influence on LLM action logs: detection at the calibrated rate, blind to two pairs, fooled by low-temperature shared priors

This is a strong paper, and an unusually honest one. I liked the pre-registration most. The predictions were frozen before the runs, the ones that turned out wrong are labeled as wrong, and the post hoc analyses are labeled post hoc. That is not how most sprint papers handle it, and it makes the rest of the paper easier to trust.

The Table 2 work is the part I would point an auditor to first. The original paper never says what its "state" is. This author worked out that the published numbers only come back if the state is the previous round's joint action, and then showed what that choice costs at small samples: a spurious pair gets named in 57% of 50-round games with no collusion at all. That is a real finding, not a replication checkbox, and it changes how anyone should use the statistic.

The calibration argument is also done right. Instead of just reporting a low detection rate on LLM logs, the author measured how much the assistant actually colluded, put that on the scripted scale at CP 0.13 to 0.33, and showed detection tracks it. That tells you far more than a raw rate would. The limited detection is about weak collusion, not about LLMs being somehow unreadable.

A few things would make it stronger. First, the temperature and mixed-model control cells need more seeds. Right now n = 5 is carrying a lot of weight in the headline numbers, and a couple of games either way would move the story. Second, test the lag-aware variant you propose for AE2. You showed lagged copying is invisible to a same-round statistic, so running the lagged version is the obvious next step, and right now it is only sketched. Third, do something about the judge's position bias. The first-listed pair gets 0.5 or more in 9 of 10 controls, so either randomize the pair order in the prompt or report the judge with that bias corrected. As it stands, the three-way ranking is hard to read as a fair comparison. Fourth, try the tool-driven assistant you propose, and push it to CP 0.5 or above at 200 rounds. The claim that detection tracks calibration is only checked in the low-to-moderate range so far, and the high-CP cell is the one that would close the case. And for the double-auction follow-up, pre-declare a price discretization up front. That is the step that turns a toy-game result into a market result.

Two things I need to be straight about. The calibration match came from a conversion worked out after the pre-registered prediction failed, not from the prediction itself, so it should be read as post hoc, not as a confirmed forecast. And the permutation fix is not the whole story: it stays silent at 60 rounds, 0 of 10, but flags 2 of 5 at 200 rounds and 2 of 3 round-3 controls, worse than the published rule there. The abstract should say that.