Stability relationship between panel size and replenishment-lag reversal

Characterize the relationship between the number of unanimous reviewers and the critical replenishment lag at which stale demographic information reverses interpreter dominance in the Publish-or-Perish population-dynamics model, including whether the relationship is monotonic and what mechanism explains the observed non-monotonic cases.

Background

The paper studies a repeated peer-review selection process in which authors survive only when all reviewers approve their submissions. Under the hostile-review counterfactual, explicators reject interpreter submissions, while replenishment may use population data from earlier generations. The critical replenishment lag is the first lag length at which stale demographic information allows explicators to recover after interpreters have crossed the equilibrium threshold.

Simulations for reviewer-panel sizes from one to ten show that the first reversal occurs at different lag lengths: typically three generations for some panel sizes and two for others. Because the reported relationship is non-monotonic and depends on discrete threshold-crossing times, the paper does not establish a general law connecting panel size to reversal susceptibility. A more complete stability analysis is therefore needed to determine the underlying relationship and mechanism.

References

Honesty check on the pattern. In this discrete simulation, the first reversal occurs at lag 3 for n = 1, 2, and 5, and at lag 2 for the other reported panel sizes. Larger panels often — but not uniformly — produce reversal at a shorter lag. The result is sensitive to the discrete crossing round and does not establish a monotonic relationship between panel size and critical lag. A precise relationship would require a denser analysis and, potentially, a continuous-time reformulation. Possible mechanism. One hypothesis is that increasing the panel size changes the sensitivity of the survival functions qⁿ and (1−q)ⁿ to differences between the current and lagged population shares, allowing stale replenishment data to exert a larger effect in some cases. The simulations reported here are consistent with that explanation for several panel sizes, but the non-monotonic result at n = 5 means that they do not establish it as a general mechanism. Confirming the explanation would require a separate sensitivity or local-stability analysis.

— Publish or Perish: A population-dynamics model of the corruption of peer review  (2609.04443 - Ranganathan, 3 Sep 2026) in Section “Does this change with a larger reviewer panel?”, final paragraph before the Conclusion