When agreement means everyone’s information is old

Same model, different update times

Imagine two lenders assessing the same borrower. Both understand how creditworthiness changes, and both received accurate information when they last checked. Yet one checked recently and the other did not. Neither needs a better forecasting model to be better informed: the timing of their observations can be enough.

In an arXiv preprint revised on November 8, 2026, Ratna K. Shrestha, Gaurav Subedi and Ayush Shrestha develop a mathematical account of this mechanism. Their evidence consists of theoretical results and numerical illustrations, not experiments or measurements of actual lenders, analysts or AI systems.

The starting point is a changing underlying condition, such as financial health. It follows a Markov process: once its current state is known, earlier states add no further information about its future evolution. Agents begin with the same information and forecasting rules. Later, they receive exact observations at different times, privately learning what they saw and when.

Provided observation timing is independent of the underlying condition, each agent can summarize its predictive information with two things: its last observed value and that observation’s age.

Why informational differences keep returning

Different ages do not automatically produce different predictions in every possible environment. The authors specify a condition under which observations of different ages always imply different predictive distributions—the probabilities assigned to possible current outcomes—even if particular point forecasts coincide.

Under that condition, asynchronous updates create asymmetric information among otherwise identical agents. If updates arrive independently across people and periods, each with a fixed probability strictly between zero and one, these differences recur infinitely often with probability one. That is an infinite-horizon result, not a claim that agents disagree continuously.

The paper also lets agents choose how frequently to seek updates. More intensive monitoring costs more but reduces expected forecasting losses. Under the stated cost and loss assumptions, a unique interior optimum can exist: updating every period need not be worthwhile.

Identical agents can choose the same update probability and still receive updates at different times. Randomness in successful updating is essential here; identical deterministic schedules would not generate that desynchronization.

Stale consensus

The most striking result concerns a stationary, mean-reverting process. In this model, deviations from a long-run average gradually lose predictive importance, while unpredictable disturbances create uncertainty.

Compare two agents whose observations remain a fixed number of periods apart. As both observations get older, each agent becomes more uncertain about the current state. Nevertheless, their forecasts become more alike on average, because both increasingly fall back on the same long-run mean.

The authors call this “stale consensus.” Expected squared forecast disagreement approaches zero while individual predictive uncertainty approaches the process’s long-run variance. Agreement therefore need not indicate precise knowledge.

One numerical example normalizes that long-run variance to one and sets persistence to 0.8. With observations aged one and three periods, the predictive variances are approximately 0.3600 and 0.7379, and expected squared disagreement is 0.3779. With observations aged four and six periods, uncertainty rises to 0.8322 and 0.9313, while disagreement falls to 0.0991. These are model quantities in normalized units, not measured percentages or probabilities of error.

The distinction depends on the dynamics. In the paper’s random-walk benchmark, which lacks mean reversion, aging both observations leaves expected squared disagreement unchanged when their age gap stays fixed.

When freshness is worth proving

The authors then model a counterparty paying for a forecasting service according to expected accuracy. The counterparty initially sees neither the forecast nor its underlying observation. Certification verifies information age, not the observed value, and carries a cost.

With two possible ages, the relatively fresh provider certifies only when its accuracy advantage covers that cost. Under mean reversion, increasing common staleness shrinks the advantage and can eliminate separation.

With many possible ages, the model supports equilibria in which sufficiently fresh providers certify and older ones remain in an undisclosed pool. Under its stationary Gaussian assumptions and unbounded age distribution, any positive certification cost prevents universal disclosure. Several disclosure cutoffs can coexist; the analysis does not select a unique market outcome.

A mechanism, not a diagnosis

The proposed applications include financial forecasting, underwriting and multi-agent AI. But the paper does not establish that stale consensus explains observed agreement in those settings. Exact observations, known dynamics and state-independent update timing are consequential simplifications.

Its practical warning is narrower: agreement alone cannot establish information quality. Observation dates and source provenance offer additional evidence about whether consensus reflects current knowledge or shared distance from it.