Target alignment, dilution and forecast selection when cross-sectional forecasts share a common target

Top AI forecasting systems are approaching superforecaster-level accuracy on future world events, but still rely primarily on off-the-shelf LLMs combined with forecasting-specific context gathering and scaffolding. We study how to improve this recipe through ensembling: given a fixed number of samples, which off-the-shelf model forecasts should be combined to maximize accuracy? On binary questions from the Metaculus AI Benchmark, we find that individual accuracy is not enough: many frontier LLMs make highly correlated predictions, limiting the value of additional forecasts from the same or similar models. Instead, the strongest ensembles combine accurate but diverse forecasters, with models such as \model{Grok 4} contributing disproportionately because their predictions are less correlated with other frontier LLMs. These results suggest that the strength of the AI crowd comes not from sampling more forecasts indiscriminately, but from combining forecasts across models with complementary errors, motivating forecasting systems that explicitly optimize for both model quality and diversity.

Forecast reconciliation usually starts from a fixed measurement system and asks how forecasts should be projected onto a coherent space. We ask a different question: which additional linear measurements should be forecast and included in the reconciliation system? We propose REGAIN, a reconciliation-gain framework that learns normalized auxiliary directions, forecasts the induced series with a frozen forecasting oracle, and selects directions by their target-weighted loss reduction after augmented generalized least-squares reconciliation. Unlike variance-based components or predictability-based auxiliary selection, REGAIN optimizes the downstream effect of an auxiliary measurement on the final reconciled forecasts. We provide a statistical characterization showing that useful auxiliary directions must provide complementary information about unresolved target uncertainty, rather than merely being easy to forecast. The analysis also clarifies the covariance-risk reduction mechanism, the role of bias changes in realized quadratic risk, and the stability of estimated gain signals. A stagewise learning algorithm with held-out gain screening is developed, together with an optional joint refinement step. Experiments on Beijing PM2.5 and Australian Tourism data show that gain-selected measurements can improve both ordinary multivariate and hierarchical forecasts, especially when they reveal residual uncertainty not captured by the original measurement system.

In the current practices of machine learning, the evaluation of forecasts has become a cornerstone of scientific progress. A multitude of evaluation metrics have been suggested and used to qualify "good" forecasts. What do those metrics share? How are they related? In this work, we use a protocol borrowed from game-theoretic probability to show that a large part of evaluation metrics can be viewed as averaged outcomes of fair gambles. Intuitively, a fair gambler is one which a forecaster would expect to fail. Hence, the gambler's ability to gain disproves the quality of the forecast. Standard evaluation metrics are then variants of choices of such fair gambles. In particular, this choice is structured along two dimensions, one of which separates calibration-type and regret-type metrics. In particular, this framework sheds light on the relationship of calibration and regret showing a theoretical equivalence in their ability to evaluate when being scaled appropriately, but the incomparability of obtained scores.