This question comes from implementing the consensus engine in iPulse AI, an Open Agentic Investment Research Platform that I'am developing with my team for 3 years now. I mention the platform purpose only to explain the applied setting and context. By “open,” I mean that the research questions, methodology, evaluation procedures, historical forecasts, limitations, results and unsuccessful approaches are intended to be publicly inspectable and subject to external scrutiny. Since launch in November 2025 (2 years after development), I have recorded each production forecast as it was originally issued, together with its timestamp, detailed AI agent configuration, specified Investment Evaluation Framework it's instructed to follow, contemporaneous market and fundamental inputs, and the subsequently realized return path. Everything runs in batches of Deep Analysis, done every two weeks or so. Each agent is intended to produce a structured investment thesis rather than merely classify an asset as going up or down. The current implementation contains 12 distinct agent configurations evaluating 380 assets. One run therefore produces 12 separate theses per asset and 4,560 analyst–asset evaluations overall. The evaluations are launched as a single time-aligned batch, using the same evaluation timestamp and a common set of inputs (Global events starting from model's knowledge cutoff date till date, and asset specific fundamentals and financials). This minimizes differences caused by news or market conditions changing during the run. However, the agents are not genuinely independent: they may share input data while differing in the model (ChatGPT vs Claude vs Gemini vs Grok), investment framework (Value Analysis Framework, Power Dynamics Framework, AI readiness and visionary disruptor framework etc) and mode (web search enabled or not). This dependence is what makes the consensus problem difficult. My initial implementation treated consensus as a democratic vote—effectively a board of AI advisors or (AI Parliament) in which every member had equal weight. I am now looking for statistically grounded criticism and established, implementable methods for aggregating these different forecasts while accounting for shared information, correlated errors and changing performance. Suppose the system contains systematic research analysts forecasting the same asset over the same horizon. An analyst is not just one model. Each analyst is a configuration consisting of: an LLM or reasoning model; an investment-analysis framework; a retrieval mode, with or without external search; a common set of market and fundamental input data. The input dataset is largely shared, while the model, framework and retrieval configuration can differ. Consequently, the analysts are neither independent nor equally correlated. For example, two analysts using the same investment framework may make similar errors even if they use different underlying models (ChatGPT vs Gemini vs Claude). At forecast origin , analyst produces a path of cumulative excess-return forecasts: $$ f_{i,t}
\left( f_{i,t}(1),\ldots,f_{i,t}(H) \right)^\top . c_t(h)
\sum_{i=1}^{m} w_{i,t} f_{i,t}(h), \qquad w_{i,t}\geq 0, \qquad \sum_{i=1}^{m}w_{i,t}=1. w_{i,t}=\frac{1}{m}. This is simple and difficult to overfit, but treats several highly similar analysts as independent confirmations. 2. Weighting by recent historical performance For a specified path-level loss $L_{i,s}$ , one possibility is an exponentially discounted rule such as w_{i,t} \propto \exp\left( -\eta \sum_{s<t}\rho^{,t-s}L_{i,s} \right). This adapts to changing performance, but may chase noise and eliminate temporarily weak analysts. 3. Covariance-aware weighting Let $e_{i,t}(h)$ denote analyst $i$ 's forecast error at horizon $h$ . An integrated error-covariance matrix could be estimated as \Omega_{ij}
\sum_{h=1}^{H} a_h, \operatorname{Cov} \left( e_{i,t}(h),e_{j,t}(h) \right), w_t
\arg\min_{w\in\Delta_m} w^\top\Omega w, where $\Delta_m$ is the probability simplex. This accounts for average error dependence, but assumes that the estimated relationship remains relevant in the current macroeconomic environment. 4. Regime-dependent weighting The weights could instead depend on observable or latent state variables $z_t$ : w_t=g(z_t), $$ where might contain volatility, inflation, liquidity, growth or other macroeconomic-state indicators. This could recognize that some analytical frameworks perform better in particular environments, but estimating many conditional weights from a limited history creates substantial overfitting risk. A further complication is the potentially valuable contrarian analyst (The Michael Burry AI for example) . An analyst may have worse unconditional performance than the group but make different errors, or perform particularly well during the relatively rare periods in which the majority suffers a common-mode failure. Weighting analysts only by individual average loss could remove exactly the analyst that provides the most useful conditional diversification. I have started storing every forecast at its original issue time, together with the analyst configuration, contemporaneous macro state and subsequently realized return path. The weights can therefore be evaluated through chronological walk-forward tests rather than fitted and tested on the same observations. For this question, assume that an economically appropriate path-level loss has already been selected. Choosing that loss is a related but separate problem: pointwise MSE can, for example, score a forecast of a useful cyclical pattern poorly when its phase is slightly displaced. Is there an established and practically implementable framework for combining: unequal and partially shared information; correlated forecast errors; regime-dependent analyst skill; and the conditional value of contrarian forecasts? Would the statistically defensible approach be a hierarchical or factor model for the analysts' shared error components combined with dynamic model averaging, a contextual prediction-with-expert-advice algorithm, or a regularized rolling optimization of the combination weights? In particular, how can one distinguish a genuinely diversifying contrarian analyst from a merely noisy one using only chronologically resolved forecasts, while limiting overfitting when the number of market regimes and analyst configurations is large relative to the available history? Related discussions include ensemble techniques for return forecasts , combining forecasts at different horizons , and combining alternative volatility estimates , but they do not appear to address this combination of structured dependence, regime-dependent skill and path forecasts.