Robust Aggregation of Correlated Information

TL;DR

This paper investigates strategies for decision-making when multiple correlated information sources are involved, revealing that optimal robustness often involves ignoring some sources and providing bounds on the number of sources used.

Contribution

It introduces a framework for robustly optimal strategies under unknown correlations, showing when to ignore sources and establishing bounds on information usage.

Findings

In two-state, two-action scenarios, the optimal strategy ignores all but one source.

In general, the number of sources used is bounded by the decision problem's complexity.

The results explain why agents might ignore certain information sources in practice.

Abstract

An agent makes decisions based on multiple sources of information. In isolation, each source is well understood, but their correlation is unknown. We study the agent's robustly optimal strategies -- those that give the best possible guaranteed payoff, even under the worst possible correlation. With two states and two actions, we show that a robustly optimal strategy uses a single information source, ignoring all others. In general decision problems, robustly optimal strategies combine multiple sources of information, but the number of information sources that are needed has a bound that only depends on the decision problem. These findings provide a new rationale for why information is ignored.