# Robust Decision Aggregation with Second-order Information

arXiv: https://arxiv.org/abs/2311.14094 · HTML: https://mlsanity.com/paper/2311.14094/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [Are You Smarter Than a Random Expert? The Robust Aggregation of Substitutable Signals](https://mlsanity.com/paper/2111.03153/) (2021)
- [The Wisdom of the Crowd and Higher-Order Beliefs](https://mlsanity.com/paper/2102.02666/) (2021)
- [Forecast Aggregation via Peer Prediction](https://mlsanity.com/paper/1910.03779/) (2019)
- [Wisdom of the Crowd Voting: Truthful Aggregation of Voter Information and Preferences](https://mlsanity.com/paper/2108.03749/) (2021)
- [Eliciting Thinking Hierarchy without a Prior](https://mlsanity.com/paper/2109.10619/) (2021)
- [Learning of Optimal Forecast Aggregation in Partial Evidence Environments](https://mlsanity.com/paper/1802.07107/) (2018)

## Built on by (most cited first, 7 of 7)

- [Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information](https://mlsanity.com/paper/2510.01499/) (2025)
- [Eliciting Informative Text Evaluations with Large Language Models](https://mlsanity.com/paper/2405.15077/) (2024)
- [Robust forecast aggregation via additional queries](https://mlsanity.com/paper/2512.05271/) (2025)
- [Robust Decision Aggregation with Adversarial Experts](https://mlsanity.com/paper/2403.08222/) (2024)
- [Prior-Agnostic Robust Forecast Aggregation](https://mlsanity.com/paper/2604.24517/) (2026)
- [Mitigating the Participation Bias by Balancing Extreme Ratings](https://mlsanity.com/paper/2502.03737/) (2025)
- [Multi-agent decision making: A Blackwell's informativeness approach](https://mlsanity.com/paper/2605.06028/) (2026)

## Abstract (arXiv)

We consider a decision aggregation problem with two experts who each make a binary recommendation after observing a private signal about an unknown binary world state. An agent, who does not know the joint information structure between signals and states, sees the experts' recommendations and aims to match the action with the true state. Under the scenario, we study whether supplemented additionally with second-order information (each expert's forecast on the other's recommendation) could enable a better aggregation. We adopt a minimax regret framework to evaluate the aggregator's performance, by comparing it to an omniscient benchmark that knows the joint information structure. With general information structures, we show that second-order information provides no benefit. No aggregator can improve over a trivial aggregator, which always follows the first expert's recommendation. However, positive results emerge when we assume experts' signals are conditionally independent given the world state. When the aggregator is deterministic, we present a robust aggregator that leverages second-order information, which can significantly outperform counterparts without it. Second, when two experts are homogeneous, by adding a non-degenerate assumption on the signals, we demonstrate that random aggregators using second-order information can surpass optimal ones without it. In the remaining settings, the second-order information is not beneficial. We also extend the above results to the setting when the aggregator's utility function is more general.