Imagine a group of AI agents tasked with making a decision. How do they ensure fairness and avoid biases? A fascinating new research paper explores the complexities of collective decision-making in multi-agent systems powered by Large Language Models (LLMs). Traditionally, these systems have relied on simple methods like 'dictatorship' (one agent decides) or plurality voting. However, researchers are finding these approaches lacking. The paper introduces GEDI, an innovative electoral system for LLM-based agents, which incorporates more nuanced voting mechanisms inspired by human social choice theory. Testing GEDI on challenging question-answering benchmarks revealed surprising results. Smaller LLMs and notably, the powerful GPT models, showed significant performance boosts when using a voting system. The research also explores the ideal 'voting quorum' – how many agents are needed for optimal collective intelligence? As it turns out, even small groups can produce significant gains. The study also delves into the robustness of these systems against unreliable agents and reveals how different voting methods perform when some agents provide faulty information. The findings highlight the importance of carefully selecting the right voting mechanism depending on the desired outcome. While the research uses question-answering as a testbed, the implications extend far beyond. Imagine AI teams designing products, negotiating contracts, or even making strategic business decisions – the ability to incorporate diverse voting methods opens exciting new possibilities. This research underscores that simply having smarter individual AI agents isn’t enough. The real magic lies in enabling them to collaborate and make decisions collectively, fairly, and robustly.