How many agents are needed to win a proximity-based vote?
The Condorcet Dimension of Metric Spaces
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This research paper explores the "Condorcet Dimension" in voting systems, particularly when voters and candidates are plotted in a 2D space (like a political compass). It aims to find the minimum number of candidates needed to create a "Condorcet winning set" – a group where no other candidate is preferred by a majority over the entire set.
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While not directly about LLMs, the paper's exploration of spatial voting models and preference aggregation is relevant. It highlights the complexity of collective decision-making even in simplified scenarios, offering insights into potential challenges and opportunities when designing LLM-based multi-agent systems where agents have preferences and need to reach consensus. The embedding of preferences in metric spaces could also be relevant for representing relationships between data points in LLM applications.