Geometry of Voting

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The book explores the complexities of election and decision-making procedures, revealing how different tallying methods can lead to unexpected and often contradictory results. It introduces a geometric theory to clarify three-candidate voting systems and critiques widely accepted concepts like the "Condorcet winner." By using "profile coordinates," it visualizes voter preferences and election outcomes, allowing for a comparative analysis of various methods. Additionally, it examines apportionment methods, uncovering new insights into their inherent challenges.