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A chaotic Exploration of Aggregation Paradoxes

Paradoxes from statistics and decision sciences form amusing, yet intriguing mathematical puzzles. On deeper examination, they constitute serious problems that could cause us, unintentionally, to adopt inferior alternatives. It is indicated here how ideas form "dynamical chaos" and orbits of symmetry groups can be modified and combined to create a mathematical theory to understand, classify, and find new properties of these puzzling phenomena.