Intransitive Classification and Choice

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The goal of this project is to develop a framework for intransitive pattern classification and models of intransitive choice. Intransitivity can arise from various forms of classifiers. This includes the augmenting of log-likelihood ratios with correction terms and collections of binary classifiers (SVMs/kernel machines, binary neural networks, etc.) when used for multi-class classifiers. Intransitivity can also arise in individual and group choice (e.g., elections, tournament-style competitions). The project is developing methods to better explain intransitivity in these classifiers and to model preference relationships in social choice. Questions being investigated by this project include: (1) why/when intransitivity occurs; (2) why/how it helps classification; (3) how to introduce intransitivity in classifier systems; (4) whether intransitivity should itself be a goal, or rather whether to treat it as an artifact of imperfection and an indication of incertitude; (5) methods to detect intransitivity; (6) how intransitivity can be used to reduce errors; (7) how to model intransitivity; (8) the relationship between intransitivity in machine learning and in sociology, psychology, voting theory, political science, operations research, mathematics, economics, and philosophy; and (9) if transitive explanations can better explain natural organisms. In addition to establishing new cross-field scientific connections, this project has a broader impact through integration of its results into new seminars, tutorial articles on intransitive decision making, and new freely-available software.