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Mathematics, Greek --- Mathématiques grecques --- Sextus, --- Greek mathematics --- Geometry --- Sextus Empiricus --- -Sekst, --- Sesto, --- Sextos, --- Sexto, --- Contributions in geometry --- -Contributions in geometry --- Mathématiques grecques --- Mathematics --- Euclid's Elements

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Space and time. --- General relativity (Physics) --- Geometry --- Physics --- Philosophy. --- -Space and time --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics --- Euclid's Elements --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Geometry. --- General relativity (Physics). --- Space and time --- Physics - Philosophy.

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A surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a new profile decomposition quickly resolves two centuries old controversies of Condorcet and Borda, demonstrates, that the rankings of pairwise and other methods differ because they rely on different information, casts series doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow`s Theorem predictable, and simplifies the construction of examples. The geometry unifies seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court.

Operational research. Game theory --- Political sociology --- Voting research --- Geometry --- Mathematics. --- Government - General --- Law, Politics & Government --- Political Institutions & Public Administration - General --- Mathematics --- 514.17 --- -Voting --- Voting behavior research --- Elections --- Euclid's Elements --- Convex sets. Geometric figure arrangements. Geometric inequalities --- Research --- -Convex sets. Geometric figure arrangements. Geometric inequalities --- 514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- -514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- Voting --- Social choice. --- Voting research - Mathematics. --- Voting theory --- Operations research. --- Decision making. --- Economic theory. --- Operations Research/Decision Theory. --- Economic Theory/Quantitative Economics/Mathematical Methods.