How to choose a winner : the mathematics of social choice

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How to choose a winner : the mathematics of social choice

Suppose a group of individuals wish to choose among several options, for example electing one of several candidates to a political office or choosing the best contestant in a skating competition. The group might ask: what is the best method for choosing a winner, in the sense that it best reflects the individual preferences of the group members? We will see some examples showing that many voting methods in use around the world can lead to paradoxes and bad outcomes, and we will look at a mathematical model of group decision making. We will discuss Arrow’s impossibility theorem, which says that if there are more than two choices, there is, in a very precise sense, no good method for choosing a winner.

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Mathematical subjects

Discrete Mathematics and Foundations

Connections to other fields

Humanities and Social Sciences


Victoria Powers


DOI (Digital Object Identifier)


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Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

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