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How to choose a winner : the mathematics of social choice

Snapshots of modern mathematics from Oberwolfach

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

Author(s)

Victoria Powers

License

DOI (Digital Object Identifier)

10.14760/SNAP-2015-009-EN

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2015-009-powers.pdf

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