Orthogonal Decomposition of Vectors in the Social Sciences
Professor William Zwicker
September 20, 2001
Bailey Hall 201
When there are more than two candidates running in an election, why do two reasonable voting methods sometimes yield different results? Will a collection of people, who like or dislike each other with varying intensities, be able to form stable groups of friends?
It's common, in Physics and Engineering, to break vectors into two components that are perpendicular to each other, if the effect o the original vector is best understood as the result of distinct effects of the separate components. This is true for a weight on an inclined plane, for example; one component tends to make the weight slide, while the other tends to make it stick. We show how this same idea applies to the theory of voting and to the theory of coalition formation.
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