New PDF release: Decisions and Elections: Explaining the Unexpected

By Donald G. Saari

ISBN-10: 0521808162

ISBN-13: 9780521808163

This hugely available ebook deals undergraduates and pros a brand new, varied interpretation and backbone of Arrow's and Sen's theorems. utilizing easy arithmetic, it indicates that those unfavourable conclusions come up simply because, in every one case, a few of their assumptions negate different the most important assumptions. as soon as this is often understood, not just do the conclusions turn into anticipated, yet a large classification of different phenomena can be expected. those comprise inter alia legislative cycles, provide and insist economics, statistical paradoxes, and numerous voting/election paradoxes.

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Extra info for Decisions and Elections: Explaining the Unexpected

Sample text

But, why concentrate just on the best? Maybe we want to know who is "second best," who is the worse, or any other specified subset of candidates. To be polite, for instance, I may select the second best piece of meat during a dinner party. Or, the faculty of a department occasionally needs to select who will not receive tenure — they are interested in determining who they find to be the worst. Nevertheless, a typical social choice function is not concerned with who is in, say, sixth or seventh place, but rather who is the winner, or who are the top two candidates.

Please do not interpret this assumption as implying the absence of irrational voters. They exist; indeed, many of us have acquaintances, colleagues, and most surely relatives whom we strongly suspect as being closet cyclic thinkers. Rather than denying the reality of irrationality, this assumption is imposed primarily as a means to identify which procedures work as desired — at least when used by rational voters. After all, what good is a procedure if it fails to be rational with rational voters?

In the figure skating example, one of the profiles, Pi, is what history recorded; it is where Kwan turned in a beautiful skate. Let the other profile, p2, be the hypothetical but expected one where Kwan succumbed to the enormous pressure of an internationally televised performance and performed poorly. The only difference in the two profiles is the ranking of Kwan. If figure skating had used a judging procedure which satisfied binary independence, the final relative ranking of Bobek and Bonaly would not have been affected by anything Kwan did or how the judge ranked her.

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Decisions and Elections: Explaining the Unexpected by Donald G. Saari

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