A Mathematical Look at Politics by E. Arthur Robinson Jr., Daniel H. Ullman

By E. Arthur Robinson Jr., Daniel H. Ullman

What Ralph Nader's spoiler function within the 2000 presidential election tells us concerning the American political approach. Why Montana went to courtroom to modify the 1990 apportionment to Dean's strategy. How the united states attempted to take advantage of video game concept to win the chilly conflict, and why it didn't paintings. whilst scholars detect that mathematical pondering can handle those different types of urgent matters of the political international it certainly sparks their curiosity within the underlying arithmetic.

A Mathematical examine Politics is designed instead to the standard arithmetic texts for college kids in quantitative reasoning classes. It applies the facility of mathematical pondering to difficulties in politics and public coverage. recommendations are accurately outlined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are acknowledged and proved. Counterexamples are provided to refute conjectures. scholars are anticipated not just to make computations but in addition to country effects, turn out them, and draw conclusions approximately particular examples.

Tying the liberal arts school room to real-world mathematical functions, this article is extra deeply attractive than a standard basic schooling ebook that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants no longer continually confident that arithmetic is suitable to them.

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Some criteria are particularly compelling, meaning that people tend to regard methods that violate them to be inappropriate or offensive. Other criteria may be less compelling, establishing requirements that people may regard as perhaps desirable but certainly not essential. We may occasionally consider criteria that do not seem desirable at all to some people. Whether or not a criterion is compelling is ultimately a question of political phi- 14 A Mathematical Look at Politics losophy. One can argue at length about what “fairness” is.

But in our setting, we may as well define “voter” to mean someone who has already voted, so the assumption that every voter goes to the polls is not unnecessarily restrictive. It is also true that, in practice, not all voters would wish to rank every single candidate. ” The preference ballot forbids this. Still, the preference ballot gives rich information about a voter’s sentiments. In particular, if the election is somehow reduced to a subset of the original slate that contains just two candidates, then we are able to discern for any voter which of these two candidates is preferred.

Tie matches award “half a victory” to each team. On the other hand, sports tournaments often use run-offs at the end to make certain that a single victor is identified; the Copeland method permits multiple winners, since several candidates may tie for the most victories. There is another common type of sports tournament, which involves the idea of an elimination grid. A team keeps playing in such a tournament as long as it keeps winning its individual contests, and once it loses it is eliminated for good.

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