Read e-book online A Mathematical Look at Politics PDF

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

What Ralph Nader's spoiler position within the 2000 presidential election tells us in regards to the American political procedure. Why Montana went to court docket to modify the 1990 apportionment to Dean's process. How the united states attempted to exploit online game concept to win the chilly warfare, and why it didn't paintings. while scholars observe that mathematical pondering can deal with those forms of urgent issues of the political global it obviously 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 ability of mathematical considering to difficulties in politics and public coverage. options 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 additionally to country effects, end up them, and draw conclusions approximately particular examples.

Tying the liberal arts school room to real-world mathematical purposes, this article is extra deeply enticing than a conventional basic schooling ebook that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants now not continuously confident that arithmetic is appropriate to them.

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The simple majority method is nearly decisive. Proof. Suppose first that the number t of voters is odd. Then no candidate can receive exactly half of the votes (because t/2 is not a whole number), so one must receive more than half. This will be a majority and that candidate will be the winner. Now suppose t is even, so that t/2 is a whole number. If both candidates get t/2 votes, they tie. Otherwise, one candidate must get more that t/2 votes for a majority (and the other gets less). The candidate with the majority is the winner.

The Coombs method has some of the same advantages as the Hare method. Coombs’s idea is to eliminate not the candidates who are least loved, as with Hare’s method, but rather the candidates who are most hated. Bland candidates who do not inflame passions at either end of the spectrum will have few strong supporters or detractors; they may be able to survive in the Coombs method but are likely to be quickly eliminated by the Hare method. One concern with the methods of Hare and Coombs is that the elimination of a candidate early on in the process is irrevocable.

It involves 100 members of the Senate, 435 members of the House of Representatives, the vice president, and the president, for a total of 537 voters. For a bill to pass, it must have a majority in the House, a majority in the Senate, with the possibility of the vice president breaking a tie, and the signature of the President; or if the president opposes the bill, it must have a 2/3 super-majority in both the House and Senate to override the veto. Otherwise the bill is defeated. Think of this as a social choice function where the alternatives are A, to pass the bill, or B, to defeat the bill.

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