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 position within the 2000 presidential election tells us in regards to the American political process. Why Montana went to courtroom to modify the 1990 apportionment to Dean's procedure. How the U.S. attempted to take advantage of video game idea to win the chilly conflict, and why it didn't paintings. while scholars discover that mathematical pondering can deal with those types of urgent issues of the political international it certainly sparks their curiosity within the underlying arithmetic.

A Mathematical examine Politics is designed in its place to the standard arithmetic texts for college students in quantitative reasoning classes. It applies the ability of mathematical considering to difficulties in politics and public coverage. strategies are accurately outlined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are said and proved. Counterexamples are provided to refute conjectures. scholars are anticipated not just to make computations but additionally to kingdom effects, turn out them, and draw conclusions approximately particular examples.

Tying the liberal arts lecture room to real-world mathematical functions, this article is extra deeply attractive than a standard normal schooling e-book that surveys the mathematical panorama. It goals to instill a keenness for arithmetic in a inhabitants no longer regularly confident that arithmetic is suitable to them.

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We formalize this observation by displaying it as a proposition. 16. A method is anonymous if and only if its outcomes depend only on the tabulated profile. Throughout the book, when we want to highlight a fact or result of special significance, we generally present it in this way as a theorem, a Two Candidates 15 proposition, a lemma, or a corollary, and then follow it with a proof. A theorem is generally a deep result of major importance. Other results of less importance are given the name proposition.

Because ties are possible in the United States Senate, the Constitution provides for the vice president to cast a tie-breaking vote. One can therefore think of the Senate as a body with 101 voters, 100 of whom are senators and one of whom is the vice president. The rules dictate that the vice president votes only to break ties and not otherwise. Is this system anonymous? 12. Consider a weighted voting method with 5 voters assigned weights 17, 15, 14, 12, and 7, respectively, with a simple majority of the weighted votes sufficient for victory.

May’s Theorem) In an election with two candidates, the only voting method that is anonymous, neutral, and monotone and that is nearly decisive is the simple majority method. Proof. Suppose that a method is anonymous, neutral, monotone, and nearly decisive. 16 tells us that we need only consider tabulated profiles. So let a be the number of voters who prefer candidate A, and let b be the number of voters who prefer candidate B. Then t = a + b is the total number of voters. Our goal is to show that the method we are imagining must in fact be the simple majority method.

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