Political Science

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 concerning the American political process. Why Montana went to court docket to change the 1990 apportionment to Dean's process. How the U.S. attempted to take advantage of video game conception to win the chilly conflict, and why it didn't paintings. whilst scholars detect that mathematical pondering can tackle those types of urgent matters of the political international it evidently sparks their curiosity within the underlying arithmetic.

A Mathematical examine Politics is designed instead to the standard arithmetic texts for college students in quantitative reasoning classes. It applies the facility of mathematical pondering to difficulties in politics and public coverage. innovations 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 kingdom effects, turn out them, and draw conclusions approximately particular examples.

Tying the liberal arts lecture room to real-world mathematical purposes, this article is extra deeply enticing than a conventional common schooling e-book that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants now not continually confident that arithmetic is suitable to them.

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5 May’s Theorem At this point we have discussed various methods for deciding two candidate elections. Many more methods exist, but we will not be concerned with them for now. We have also identified five criteria for evaluating methods. So this begs the question: Which methods satisfy which criteria? 1 answers this question. The answer “yes” or “no” in a box in this chart indicates whether or not the method to the left satisfies the criterion above. The diligent reader will want to verify that the answers are as we claim.

3. Here candidate A wins the plurality election with 5 votes, more than any of the other four candidates. However, candidate A is considered to be the worst choice by a whopping 75% of the electorate, all of whom seem to prefer candidate B by a wide margin. This is not to say that candidate A definitely ought to lose the election. It is merely to say that it is not overwhelmingly clear that A is the only rational, reasonable choice. 3. 3 One such method is named after the French military engineer Jean Charles de Borda (1733–1799).

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. The team that wins its final contest is the tournament winner. In the theory of elections, the schedule of head-tohead match-ups is known as the agenda. One possibility for an agenda comes from a list of the candidates in a particular order. In the first round, the first two candidates on the list compete in a head-to-head match.

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