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 change the 1990 apportionment to Dean's procedure. How the united states attempted to exploit video game thought to win the chilly conflict, and why it didn't paintings. while scholars discover that mathematical pondering can deal with those types of urgent matters of the political global it obviously 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 facility of mathematical considering 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 kingdom 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 standard common schooling e-book that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants now not continuously confident that arithmetic is proper to them.
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Additional info for A Mathematical Look at Politics
0, 0). The positional method P (1, 1, 1, . . , 1, 0) is known as the antiplurality method. Candidates earn a point for every voter that does not place them in last place. In effect, then, the antiplurality winner is the candidate with the fewest last-place votes. The positional method P (1, 1, 0, . . , 0, 0) is called the vote-for-two method. We examine a number of other interesting social choice functions in the exercises. Most of these are variants on the methods explored in this section.
Our goal is to show that the method we are imagining must in fact be the simple majority method. First consider the case when t is even. If a = b = t/2, then each candidate has exactly half the votes. By the neutrality criterion the result must be a tie, because the method must treat the candidates in the same way. Next suppose that candidate A has a majority. That is, suppose that a ≥ t/2 + 1. We need to show that candidate A must win, and for this it is enough to show that the result cannot be a tie or a win 20 A Mathematical Look at Politics for candidate B.
The domain of a social choice function is the set of all profiles. The codomain (the set of all allowed outputs) is the set of nonempty subsets of the slate. To say “function” here is to forbid random elements such as coin tossing and to insist that the method does not change with the weather or other irrelevancies. To say that the domain of the function is the set of all profiles is to mandate that a decision of some sort must Social Choice Functions 29 be rendered, no matter how the electorate votes.
A Mathematical Look at Politics by E. Arthur Robinson Jr., Daniel H. Ullman