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 method. Why Montana went to court docket 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 battle, and why it didn't paintings. while scholars notice 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 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 in addition 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 standard basic schooling publication that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants now not constantly confident that arithmetic is proper to them.
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Extra info for A Mathematical Look at Politics
It does not seem desirable for a change like the one in the preceding proof to cause candidate A to go down to defeat — after all more voters voted for A in the second profile! For this reason it seems essential to always require our decision procedures to satisfy monotonicity. Monotonicity is a compelling criterion. Non-monotone methods, like the parity method, seem like especially inappropriate ways to run elections. Whenever possible we would like elections between two candidates to end in a decision for one candidate over the other.
What if some candidate drops out of the race? What other ways of collecting information from voters — more or less informative than asking for preference orders — might be useful? How many reasonable methods can you come up with for deciding elections with three or more candidates? 1 Ballots In this chapter we consider elections with more than two candidates. This situation features a richer set of possible voting methods than we encountered in the previous chapter, and a number of curious examples 25 26 A Mathematical Look at Politics emerge that challenge intuition.
The candidate with the most points becomes the winner. If there is a tie for most points, then all candidates with the most points become winners. This method gets its name from A. H. Copeland (1910–1990), who was a professor of mathematics at the University of Michigan. 6 For any pair of candidates, we can determine how many voters prefer one to the other. For example, looking at candidates A and D, we see that the first three voters prefer A to D, while the last two voters prefer D to A. We record this as: 3 A 2 D It is as if we are momentarily imagining that candidates B, C, and E have dropped out of the race and that the resulting two-candidate election is executed according to the simple majority method.
A Mathematical Look at Politics by E. Arthur Robinson Jr., Daniel H. Ullman