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 courtroom to change the 1990 apportionment to Dean's procedure. How the USA attempted to exploit video game concept to win the chilly conflict, and why it didn't paintings. while scholars become aware of that mathematical considering can deal with those kinds of urgent matters of the political global 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 pondering to difficulties in politics and public coverage. techniques 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 school room to real-world mathematical purposes, this article is extra deeply attractive than a standard normal schooling booklet that surveys the mathematical panorama. It goals to instill a keenness for arithmetic in a inhabitants no longer consistently confident that arithmetic is appropriate to them.
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Extra info for A Mathematical Look at Politics
A) Suppose the rules say that Jones wins if she receives 50 or more votes; otherwise Smith wins. Is this method neutral? (b) Suppose the rules say that a candidate wins if he or she receives a number of votes that is between 60 and 89. ) Is this method monotone? (c) Suppose the rules say that a candidate wins if he or she receives an odd number of votes. ) Is this method decisive? (d) Suppose that the rules say that Smith wins the election no matter what. Is this method anonymous? 0 Scenario Three candidates, denoted A, B, and C, are running for public office.
Suppose that the amendment is put to a vote, and the results are given by the following profile. B A A A B A We assume this profile lists the partners in the same order as the list of voting strength. The number of votes is t = 10+5+5+3+2+1 = 26. 6 = 16. Thus the status quo B prevails. Now suppose that the fifth voter changes his vote to A, as follows. 12 A Mathematical Look at Politics B A A A A A This time the vote in favor is 5 + 5 + 3 + 2 + 1 = 16, so the amendment passes. Another potential twist in election procedures is what one finds in the case of the election for the American president.
In the end, it is probably pointless to defend our assumptions, since they are imposed not because they best capture reality but for the convenience of our theory. We will consider other kinds of ballots in Chapter 6. , every voter casts a ballot), we obtain what we call a profile: a set of preference orders, one for each voter. After all ballots are cast and tallied, the profile contains all the information about the preferences of the voters. As an example with 3 candidates and 7 voters, we may have 3 voters (voters 1, 3, and 5, say) who vote A > B > C, 2 voters (2 and 6, say) who vote B > C > A, and 2 voters (4 and 7, say) who vote C > A > B.