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 approach. Why Montana went to courtroom to modify the 1990 apportionment to Dean's technique. How the united states attempted to exploit online game thought to win the chilly conflict, and why it didn't paintings. while scholars detect that mathematical considering can handle those types of urgent issues of the political international it obviously 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. techniques 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 school room to real-world mathematical functions, this article is extra deeply enticing than a standard common schooling ebook that surveys the mathematical panorama. It goals to instill a passion for arithmetic in a inhabitants no longer regularly confident that arithmetic is correct to them.
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Additional info for A Mathematical Look at Politics
Near decisiveness is meant to be inclusive in the sense that any method that is decisive must also be nearly decisive. The converse of this statement, however, is false. A nearly decisive method need not be decisive. The simple majority method, for example, is nearly decisive without being decisive. Many methods fail to satisfy near decisiveness. For example, every super-majority method (without status quo) fails to be nearly decisive, because with a nearly 50:50 split in the electorate, neither candidate will have enough votes to win.
Does the US federal system satisfy: (a) the anonymity criterion? (b) the neutrality criterion? (c) the monotonicity criterion? (d) the decisiveness criterion? (e) the near decisiveness criterion? 11. 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.
Note that we do not require a majority, because doing so would sometimes result in no winner being selected. To determine the plurality winner of an election, one need know only the first-choice preference of each voter. In other words, this method permits us to ignore all the information in the profile about second, third, and further preferences of the voters. In many elections, voters are given the chance to submit only a vote-forone ballot and we do not have any further information about the voters’ preferences.