Mathematics of choice: How to count without counting. Ivan Morton Niven

Mathematics of choice: How to count without counting


Mathematics.of.choice.How.to.count.without.counting.pdf
ISBN: 0883856158,9780883856154 | 213 pages | 6 Mb


Download Mathematics of choice: How to count without counting



Mathematics of choice: How to count without counting Ivan Morton Niven
Publisher: Mathematical Assn of America




In the Unites States and many other countries, the choice was made - perhaps unreflectively - long ago to take our facility for counting as the starting point, and thus to start the mathematical journey with the natural numbers. In a scenario with more than two competitors, the existence of a Arrow's Theorem provides a mathematical explanation for the apparent inconsistencies intrinsic in rank voting – given a set of ballots, single runoff voting, Concordet counting, Borda counts, and Bucklin voting have the potential to yield distinct outcomes. Actually, Weight Watchers has changed their plan so that people make better choices. That's because we all fall prey to the belief that we can have our own side conversations that are quiet enough not to disrupt the counting – unlike those other loudmouths. It works and I don't have to do math. However, the single-choice system does not necessarily guarantee the fairest outcome. Well, there are n objects we could choose to put first; once we've made that choice, there are n-1 remaining objects we could choose to go second; then n-2 choices for the third object, and so on, for a total of n (n-1) (n-2) \dots 1 = n choices. Math by Starting with Counting? I'm counting weight watchers points right now….I'd like to think by the time I get to my goal my healthy habits will be fairly engrained so not every morsel that goes in needs to be 'counted'. Should I Count calories on a diet. Counts the number of permutations of n objects, that is, the number of different ways to take n distinct objects and arrange them in an ordered list. Two roads diverged in a yellow wood, And sorry I could not travel both, And be one traveler, long I stood, And looked down one as far as I could, To where it bent in the undergrowth; .