103s11chap1Asolutions

103s11chap1Asolutions - Math 103, Spring 2011, Solutions to...

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Math 103, Spring 2011, Solutions to Chapter 1 homework 25 total points constitute a perfect score Problem 12: 6 points The plurality method requires us to examine first place votes, and only first place votes. A receives 3 + 4 + 9 = 16 first place votes. B receives 9 + 2 + 5 = 16 first place votes. C receives 8 + 3 = 11 first place votes. D receives 12 first place votes. (a) The plurality method, in and of itself, declares that A and B are tied . It does not declare either one the winner. (b) A has 9 + 8 = 17 last place votes while B has only 3 + 12 = 15 last place votes. Using the indicated tie-breaking procedure, B wins the election . Caution: we examine only the last place vote totals of A and B, not of C or D. This is a tie breaking procedure, and applies only to those candidates involved in the tie. In particular, C is not the winner. (c) Under a head to head comparison between A and B, 3 + 4 + 9 + 3 + 12 = 31voters prefer A over B, i.e. voters rank A above B on their preference ballots. The remaining 9 + 2 + 5 + 8 = 24 voters prefer B over A. Using the indicated tie-breaking procedure, A wins the election . [Conclusion: Different tie-breaking procedures applied to the same election can result in different winners.] __________________________________________________________________
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103s11chap1Asolutions - Math 103, Spring 2011, Solutions to...

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