## Solutions for Excursions in Modern Mathematics (9th Edition)

Problem 1E:

Figure 1-8 shows the preference ballots for an election with 21 voters and 5 candidates. Write out...Problem 2E:

Figure 1-9 shows the preference ballots for an election with 17 voters and 4 candidates. Write out...Problem 3E:

An election is held to choose the Chair of the Mathematics Department at Tasmania State University....Problem 4E:

The student body at Eureka High School is having an election for Homecoming Queen. The candidates...Problem 5E:

An election is held using the printed-names format for the preference ballots. Table 1-27 shows the...Problem 8E:

Table 1-30 shows a conventional preference schedule for an election. Rewrite Table 1-30 using a...Problem 9E:

The Demublican Party is holding its annual convention. The 1500 voting delegates are choosing among...Problem 10E:

The Epicurean Society is holding its annual election for president. The three candidates are A, B,...Problem 11E:

Table 1-31 shows the preference schedule for an election with four candidates A, B, C, and D. Use...Problem 12E:

Table 1-32 shows the preference schedule for an election with four candidates A, B, C, and D. Use...Problem 13E:

Table 1-33 shows the preference schedule for an election with four candidates A, B, C, and D. Use...Problem 14E:

Table 1-34 shows the preference schedule for an election with four candidates A, B, C, and D. Use...Problem 15E:

Table 1-35 shows the preference schedule for an election with five candidates A, B, C, D, and E. The...Problem 16E:

Table1-36 shows the preference schedule for an election with five candidates A, B, C, D, and E. The...Problem 17E:

Table 1-25 see Exercise 3 shows the preference schedule for an election with five candidates A, B,...Problem 18E:

Table 1-26 see Exercise 4 shows the preference schedule for an election with five candidates A, B, C...Problem 19E:

Table 1-25 see Exercise 3 shows the preference schedule for an election with five candidates A, B,...Problem 20E:

Table 1-26 see Exercise 4 shows the preference schedule for an election with five candidates A, B, C...Problem 21E:

Table 1-31see Exercise 11 shows the preference schedule for an election with four candidates A. B,...Problem 22E:

Table 1-32 see Exercise 12 shows the preference schedule for an election with four candidates A, B,...Problem 23E:

Table 1-33 see Exercise 13 shows the preference schedule for an election with four candidates A, B,...Problem 24E:

Table 1-34 Number of voters 6 6 5 4 3 3 1st A B B D A B 2nd C C C A B A 3rd D A D C C C 4th B D A B...Problem 25E:

Table 1-35 Percent of voters 24 23 19 14 11 9 1st C D D B A D 2nd A A A C C C 3rd B C E A B A 4th E...Problem 26E:

Table 1-36 Percent of voters 25 21 15 12 10 9 8 1st C E B A C C C 2nd E D D D D B E 3rd D B E B E A...Problem 27E:

The Heisman Award. Table 1-37 shows the results of the balloting for the Heisman Award. Find the...Problem 28E:

The 2014 AL Cy Young Award. Table 1-38 shows the top 5 finalists for the 2014 American League Cy...Problem 29E:

An election was held using the conventional Borda count method. There were four candidates (A, B, C....Problem 30E:

Imagine that in the voting for the American League Cy Young Award (7 points for first place, points...Problem 31E:

Table 1-31 see Exercise 11 shows the preference schedule for an election with four candidates A. B,...Problem 32E:

Table 1-32 see Exercise 12 shows the preference schedule for an election with four candidates A. B,...Problem 33E:

Table1-33 Number of voters 6 5 4 2 2 2 2 1st C A B B C C C 2nd D D D A B B D 3rd A C C C A D B 4th B...Problem 34E:

Table 1-34 See Exercise 14 shows the preference schedule for an election with four candidates A. B,...Problem 35E:

Table1-39_ shows the preference schedule for an election with five candidates A, B, C, D, and E....Problem 36E:

Table1-40_ shows the preference schedule for an election with five candidates A, B, C, D and E. Find...Problem 37E:

Table 1-35 see Exercise 15 shows the preference schedule for election with five candidates A, B, C,...Problem 38E:

Table 1-36 see Exercise 16 shows the preference schedule for an election with five candidates A, B,...Problem 39E:

Top-Two Instant-Runoff Voting. Exercises 39 and 40 refer to a simple variation of the...Problem 40E:

Top-Two Instant-Runoff Voting. Exercises 39 and 40 refer to a simple variation of the...Problem 41E:

Table 1-31 see Exercise 11 shows the preference schedule for an election with four candidates A. B,...Problem 42E:

Table 1-32 See Exercise 12 shows the preference schedule for an election with four candidates A. B,...Problem 43E:

Table 1-33 see Exercise 13 shows the preference schedule for an election with four candidates A. B,...Problem 44E:

Table 1-34 see Exercise 14 shows the preference schedule for an election with four candidates A. B,...Problem 45E:

Table 1-35 see Exercise 15 shows the preference schedule for an election with five candidates A, B,...Problem 46E:

Table 1-36 see Exercise 16 shows the preference schedule for an election with five candidates A, B,...Problem 47E:

Table 1-39 see Exercise 35 shows the preference schedule for an election with 5 candidates. Find the...Problem 48E:

Table1-40 see Exercise36 shows the preference schedule for an election with 5 candidates. Find the...Problem 49E:

An election with five candidates A, B. C, D, and E is decided using the method of pairwise...Problem 50E:

An election with six candidates A, B, C, D, E, and F is decided using the method of pairwise...Problem 51E:

Use Table 1-41 to illustrate why the Borda count method violates the Condorcet criterion. Table 1-41...Problem 52E:

Use Table 1-32 to illustrate why the plurality-with-elimination method violates the Condorcet...Problem 53E:

Use Table 1-42 to illustrate why the plurality method violates the IIA criterion.Hint: Find the...Problem 54E:

Use the Math Club election Example 1.10 to illustrate why the Borda count method violates the IIA...Problem 55E:

Use Table 1-43 to illustrate why the plurality-with-elimination method violates the IIA criterion....Problem 61E:

Two-candidate elections. Explain why when there are only two candidates, the four voting methods we...Problem 62E:

Alternative version of the Borda count. The following simple variation of the conventional Borda...Problem 63E:

Reverse Borda count. Another commonly used variation of the conventional Borda count method is the...Problem 64E:

The average ranking. The average ranking of a candidate is obtained by taking the place of the...Problem 65E:

The 2006 Associated Press college football poll. The AP college football poll is a ranking of the...Problem 66E:

The Pareto criterion. The following fairness criterion was proposed by Italian economist Vilfredo...Problem 67E:

The 2003-2004 NBA Rookie of the Year vote. Each year, a panel of broadcasters and sportswriters...Problem 68E:

Top-two IRV is a variation of the plurality-with-elimination method in which all the candidates...Problem 69E:

The Coombs method. This method is just like the plurality-with-elimination method except that in...Problem 70E:

Bucklin voting. This method was used in the early part of the 20th century to determine winners of...Problem 71E:

The 2016 NBA MVP vote. The National Basketball Association Most Valuable Player is chosen using a...Problem 72E:

The Condorcet loser criterion. If there is a candidate who loses in a one-to-one comparison to each...Problem 73E:

Consider the following fairness criterion: If a majority of the voters have candidate X ranked last,...# Browse All Chapters of This Textbook

Chapter 1 - The Mathematics Of Elections The Paradoxes Of DemocracyChapter 2 - The Mathematics Of Power Weighted VotingChapter 3 - The Mathematics Of Sharing Fair-division GamesChapter 4 - The Mathematics Of Apportionment Making The RoundsChapter 5 - The Mathematics Of Getting Around Euler Paths And CircuitsChapter 6 - The Mathematics Of Touring Traveling Salesman ProblemsChapter 7 - The Mathematics Of Networks The Cost Of Being ConnectedChapter 8 - The Mathematics Of Scheduling Chasing The Critical PathChapter 9 - Population Growth Models There Is Strength In NumbersChapter 10 - Financial Mathematics Money Matters

Chapter 11 - The Mathematics Of Symmetry Beyond ReflectionChapter 12 - Fractal Geometry The Kinky Nature Of NatureChapter 13 - Fibonacci Numbers And The Golden Ratio Tales Of Rabbits And GnomonsChapter 14 - Censuses, Surveys, Polls, And Studies The Joys Of Collecting DataChapter 15 - Graphs, Charts And Numbers The Data Show And TellChapter 16 - Probabilities, Odds, And Expectations Measuring Uncertainty And RiskChapter 17 - The Mathematics Of Normality The Call Of The Bell

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