Chapter 9 Social Choice: The Impossible Dream Videos and Lecture Notes

Videos and lecture notes are based on the 9th ed. textbook. The 9th or 10th edition of the textbook can be used for this course. All material covered is the same and independent of textbook editions.
Textbook
Video
9th ed.
Lecture Notes
9th ed.
 9.2 Majority Rule and Condorcet's Method 9th ed. pages 328 - 332 10th ed. pages 407 - 411
Section 9.2
Video
Section 9.2
Lecture notes
 9.3 Other Voting Systems for Three or More Candidates 9th ed. pages 332 - 342 10th ed. pages 412 - 424
Section 9.3
Video
Section 9.3
Lecture notes
 9.4 Insurmountable Difficulties: Arrow's Impossibility Theorem 9th ed. pages 342 - 346 10th ed. pages 424 - 428
Section 9.4
Video
Section 9.4
Lecture notes

Chapter 9 Objectives (Skills)

• Analyze and interpret preference list ballots.
• Explain three desired properties of Majority Rule.
• Explain May’s theorem.
• Explain the difference between majority rule and the plurality method.
• Discuss why the majority method may not be appropriate for an election in which there are more than two candidates.
• Apply the plurality voting method to determine the winner in an election whose preference list ballots are given.
• Explain the Condorcet winner criterion (CWC).
• Rearrange preference list ballots to accommodate the elimination of one or more candidates.
• Structure two alternative contests from a preference schedule by rearranging preference list ballots; then determine whether a Condorcet winner exists.
• Apply the Borda count method to determine the winner from preference list ballots.
• Explain independence of irrelevant alternatives (IIA).
• Apply the sequential pairwise voting method to determine the winner from preference list ballots.
• Explain Pareto condition.
• Apply the Hare system to determine the winner from preference list ballots.
• Explain monotonicity.
• Explain Arrow’s impossibility theorem.

Quiz 4 Chapter 9 (Sakai-> Tests & Quizzes)

• The quiz for Chapter 9 will be available from 12:00am Mar. 17 - 11:55pm Mar. 30.
• The quiz will consist of 10 multiple choice questions.
• You will have a maximum of two hours to complete the quiz.
• You will be allow two tries. The computer will accept the best score.
• Failure to take the quiz by 11:55pm Mar. 30 will be given a zero. No exceptions!

Textbook Homework Problems (Practice/Not Graded)

The 9th or 10th edition of the textbook can be used for this course. All material covered is the same and independent of textbook editions. Homework problems between editions are the same.
 9th ed. 6, 9, 10, 14, 15, 16, 23, 24, 25, 39 pages 350 - 354 10th ed. 5, 8, 9, 13, 14, 15, 19, 20, 21, 32 pages 433 - 436

Chapter worksheets (Sakai -> Assignments)

• Due by 11:55 pm Friday Mar. 23
• Use the Assignments tool within Sakai to submit worksheet.

Discussion Topic (Sakai-> Forums)

You will be required to participate in the discussion groups, i.e. Forums. The forums are aligned with the Learning Outcomes to provide practice and feedback and assessment for outcomes 3 and 4.

• Probably, very few of (if any) of you have been exposed to different methods for determining a winner of an election or fairness criteria. So it would be very helpful for you to read the chapter before trying to respond.
• Topic #1: In the 2016 presidential election, consider the final results for two states with very close results (as reported by CNN): New Hampshire were Clinton (47.6% - 348,521), Trump (47.2% - 345,789), Johnson (4.2% - 30,827), and Stein (0.9% - 6,416) and Michigan were Trump (47.6% - 2,279,805), Clinton (47.3% - 2,268,193), Johnson (3.6% - 173,057), and Stein (1.1% - 50,700). Making reasonable assumptions about voters' preference schedules, discuss how the election for these two states might have turned out under the different voting methods discussed in this chapter. That is, experiment with the preference list using a different voting method.
• Topic #2: Explain why the Borda count method satisfies the monotonicity criterion. An example will not work here. What you need to say here is why the Borda count always satisfies the monotonicity fairness criterion for every possible preference list and every possible election. Can you find another method from the the text that satisfy the monotonicity criterion? Why or why not?
• Topic #3: Explain why the Hare method always satisfies the Pareto fairness criterion. Remember, an example cannot show why something is true. We need some valid reasoning here as well. Can you find another method from the the text that satisfy the Pareto criterion? Why or why not?
• Discussion for Chapter 9 will open at 12:00 am Saturday Mar. 17
• You are required to participate in the discussion boards.
• Discussion topic will end at 11:55 pm Friday Mar. 30.
• See the syllabus on the grading rubric for discussions.

James Baglama

Email: j(lastname)(AT)uri.edu
Office hours: By appointment
Office: Lippitt Hall 200D
Phone: (401) 874-2709

For All Practical Purposes

The textbook for the course can be either 9th or 10th edition.

Videos and lecture notes are based on the 9th ed. textbook. The 9th or 10th edition of the textbook can be used for this course. All material covered is the same and independent of textbook editions. The course does NOT use any material/resources form the Publisher's online system LaunchPad.

Student Resources (Publisher)

Math Applets and suggested websites are very helpful resources.

URI General Education Course

General Education program 2016 (GE): This course fully satisfies both the general education Knowledge area A1: Scientific, Technology, Engineering, and Mathematical Disciplines (STEM) and Competency area B3: Mathematical, Statistical, or Computational Strategies (MSC).
General education program 2001 - 2015 (MQ): This course satisfies the general education requirement for Mathematical and Quantitative Reasoning.

Course Description

LEC: (3 crs.) Introduces students to the spirit of mathematics and its applications. Emphasis is on development of reasoning ability as well as manipulative techniques. (Lec. 3/Online) Not open to students with credit in MTH 106 or MTH 109 and not for major credit in mathematics. (MQ)/(GE)

Course Goals

The goal of this course is to prepare you for the mathematical and analytical aspects of the world around you, and to help you develop a stronger, deeper mathematical knowledge. This course is intended for students majoring in the liberal arts or other fields that do not have a specific mathematical requirement.

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There is help available from the Academic Enhancement Center (AEC). For more information on AEC services visit the AEC website at http://web.uri.edu/aec/ .

Special Needs

Any student with a documented disability should contact your instructor early in the semester so that he or she may work out reasonable accommodations with you to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 302 Memorial Union, 401-874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

University of Rhode Island regulations concerning incomplete grades will be followed. See University Manual sections 8.53.20 and 8.53.21 for details.

Religious holidays

It is the policy of the University of Rhode Island to accord students, on an individual basis, the opportunity to observe their traditional religious holidays. Students desiring to observe a holiday of special importance must provide written notification to each instructor.

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Assignments, quizzes, and discussions are available for multiple days. Deadlines are given on all assignments. Missed deadlines will require documentation and the University Manual sections 8.51.10 to 8.51.14 will be followed.