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.
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
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
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
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 Oct. 22 - 11:55pm Nov. 4.
  • 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 Nov. 4 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)

Each worksheet will have 10 questions each worth 1 point (partial credit is possible). The worksheets are designed to help you understand material and are aligned with the Learning Outcomes to provide practice and feedback. The worksheets are downloadable from the Assignment tool within Sakai as a Microsoft Word (or OpenOffice) and also as a pdf file. You can write on the worksheets and upload your answers or (similar to homework submissions) take a digital picture of your handwritten assignment with a camera or smart phone. All worksheet answers must be submitted within Sakai. Worksheets with answers only will be given a zero. You must show the work for credit. The due dates for the worksheets are one week before the due date for homework assignments, so that you can get feedback on problems before submitting your homework and doing your quizzes. DO NOT SUBMIT ASSIGNMENTS VIA EMAILS OR FAXES! I will not accept them! Do not ask to submit late worksheets.

  • Due by 11:55 pm Friday Oct. 28
  • 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. The first topic, for example, has nothing to do with the national popular vote, nor the Supreme Court, nor the Electoral college, nor ballot chads, nor counting irregularities nor misrepresentation of minorities. I hope several of you give #1 a go. It is probably the most interesting.
    • Topic #1: In the 2000 presidential election in Florida, the final results were as follows: (available in Forums) Making reasonable assumptions about voters' preference schedules, discuss how the election might have turned out under the different voting methods discussed in this chapter. Optionally, experiment with the preference list in example 1 on page 288 using a different voting method. This may help you understand the actual Florida election.
    • 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 Oct. 22
  • You are required to participate in the discussion boards.
  • Discussion topic will end at 11:55 pm Friday Nov. 4.
  • See the syllabus on the grading rubric for discussions.

James Baglama

Email: jbaglama(AT)
Office hours: By appointment
Office: Lippitt Hall 200D
Phone: (401) 874-2709

For All Practical Purposes For All Practical Purposes

For All Practical Purposes

The textbook for the course can be either 9th or 10th edition.
For All Practical Purposes, 9th edition by COMAP
For All Practical Purposes, 10th edition by COMAP

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.

Academic Enhancement Center (AEC)

There is help available from the Academic Enhancement Center (AEC). The AEC offers three types of help: Supplemental Instruction (SI), Tutoring (both walk-in and appointment-based types), and academic coaching. For more information on AEC services, study tips, and SI session, visit the AEC website at .

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: Onlinece of Student Life, 330 Memorial Union, 874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Incomplete Grade

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.

Makeup Policy

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.

Academic Integrity

Cheating is defined in the University Manual section 8.27.10 as the claiming of credit for work not done independently without giving credit for aid received, or any unauthorized communication during examinations. Students are expected to be honest in all academic work. The resolution of any charge of cheating or plagiarism will follow the guideline set forth in the University Manual 8.27.10-8.27.20, Online quizzes must be done independently. Suspicious scores may require additional explanation.