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
Readings
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 June 13 - 11:55pm June 18.
  • 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 June 18 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)

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 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 two days before the due date for quizzes, so that you can get feedback on problems before submitting your chapter quiz. 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 June 15.
  • 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 June 13
  • You are required to participate in the discussion boards.
  • Discussion topic will end at 11:55 pm June 18.
  • See the syllabus on the grading rubric for discussions.

James Baglama

Email: jbaglama(AT)uri.edu
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
OR
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)

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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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