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

Reading Assignment Video Lecture Notes
9.2 Majority Rule and
Condorcet's Method
pages 328 - 332
Section 9.2
Video
Section 9.2
Lecture notes
9.3 Other Voting Systems for
Three or More Candidates
pages 332 - 342
Section 9.3
Video
Section 9.3
Lecture notes
9.4 Insurmountable Difficulties:
Arrow's Impossibility Theorem
pages 342 - 346
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 Oct. 18 - 11:55pm Oct. 31.
  • 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 Oct. 31 will be given a zero. No exceptions!

Homework Assignments (Sakai -> Assignments)

  • Chapter 9
    pages 350-352 Problems 2, 9, 10, 14, 16
    Due by 11:55pm Friday Oct. 31.
  • Use the Assignments tool to submit homework.
  • Homework Help.
    • Problem 2. Carefully read Section 9.2 before responding to this exercise. Consider all three desirable properties.
    • Problems 9 and 10. Determine the outcome of six one-on-one competitions, A vs. B, A vs. C, A vs. D, B vs. C, B vs. D, and C vs. D.
    • Problem 14. Part (a): The plurality winner would be the candidate with the highest number of votes . Part (b): For Borda count, use the number of 1st place votes times 3, the number of 2nd place votes times 2, the number of 3rd place votes times 1, and the number of 4th place votes times 0. Then sum of the values for each letter, A, B, C, and D. Part (c): Hare system Eliminate the candidate(s) with the least number of first-place votes. Repeat if necessary until there are two candidates. The one with the majority of votes wins. Part (d): Sequential pairwise. Be sure to pay attention to the agenda in determining the three one-on-one competitions.
    • Problem 16. Part (a): The plurality winner would be the candidate with the highest number of votes. Part (b): For Borda count, use the number of 1st place votes times 4, the number of 2nd place votes times 3, the number of 3rd place votes times 2, the number of 4th place votes times 1, and the number of 5th place votes times 0. Then sum of the values for each letter, A, B, C, D, and E. Part (c): Hare system Eliminate the candidate(s) with the least number of first-place votes. Repeat if necessary until there are two candidates. The one with the majority of votes wins. Part (d): Sequential pairwise. Be sure to pay attention to the agenda in determining the three one-on-one competitions.
  • I will NOT accept homework with answers only.

Companion Website

  • Go to the companion website and navigate to the applet exercises for chapter 9 and try the applet Insincere Voting.
  • In the companion website navigate to Online Quizzes and try the online quiz.

Chapter worksheets (Sakai -> Assignments)

Each worksheet will have 10 questions (each worth 1 point). The worksheets are designed to help you understand material. 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. 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. 24
  • Use the Assignments tool to submit worksheet.

Discussion Topic (Sakai-> Forums)

  • 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: (See table of candidates given on page 355 and is also attached here as pdf) 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. 18
  • You are required to participate in the discussion boards.
  • Discussion topic will end at 11:55 pm Friday Oct. 31
  • See the syllabus on the grading rubric for discussions.

James Baglama

Texting Number: (401) 268-7160
Email: jbaglama@math.uri.edu
Office hours: By appointment
Office: Lippitt Hall 200D
Office Phone: (401) 874-2709

For All Practical Purposes

The required textbook, "For All Practical Purposes", 9th edition by COMAP, Publisher W.H. Freeman. Do NOT use an older edition. All students must have either a phyiscal copy of the textbook or an ebook.Click on the textbook above to go to the ebook.

For All Practical Purposes Campanion Site

The required textbook, The textbook "For All Practical Purposes", 9th edition by COMAP,Publisher W.H. Freeman has a campanion website. The campanion website contains a lot helpful material,e.g. Java Applets, falshcards, practice quizzes. The site can be accessed via the link Campanion or click on the picture above to go to the campanion website.