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# class_january18 - Math 103 Topics in Math for the Liberal...

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Math 103: Topics in Math for the Liberal Arts, Section 11, Winter 2011 January 18, 2011 Class 1. Introductions 2. Information Sheet at Sakai 3. Syllabus at Sakai, Class notes put on Sakai each class 4. Homework to be submitted and graded for Chapter 1: pages 31-38, Exercises 12,18,20,24 due on Tuesday, January 25. Pages 31-38: Exercises 34,38,42,60 due later. 5. Homework not to be submitted. Will be discussed on Friday, January 21: Pages 31-33: Exercises 11, 17, 19, 23. 6. Please bring your calculator to our next class. We will have a quiz that tests skills needed for this course. It will not count as a quiz grade, but will show you which skills, if any, you need to learn. I will cover all the needed skills as the course progresses. I will return your quizzes and post the answers at Sakai. Terms we will discuss today: Candidate, choice, preference ballots, first-place votes, preference schedules, voter’s preferences are transitive, 2 candidates, more than 2 candidates, plurality, majority, head to head matches, Condorcet candidate, 2 Voting Methods: Plurality and Borda Count, 2 Fairness Criteria: Majority and Condorcet In every election there are a set of voters and a set of candidates or choices. A ballot in which the voters are asked to rank the candidates in order of preference is called a preference ballot . Example 1 :  The Debating Club is in the process of selecting a new president. They have narrowed  the field to four candidates – Allen, Barbara, Cathy, and David. Each of the club’s 32 members has  voted using a preference ballot.

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a.  Summarize the results of the election using a preference schedule. b. Which candidate received the most first-place votes? Class Example with voting: Nielsen ratings Most Listened to Radio Songs Issue Date Dec. Jan, 15 2011 RANK ARTIST SONG 1 RIHANNA FEAT. DRAKE WHAT'S MY NAME? (W) 2 KATY PERRY FIREWORK (F) 3 RIHANNA ONLY GIRL (IN THE WORLD) (O) A ballot in which the voters are asked to rank the candidates in order of preference is called a preference ballot . Example: Ballot 1 st Firework 2 nd Only Girl
3 rd What’s My Name? For short, let’s write: 1 st F 2 nd O 3 rd W Given 3 candidates (or choices), let’s list all the preference ballots we can form: How many are there? Let’s pick 2 preference ballots: Ballot and Ballot 1 st F 1 st O 2 nd O 2 nd W 3 rd W 3 rd F Let’s vote for these ballots. Preference schedule for Radio Songs Number of voters 1 st choice F O 2 nd choice O W 3 rd choice W F With the plurality method , all we care about is first-place votes. Voting Method #1: The Plurality Method The candidate with the most first-place votes (called the plurality candidate) wins. Who is the plurality candidate? The candidate with a majority (more than half) of the first-place votes is called a majority candidate.

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class_january18 - Math 103 Topics in Math for the Liberal...

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