Name Date I. Consider the preference schedule in an election with 5 candidates.

Similar documents
Write all responses on separate paper. Use complete sentences, charts and diagrams, as appropriate.

Exercises For DATA AND DECISIONS. Part I Voting

Voting Criteria: Majority Criterion Condorcet Criterion Monotonicity Criterion Independence of Irrelevant Alternatives Criterion

The Impossibilities of Voting

Elections with Only 2 Alternatives

Social welfare functions

answers to some of the sample exercises : Public Choice

12.2 Defects in Voting Methods

Voting: Issues, Problems, and Systems, Continued. Voting II 1/27

Today s plan: Section : Plurality with Elimination Method and a second Fairness Criterion: The Monotocity Criterion.

Section Voting Methods. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Voting rules: (Dixit and Skeath, ch 14) Recall parkland provision decision:

Chapter 1 Practice Test Questions

9.3 Other Voting Systems for Three or More Candidates

Economics 470 Some Notes on Simple Alternatives to Majority Rule

Chapter 9: Social Choice: The Impossible Dream Lesson Plan

Section Voting Methods. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Desirable properties of social choice procedures. We now outline a number of properties that are desirable for these social choice procedures:

Josh Engwer (TTU) Voting Methods 15 July / 49

Voting: Issues, Problems, and Systems, Continued

Arrow s Impossibility Theorem

Approval Voting has the following advantages over other voting procedures:

1.6 Arrow s Impossibility Theorem

Math for Liberal Arts MAT 110: Chapter 12 Notes

Section Voting Methods. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

The Mathematics of Voting. The Mathematics of Voting

Introduction to Theory of Voting. Chapter 2 of Computational Social Choice by William Zwicker

The Mathematics of Voting

Homework 7 Answers PS 30 November 2013

Chapter 10. The Manipulability of Voting Systems. For All Practical Purposes: Effective Teaching. Chapter Briefing

Social Choice: The Impossible Dream. Check off these skills when you feel that you have mastered them.

The Manipulability of Voting Systems. Check off these skills when you feel that you have mastered them.

Head-to-Head Winner. To decide if a Head-to-Head winner exists: Every candidate is matched on a one-on-one basis with every other candidate.

Measuring Fairness. Paul Koester () MA 111, Voting Theory September 7, / 25

CS 886: Multiagent Systems. Fall 2016 Kate Larson

MATH4999 Capstone Projects in Mathematics and Economics Topic 3 Voting methods and social choice theory

Fairness Criteria. Majority Criterion: If a candidate receives a majority of the first place votes, that candidate should win the election.

Many Social Choice Rules

Fairness Criteria. Review: Election Methods

Mathematical Thinking. Chapter 9 Voting Systems

Recall: Properties of ranking rules. Recall: Properties of ranking rules. Kenneth Arrow. Recall: Properties of ranking rules. Strategically vulnerable

Syllabus update: Now keeping best 3 of 4 tests

Introduction to Social Choice

Voting Systems. High School Circle I. June 4, 2017

PROBLEM SET #2: VOTING RULES

SOCIAL CHOICES (Voting Methods) THE PROBLEM. Social Choice and Voting. Terminologies

CSC304 Lecture 14. Begin Computational Social Choice: Voting 1: Introduction, Axioms, Rules. CSC304 - Nisarg Shah 1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Mathematics and Social Choice Theory. Topic 4 Voting methods with more than 2 alternatives. 4.1 Social choice procedures

The Math of Rational Choice - Math 100 Spring 2015

Lecture 16: Voting systems

(c) 2013 Janice L. Epstein Voting Methods 1

Sect 13.2 Flaws of Voting Methods

How to Manipulate Staff Decisions using Voting:

The mathematics of voting, power, and sharing Part 1

Voting and preference aggregation

Voting and preference aggregation

Math for Liberal Studies

Introduction: The Mathematics of Voting

MATH 1340 Mathematics & Politics

In this lecture we will cover the following voting methods and fairness criterion.

Math for Liberal Studies

The Mathematics of Voting

Math116Chap1VotingPart2.notebook January 12, Part II. Other Methods of Voting and Other "Fairness Criteria"

that changes needed to be made when electing their Presidential nominee. Iowa, at the time had a

Voting Criteria April

Section 7.1: Voting Systems. Plurality Method The candidate who receives the greatest number of votes is the winner.

Algorithms, Games, and Networks February 7, Lecture 8

Chapter 9: Social Choice: The Impossible Dream Lesson Plan

Voting Methods

Four Condorcet-Hare Hybrid Methods for Single-Winner Elections

Voting. Suppose that the outcome is determined by the mean of all voter s positions.

Presidential Election Democrat Grover Cleveland versus Benjamin Harrison. ************************************ Difference of 100,456

Intro to Contemporary Math

Warm-up Day 3 Given these preference schedules, identify the Plurality, Borda, Runoff, Sequential Runoff, and Condorcet winners.

The Iowa Caucuses. (See Attached Page Below) B R C T R B R R C C B C T T T B

(67686) Mathematical Foundations of AI June 18, Lecture 6

Fair Division in Theory and Practice

Kybernetika. Robert Bystrický Different approaches to weighted voting systems based on preferential positions

Voting: Issues, Problems, and Systems

n(n 1) 2 C = total population total number of seats amount of increase original amount

Introduction to the Theory of Voting

Voting: Issues, Problems, and Systems. Voting I 1/31

Voting and Apportionment(Due by Nov. 25)

The search for a perfect voting system. MATH 105: Contemporary Mathematics. University of Louisville. October 31, 2017

BY-LAWS THE ENGLISH GRADUATE ORGANIZATION (EGO) OF WASHINGTON STATE UNIVERSITY. ARTICLE I Name

Voting: Issues, Problems, and Systems. Voting I 1/36

Main idea: Voting systems matter.

Public Choice. Slide 1

Computational Social Processes. Lirong Xia

Rationality of Voting and Voting Systems: Lecture II

Practice TEST: Chapter 14

Section 3: The Borda Count Method. Example 4: Using the preference schedule from Example 3, identify the Borda candidate.

The actual midterm will probably not be multiple choice. You should also study your notes, the textbook, and the homework.

A fair three-option referendum? Denis Mollison (Heriot-Watt University)

Warm-up Day 3. Phones OFF and in pockets! 1) Given these preference schedules, identify the Condorcet, Runoff, and Sequential Runoff winners.

Notes for Session 7 Basic Voting Theory and Arrow s Theorem

Voting and Apportionment(Due with Final Exam)

Voting Protocols. Introduction. Social choice: preference aggregation Our settings. Voting protocols are examples of social choice mechanisms

POSITIVE POLITICAL THEORY

Transcription:

Name Date I. Consider the preference schedule in an election with 5 candidates. 1. How many voters voted in this election? 2. How many votes are needed for a majority (more than 50% of the vote)? 3. How many first place votes does candidate A have? 4. How many first place votes does candidate B have? 5. How many first place votes does candidate C have? 6. How many first place votes does candidate D have? 7. How many first place votes does candidate E have? 8. Who is the winner of the election by the Plurality Method? II. Consider the preference schedule in an election with 5 candidates above. 1. Who is the first candidate to be eliminated in the Plurality with Elimination (Hare) method? 2. When the candidate in #1 gets eliminated, which candidate gets those votes in the second round? 3. In the Plurality with Elimination (Hare) method, who gets eliminated in the second round? 4. In the Plurality with Elimination (Hare) method, who wins? 5. How many votes does the winner have in the last round of the Plurality with Elimination (Hare) method? 6. In the Plurality with Run-off method, who are the top two candidates who get to be in the run-off? A. A and B B. A and C C. B and D D. C and E 7. Which candidate wins in the Plurality with Run-off method?

III. Consider the following preference schedule in an election with 3 candidates. 1. In the Borda Count method, how many points does each candidate get for a first place vote? 2. In the Borda Count method, how many points does each candidate get for a 2nd place vote? 3. What is candidate A s Borda score? 4. What is candidate B s Borda score? 5. What is candidate C s Borda score? 6. Who is the winner by the Borda Count method? IV. Consider the following preference schedule in an election with 3 candidates above. 1. In the method of Pairwise Comparisons, who wins in the A v B? 2. In the method of Pairwise Comparisons, who wins in the A v C? 3. In the method of Pairwise Comparisons, who wins in the B v C? 4. Who is the winner in the method of Pairwise Comparisons? V. Consider the preference schedule in an election with 5 candidates. 1. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins in AvB? 2. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who will the winner of AvB be paired with in the second match-up? 3. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins round 2? 4. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins round 3? 5. In the method of sequential pairwise voting with the agenda of A,B,C,D,E, who wins the election?

VI. 1. Consider the following preference schedule in an election with 5 candidates. 2. How many voters voted in this election? 3. Which candidate will be elected using the plurality method? 4. Which candidate will be elected using the Borda Count method? 5. Which candidate will be elected in Plurality with Elimination (Hare) method? 6. Which candidate will be elected using the sequential pairwise agenda A,B,C,D,E? 7. Which candidate will be elected using the sequential pairwise agenda A,C,B,D,E? VII. Consider the preference schedule for an election with 4 candidates. 1. Which candidate will be elected using the plurality method? 2. Which candidate will be elected using the Borda Count method? 3. Which candidate will be elected in Plurality with Elimination (Hare) method? 4. Which candidate will be elected using the sequential pairwise agenda A,B,C,D? 5. How many votes are required for a majority in this election?

VIII. Consider the preference schedule for an election with 3 candidates. 1. How many voters voted in this election? B 2. Which candidate will be elected using the plurality method? 3. Which candidate will be elected using the Borda Count method? 4. Which candidate will be elected in Plurality with Elimination (Hare) method? 5. Which candidate will be elected using the sequential pairwise agenda A,B,C? 6. How many votes are required for a majority in this election? IX. Consider the preference schedule for an election with 4 candidates. 1. Which candidate will be elected using the plurality method? 2. Which candidate will be elected using the Borda Count method? 3. Which candidate will be elected in Plurality with Elimination (Hare) method? 4. How many votes are required for a majority in this election?

X. Consider the following approval voting results: Candidate VOTER 1 VOTER 2 VOTER 3 VOTER 4 VOTER 5 VOTER 6 VOTER 7 A X X X X B X X X X X C X X X X D X X X F X X 1. Which candidate is chosen if only one of them is to be selected? 2. Which candidate(s) is (are) chosen if a 50% approval rating is required and at most 3 are elected? 3. Which candidate(s) is (are) chosen if a 60% approval rating is required and at most 3 are elected? 4. Which candidate(s) is (are) chosen if a 70% approval rating is required and at most 3 are elected? 5. Which candidate(s) is (are) chosen if an 80% approval rating is required and at most 3 are elected?