Warm Up – 1/27 - Monday Who wins by Plurality with Elimination?

Slides:

Advertisements

Similar presentations

Which units are you most interested in covering? Unit A –Management Science Unit B – Growth Unit C – Shape and Form Unit D – Statistics.

Advertisements

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 1 The Mathematics of Voting 1.1Preference Ballots and Preference.

Voting Methods Continued

Math 1010 ‘Mathematical Thought and Practice’ An active learning approach to a liberal arts mathematics course.

Mark Wang John Sturm Sanjeev Kulkarni Paul Cuff.  Basic Background – What is the problem?  Condorcet = IIA  Survey Data  Pairwise Boundaries = No.

IMPOSSIBILITY AND MANIPULABILITY Section 9.3 and Chapter 10.

Chapter 1: Methods of Voting

The Mathematics of Elections

Mathematics The study of symbols, shapes, algorithms, sets, and patterns, using logical reasoning and quantitative calculation. Quantitative Reasoning:

VOTING SYSTEMS Section 2.5.

Excursions in Modern Mathematics Sixth Edition

MAT 105 Spring  As we have discussed, when there are only two candidates in an election, deciding the winner is easy  May’s Theorem states that.

1.1, 1.2 Ballots and Plurality Method

1 The Mathematics of Voting

Voting Review Material

CRITERIA FOR A FAIR ELECTION

Homework Discussion Read Pages 48 – 62 Page 72: 1 – 4, 6 TEST 1 ON THURSDAY FEBRUARY 8 –The test will cover sections 1.1 – 1.6, and 2.1 – 2.3 in the textbook.

1 The Process of Computing Election Victories Computational Sociology: Social Choice and Voting Methods CS110: Introduction to Computer Science – Lab Module.

How is this math? Mathematics is essentially the application of deductive reasoning to the study relations among patterns, structures, shapes, forms and.

Voting Rules: What’s Fair? Q. What is the most fair voting rule? Suppose three proposals to spend $15: Z=Status Quo (currently, we spend $10 on guns and.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 11.2, Slide 1 11 Voting Using Mathematics to Make Choices.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 1 The Mathematics of Voting The Paradoxes of Democracy Vote! In.

Copyright © 2009 Pearson Education, Inc. Chapter 15 Section 2 - Slide Election Theory Flaws of Voting.

May 19, 2010Math 132: Foundations of Mathematics 12.5 Homework Solutions 27. (a) 28. (b) 29. (d) 30. (e) 53. Positive Correlation, Weak 54. Negative Correlation,

Ch Voting Preference tables E, F, G, and H are running for math club president If everyone is asked to rank their preferences, how many different.

The Mathematics of Voting Chapter 1. Voting theory: application of methods that affect the outcome of an election. Sec 1: Preference Ballots and Schedules.

Voting and Apportionment. The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters.

Chapter 15 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 1 The Mathematics of Voting 1.1Preference Ballots and Preference.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 11.1, Slide 1 11 Voting Using Mathematics to Make Choices.

Voting Tie Breakers. With each method described – plurality method, Borda count method, plurality with elimination method, and pairwise comparison method.

Fairness Criteria and Arrow’s Theorem Section 1.4 Animation.

Warm-Up Rank the following soft drinks according to your preference (1 being the soft drink you like best and 4 being the one you like least)  Dr. Pepper.

The Mathematics of Voting Chapter 1. Preference Ballot A Ballot in which the voters are asked to rank the candidates in order of preference. 1. Brownies.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 15.2 Flaws of Voting.

14.2 Homework Solutions Plurality: Musical play Borda count: Classical play Plurality-with-elimination: Classical play Pairwise Comparison: Classical play.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 1 The Mathematics of Voting 1.1Preference Ballots and Preference.

Chapter 9: Social Choice: The Impossible Dream Lesson Plan Voting and Social Choice Majority Rule and Condorcet’s Method Other Voting Systems for Three.

Excursions in Modern Mathematics, 7e: 1.Conclusion - 2Copyright © 2010 Pearson Education, Inc. 1 The Mathematics of Voting CONCLUSION Elections, Fairness,

Voting System Review Borda – Sequential Run-Off – Run-Off –

My guy lost? What’s up with that….  In the 1950’s, Kenneth Arrow, a mathematical economist, proved that a method for determining election results that.

1 The Process of Computing Election Victories Computational Sociology: Social Choice and Voting Methods CS110: Introduction to Computer Science – Lab Module.

Voting and Apportionment

Voting and Apportionment

1 The Mathematics of Voting

Plurality with elimination, Runoff method, Condorcet criterion

Chapter 9: Social Choice: The Impossible Dream Lesson Plan

Chapter 10: The Manipulability of Voting Systems Lesson Plan

8.2 Voting Possibilities and Fairness Criteria

Introduction If we assume

Chapter 9: Social Choice: The Impossible Dream Lesson Plan

1.3 The Borda Count Method.

Lecture 1: Voting and Election Math

Elections with More Than Two Candidates

Let’s say we have a town of 10,000 people electing a mayor using the Plurality with Elimination Voting Method. There are 4 candidates, candidate A, candidate.

Warm Up – 5/27 - Monday How many people voted in the election?

Warm Up – 1/23 - Thursday How many people voted in the election?

Social Choice Theory [Election Theory]

Voting Rules: What’s Fair?

Classwork: p.33 (27abc run off, 29ab run off, 31, 33ab run off)

Section 15.2 Flaws of Voting

5-2 Election Theory Flaws of Voting.

Which type of Voting Scheme would you vote for?

p.33 (28 run off, 30 run off, 32, 34ab run off)

Quiz – 1/24 - Friday How many people voted in the election?

Flaws of the Voting Methods

Voting Fairness.

Chapter 9: Social Choice: The Impossible Dream Lesson Plan

Presentation transcript:

Warm Up – 1/27 - Monday Who wins by Plurality with Elimination? Who wins by Pairwise Comparison?

Mid-Chapter Quiz Tomorrow Things to Know: -Make a preference schedule -Read information from a preference schedule -4 voting methods -4 fairness criterion

Fairness conditions

Criterion Violations Majority Criterion: Can be violated by Borda Count Condorcet Criterion: Can be violated by any besides pairwise comparisons Monotonicity Criterion: Violated by Plurality with Elimination IIA Criterion: Can be violated by all!

Condorcet

Criterion Violation Worksheet

Sincere Voting vs. Strategic Voting Sincere Voting means submitting a ballot that goes along with someone’s true preferences. Strategic Voting means submitting a ballot that would give a more preferred result than if someone voted sincerely.

2000 Election

Math’s Role