1.3 More Group Ranking and Paradoxes Ms. Magne Discrete Math.

Slides:

Advertisements

Similar presentations

1.4 Arrow’s Conditions and Approval Voting

Advertisements

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

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.

Math for Liberal Studies.  We have studied the plurality and Condorcet methods so far  In this method, once again voters will be allowed to express.

Brittany Vacchiano. » Voting procedure in which voters can vote for as many candidate as they wish » Each candidate approved of receives one vote » Single.

MA 110: Finite Math Dr. Maria Byrne Instructional Laboratory 0345 Lecture 10/31/2008.

MAT 105 Spring  There are many more methods for determining the winner of an election with more than two candidates  We will only discuss a few.

Social Choice: The Impossible Dream Michelle Blessing February 23, 2010 Michelle Blessing February 23, 2010.

Excursions in Modern Mathematics Sixth Edition

But, how?? Explaining all possible positional, pairwise voting paradoxes & prop. Don Saari Institute for Math Behavioral Sciences University of California,

1.1, 1.2 Ballots and Plurality Method

What is your favorite food?. Preference Schedule A Preference Schedule is a way to represent the order in which people like (prefer) certain items. The.

Voting Review Material

Plurality with elimination, Runoff method, Condorcet criterion.

Math for Liberal Studies.  There are many more methods for determining the winner of an election with more than two candidates  We will only discuss.

CRITERIA FOR A FAIR ELECTION

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.

Social choice (voting) Vincent Conitzer > > > >

CPS Voting and social choice Vincent Conitzer

Slide 15-1 Copyright © 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION.

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.

Chapter 12 sec 1. Def. Each person votes for his or her favorite candidate. The candidate receiving the most votes is declared the winner.

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

Math for Liberal Studies.  We have seen many methods, all of them flawed in some way  Which method should we use?  Maybe we shouldn’t use any of them,

Voting Methods Examples of Voting Methods (other than majority rules) –Plurality –Borda Count –Hare System –Sequential Pairwise –Approval Voting.

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

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 15.1 Voting Methods.

VOTING PARADOXES AND HOW TO DEAL WITH THEM Hannu Nurmi University of Turku Turku, Finland.

Name Next Spelling Word #1 Next Previous Spelling Word #2 Next.

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.

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,

Review of Common Test #1 Mistakes. Plurality versus Majority Plurality winner = candidate with more first place votes than any other Majority winner =

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.

Activity 3 Improving on Plurality? Decision methods using ordinal ballots.

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

Condorcet Method Another group-ranking method. Development of Condorcet Method  As we have seen, different methods of determining a group ranking often.

Voting: Does the Majority Always Rule?

Voting and Apportionment

Plurality with elimination, Runoff method, Condorcet criterion

1.5 Weighted Voting and Voting Power

8.2 Voting Possibilities and Fairness Criteria

1.3 The Borda Count Method.

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]

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

5-2 Election Theory Flaws of Voting.

Voting systems Chi-Kwong Li.

Plurality with Elimination

MAT 105 Fall 2008 More Voting Methods.

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

Year 5 Beat It.

Year 4 Beat It.

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

Year 3 Beat It.

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

Discrete Mathematics Blog: jgillncs.weebly.com After School tutoring:

Section 14.1 Voting Methods.

Presentation transcript:

1.3 More Group Ranking and Paradoxes Ms. Magne Discrete Math

Group Ranking Condorcet Winner – the winner is the choice that wins over every other choice individually 1st ABCD 2ndBCBB 3rdCDDC 4thDAAA 8567

ABCD A B C D 1st ABCD 2ndBCBB 3rdCDDC 4thDAAA 8567 The Condorcet Winner is _____. B

Group Ranking Paradox – When what happens in contrary to logic/intuition. Ex. A beats B and B beats C. Who would your expect to win between A and C? We would expect A to beat C, but like to example previously done, this is not always the case.

Group Ranking Pairwise Voting – two choices are selected and a vote is taken, the loser is eliminated and a new vote is taken between the winner and a new choice. This process continues until all but one has been eliminated.

Group Ranking Find the Pairwise winner using the following order: BCAD. 1st ABCD 2ndBCBB 3rdCDDC 4thDAAA 8567 The Pairwise Winner is _____. B