Plurality and Borda Count Method

Slides:

Advertisements

Similar presentations

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

Advertisements

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

The Plurality Method The Borda Count Method

1.1, 1.2 Ballots and Plurality Method

1 The Mathematics of Voting

Presidential Selection: The Framers Plan

CRITERIA FOR A FAIR ELECTION

1.3 The Borda Count Method. The Borda Count Method In an election of N candidates, give 1 point for the last place, 2 points for the second from last.

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

MAT 105 Spring  We have studied the plurality and Condorcet methods so far  In this method, once again voters will be allowed to express their.

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

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 14 Voting and Apportionment.

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.

The Election Electoral College What is it? –Representatives from the states who cast ballots for the President How are they chosen? –Based on the.

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

How are Presidents Elected? Unit 10 Part 2. Electoral College – Today – New Way The electoral college elects the president – NOT THE DIRECT or “POPULAR”

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.

1.6 Rankings. Sometimes, we are not just interested in the first place winner of the election, but also want to know who comes in second, third … There.

Why We Should Use the Plurality with Elimination Voting Method.

Copyright © 2009 Pearson Education, Inc. Chapter 15 Section 1 - Slide Election Theory Voting Methods.

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.

Voting Methods Introduction.

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.

The mathematics of voting The paradoxes of democracy.

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.

Voting: Does the Majority Always Rule?

Electoral College Process of how we elect our Presidents

Voting and Apportionment

Plurality with elimination, Runoff method, Condorcet criterion

Fair Division The Value of a Slice.

8.2 Voting Possibilities and Fairness Criteria

1.3 The Borda Count Method.

7th Grade Social Studies Name____________________

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.

Electoral College.

Homework (day 2): p , 4, 6, 10, 12ab, 16, 18abc, 24, 26

Election (Starter) Here are three ballot papers from an election for a single candidate to represent a group of voters. If these were the only three votes.

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)

Section 15.2 Flaws of Voting

5-2 Election Theory Flaws of Voting.

Voting Preference Ballots and Preference Schedules

Approval Voting.

Plurality with Elimination

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

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

How the Electoral College Works STEPS TO BECOMING A PRESIDENT

Voting Methods Introduction.

Voting Pairwise Comparison.

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

Homework (day 1): p , 4, 6, 10, 12ab, 16, 18abc, 24, 26

Section 14.1 Voting Methods.

Flaws of the Voting Methods

The Electoral College.

Probability & Statistics

Voting Fairness.

Presentation transcript:

Plurality and Borda Count Method Voting Methods Plurality and Borda Count Method

Plurality and Borda Count T. Serino Plurality and Borda Count Content Objective: Students will be able to determine the winner of an election using the Plurality method and the Borda Count Method. Language Objective: Students will be able to distinguish between number of points received and number of votes received (1st place, 2nd place, 3rd place etc.).

Plurality Method T. Serino The Plurality Method simply says that the candidate with the most first place votes wins. This is a popular method, but is it always reasonable? Remember the election between these three candidates?

Plurality Method How does this election turn out using plurality? T. Serino How does this election turn out using plurality?

Plurality Method T. Serino A B C B A C C B A C B A B A C C A B A B C Making a guess on the two unknown ballots, the preference table would look like this.

Plurality Method T. Serino The result of the election by plurality method is that Carl (C) wins with 3 first place votes. Amy: 2 votes Beatrice: 2 votes Carl: 3 votes Is this fair? Why is the majority unhappy?

Plurality Method A wins! T. Serino Remember the Mathematics Anxiety Club? The preference table for their election is shown below. A = 14 B = 4 C = 11 D = 8 Tally the number of first place votes for each candidate. Who wins? A wins!

Plurality Method T. Serino Using the plurality method, determine the winner of the election that produced the preference table below. 10 4 8 6 2 1 1st B C A D A A 2nd D B D B D C 3rd C D B C B B 4th E E E E C D 5th A A C A E E How many votes did the winner receive?

Borda Count T. Serino Using the Borda Count method, votes are weighted according to order of preference. Each last place vote earns a candidate 1 point. Each second to last place vote earns a candidate 2 points. Each third to last place vote earns a candidate 3 points. Etc. If there are N candidates, first place is votes are worth N points, second place votes are worth (N-1) points, etc.

Weighted Voting With three candidates: With four candidates: T. Serino With three candidates: Each 1st place vote is worth 3 pts. Each 2nd place vote is worth 2 pts. Each 3rd (last) place vote is worth 1 pt. With four candidates: Each 1st place vote is worth 4 pts. Each 2nd place vote is worth 3 pts. Each 3rd place vote is worth 2 pts. Each 4th (last) place vote is worth 1 pt.

Borda Count Remember the election between these three candidates? T. Serino Remember the election between these three candidates?

Borda Count T. Serino Amy receives 2 first place votes worth 3 points each = 6 pts. Amy receives 3 second place votes worth 2 pts. ea. = 6 pts. Amy receives 2 last place votes worth 1 point each = 2 pts. Amy earns a total of 6 + 6 + 2 = 14 points Use tables to organize the results for each candidate.

Borda Count Amy: 1st 2 x 3 = 6 2nd 3 x 2 = 6 3rd 2 x 1 = 2 14 points T. Serino Amy: 1st 2 x 3 = 6 2nd 3 x 2 = 6 3rd 2 x 1 = 2 14 points Beatrice: 1st 2 x 3 = 6 2nd 4 x 2 = 8 3rd 1 x 1 = 1 15 points Carl: 1st 3 x 3 = 9 2nd 0 x 2 = 0 3rd 4 x 1 = 4 13 points Number of votes. Points per vote. Total points earned.

Try this. By the Borda Count method, who will be T. Serino By the Borda Count method, who will be the new president of the MAC?

Borda Count 14 56 4 16 24 72 9 18 23 23 79 points 106 points 11 44 8 T. Serino 14 56 4 16 24 72 9 18 23 23 79 points 106 points 11 44 8 32 8 24 5 15 18 36 10 20 14 14 104 points 81 points

athematical M D ecision aking