BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.3, Problem 28ES

Textbook Problem

9 views

**28.** a. In a weighted voting system, suppose that two voters have the same weight. Must they also have the same Banzhaf power index?

b. In a weighted voting system, suppose that voter A has a larger weight than voter B. Must the Banzhaf power index for voter A be larger than the Banihaf power index for voter B?

Most voting systems are susceptible to fraudulent practices. In the following exercise, the Hanzhaf power index is used to examine the power shift that occurs when a fraudulent practice is used.

To determine

**(a)**

Explain why voter

**Given Information:**

Consider four people

**Concept used:**

Voters will be dummy if he has never critical votes.

**Calculation:**

Winning Coalition | Number of Votes | Critical Voters |

â€ƒâ€ƒ | â€ƒâ€ƒ |

To determine

**(b)**

Explain an easy way to compute the Banzhaf power indices for this system.

Mathematical Excursions (MindTap Course List)

Show all chapter solutions

Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Give each state one representative. Use the...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - What is quota rule?Ch. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...

Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - College Security A college apportions 40 security...Ch. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Education The science division of a college...Ch. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - 25. The population of Louisiana increased 1.4%...Ch. 4.1 - House of Representatives Currently. the U.S. House...Ch. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - 32. According to the 2010 census, what is the...Ch. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Deriving the Huntington-Hill Number The...Ch. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise 1 of...Ch. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Suppose the assignment of points for first,...Ch. 4.2 - What is the difference between a majority and a...Ch. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Explain how the Borda Count method of voting...Ch. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - 5. Explain how the pairwise comparison voting...Ch. 4.2 - What does the Condorcet criterion say?Ch. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Cartoons Use the Borda count method of voting to...Ch. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Cell Phone Usage Use plurality with elimination to...Ch. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Family Reunion The Nelson family is trying to...Ch. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Baseball Uniforms Use the pairwise comparison...Ch. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Does the winner in Exercise 2k satisfy the...Ch. 4.2 - Does the winner in Exercise 24c satisfy the...Ch. 4.2 - Does the winner in Exercise 17 satisfy the...Ch. 4.2 - Does the winner in Exercise 20 satisfy the...Ch. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Approval voting is a system in which voters may...Ch. 4.2 - Restaurants Suppose you and three friends. David,...Ch. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Using the data in Check Your Progress 3 on page...Ch. 4.3 - For the data in Check Your Progress 3 on page 215,...Ch. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Create a voting system with four members in which...Ch. 4.3 - Create a voting system with five members that...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Which, if any, of the voting systems in Exercises...Ch. 4.3 - Explain why it is impossible to calculate the...Ch. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Four voters. A, B. C, and D. make decisions by...Ch. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Football The head coach in Exercise 23 has decided...Ch. 4.3 - Consider the weighted voting system { 60:4,56,58...Ch. 4.3 - 26. Consider the weighted voting system {...Ch. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - 28. a. In a weighted voting system, suppose that...Ch. 4.3 - Voter Intimidation and Tampering Consider the...Ch. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Is the Hamilton apportionment method susceptible...Ch. 4 - Is the Jefferson apportionment method susceptible...Ch. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Campus Election Four students are running for the...Ch. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Use the pairwise comparison method of voting to...Ch. 4 - Use the pairwise comparison method of voting to...Ch. 4 - Homecoming Queen Three high school students are...Ch. 4 - Homecoming Queen In Exercise I. suppose Cynthia L....Ch. 4 - Scholarship Awards A scholarship committee must...Ch. 4 - A weighted voting system for voters A, B, C, and D...Ch. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Calculate the Banzhaf power indices for voters A....Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Identify any dictator and all dummies for each...Ch. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - A weighted voting system for voters A, B, C, D....Ch. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Executives Preferences A company with offices...Ch. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Budget Proposal A committee must vote on which of...Ch. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...

Find more solutions based on key concepts

Show solutions Convert the expressions in Exercises 6584 to power form. xx

Finite Mathematics

In Problems 43-46, rewrite each of the following so that only positive exponents remain and simplify.
46.
...

Mathematical Applications for the Management, Life, and Social Sciences

If the following scores are placed in a frequency distribution table, then what is the frequency value correspo...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find the radius of convergence and interval of convergence of the series. 21. n=1nbn(xa)n,b0

Multivariable Calculus

Four universities1, 2, 3, and 4are participating in a holiday basketball tournament. In the first round, 1 will...

Probability and Statistics for Engineering and the Sciences

(a) Find the differential dy and (b) evaluate dy for the given values of x and dx. 16. y=cosx,x=13,dx=0.02

Calculus: Early Transcendentals

Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of th...

Statistics for The Behavioral Sciences (MindTap Course List)

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed...

Calculus (MindTap Course List)

Finding an Equation of a Tangent Line In Exercises 107110, use implicit differentiation to find an equation of ...

Calculus: An Applied Approach (MindTap Course List)

Using Newton's Method In Exercises 3-6, calculate two iterations of Newton's Method to approximate a zero of th...

Calculus: Early Transcendental Functions

Median Ace of Eu-27 Population The European Union (EU) was established on November 1, 1993, with 12 member stat...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Let g(x)=1x33. (a) Find g1. How is it related to g? (b) Graph g. How do you explain your answer to part (a)?

Single Variable Calculus: Early Transcendentals, Volume I

Demand and Profit To generate a profit from its new oTunes service, OHaganBooks.com needs to know how the deman...

Finite Mathematics and Applied Calculus (MindTap Course List)

Solving Basic Trigonometric Equations Solve the given equation, and list six specific solutions. 22. tan = 2.5

Precalculus: Mathematics for Calculus (Standalone Book)

Express the function F(x)=1/x+x as a composition of three functions.

Single Variable Calculus

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 2a3a+7...

Intermediate Algebra

Baseball: Batting Averages and Home Runs In baseball, is there a linear correlation between batting average and...

Understanding Basic Statistics

SOC The World Values Survey is administered periodically to random samples from societies around the globe. Lis...

Essentials Of Statistics

A business owner plans to build a storage garage for 85 automobiles. Each automobile needs a space of 15.0 ft b...

Elementary Technical Mathematics

In Exercises 31 and 32, use the calculator value of . For a sphere whose radius has length 7cm, find the approx...

Elementary Geometry For College Students, 7e

Prove that every ideal of n is a principal ideal. (Hint: See corollary 3.27.)

Elements Of Modern Algebra

For the limit limxxlnx= illustrate Definition 9 by finding a value of N that corresponds to M = 100. Definition...

Single Variable Calculus: Early Transcendentals

Show that each of the following is true. sin(90+)=cos

Trigonometry (MindTap Course List)

Subtract the following numbers.
17.

Contemporary Mathematics for Business & Consumers

A bank deposit paying simple interest grew from an initial amount of 1000 to 1075 in 9months. Find the interest...

Finite Mathematics for the Managerial, Life, and Social Sciences

Think About It The function f(x)=k(2xx3) one-to-one and f1(3)=2. Find k.

Calculus of a Single Variable

Finding the Arc Length of a Polar Curve In Exercises 5156, find the length of the curve over the given interval...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercise 19 and 20, state a conclusion for the argument. Statements 1 and 2 are true. 1. If two triangles do...

Elementary Geometry for College Students

State the Exponent-Becomes-Multiplier Properties of the natural logarithm.

Mathematics: A Practical Odyssey

Find the length of x. Round the answer to 2 decimal places.

Mathematics For Machine Technology

Finding a Jacobian In Exercises 3-10, find the Jacobian (x,y)/(u,v) for the indicated change of variables. x=uc...

Multivariable Calculus

Comcast Corporation is the largest cable television company, the second largest Internet service provider, and ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

For the family of functions f(x) = x2 ax, each function is: a) a parabola through (0, 0) and (a, 0). b) is con...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Describe, compare, and contrast the five research strategies (descriptive, correlational, experimental, quasi-e...

Research Methods for the Behavioral Sciences (MindTap Course List)

A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter for the...

Introduction To Statistics And Data Analysis

Practice Solve each exponential equation using logarithms. Give the answer in decimal form, rounding to four de...

College Algebra (MindTap Course List)

Think About It In Exercises 69 and 70, F(x)=fgh). Identify functions for f, g and h. (There are many correct an...

Calculus (MindTap Course List)

Explain how the purpose of a correctional study differs from the purpose of an experimental study.

Research Methods for the Behavioral Sciences (MindTap Course List)

For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a. To the right...

Statistics for Business & Economics, Revised (MindTap Course List)

True or False:
The curve at the right appears to be piecewise smooth.

Study Guide for Stewart's Multivariable Calculus, 8th