BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.3, Problem 26ES

Textbook Problem

1 views

**26.** Consider the weighted voting system

a. Explain why voter D is a dummy in this system.

b. Explain an *easy* way to compute the Banzhaf power indices for the systems

To determine

**To Verify:**

Verify that this theorem is true for the weighted voting system

**Given Information:**

It can be proved that for any natural number constant

**Concept used:**

â€ƒâ€ƒ

**Calculation:**

Consider one voting system is

Therefore,

Winning Coalition | Number of Votes | Critical Voters |

â€ƒâ€ƒ | â€ƒâ€ƒ â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | â€ƒâ€ƒ |

â€ƒâ€ƒ | â€ƒâ€ƒ | None |

In above table we look in Critical voters column and find that

Formula of Banzhaf power index of a voter

â€ƒâ€ƒ

Then

â€ƒâ€ƒ

The Banzhaf power index of voters

Consider one voting system is

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 In problems 13-16, Use notation to indicate which set is a subset of the other.
16.

Mathematical Applications for the Management, Life, and Social Sciences

Convert the expressions in Exercises 8596 radical form. 34/5

Finite Mathematics

Calculate y'. 6. y = x cos1x

Calculus: Early Transcendentals

Find parametric equations for the tangent line to the curve with the given parametric equations at the specifie...

Multivariable Calculus

a. SW Statewide, social workers average 10.2 years of experience. In a random sample, 203 social workers in gre...

Essentials Of Statistics

Education: Teacher Evaluation If you were going to apply statistical methods to analyze teacher evaluations, wh...

Understanding Basic Statistics

Several factors influence the size of the F-ratio. For each of the following, indicate whether it would it woul...

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

Describe the set of points (x,y) such that x2+y2=0.

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluating a Line Integral In Exercises 27-30, evaluate the line integral along the given path(s). Cxyds (a)C: ...

Calculus: Early Transcendental Functions

Real Zeros of a Polynomial Find all the real zeros of the polynomial. Use the Quadratic Formula if necessary, a...

Precalculus: Mathematics for Calculus (Standalone Book)

Suppose that a function f is continuous on [0, 1] except at 0.25 and that f(0) = 1 and f(1) = 3. Let N = 2. Ske...

Single Variable Calculus

High concentration of the toxic element arsenic is all too common in groundwater. The article Evaluation of Tre...

Probability and Statistics for Engineering and the Sciences

A roulette wheel has alternating red and black numbered slots into which the ball finally stops to determine th...

Statistics for The Behavioral Sciences (MindTap Course List)

The volume of a sphere of radius r is given by V(r)=43r3 Compute V(2.1) and V(2). What does the quantity V(2.1)...

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

30-45 Find the derivative. Simplify where possible. y=coth1(secx)

Calculus (MindTap Course List)

Find the limit: limx2x38x2.

Calculus: An Applied Approach (MindTap Course List)

For Problems 55-94, simplify each numerical expression. Objective 7 3(12)+4(23)2(56)

Intermediate Algebra

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. (x21)...

Applied Calculus

A high-speed bullet train accelerates and decelerates at the rate of 4 ft/s2. Its maximum cruising speed is 90 ...

Single Variable Calculus: Early Transcendentals, Volume I

Divide: (16m2n)(2m3n2)

Elementary Technical Mathematics

Solve the differential equation. 5. y = xesin x y cos x

Single Variable Calculus: Early Transcendentals

In DEF,D is a right angle and m F=30. a Find DE if EF = 10m. b Find EF if DF=63 ft.

Elementary Geometry For College Students, 7e

For each of the following problems, is a central angle in a circle of radius r. In each case, find the length ...

Trigonometry (MindTap Course List)

Calculate the assessed value and the property tax due on the following properties. FairMarketValue240,000Assess...

Contemporary Mathematics for Business & Consumers

Consider the additive groups 8 and 4 and define :84 by ([x]8)=[x]4. Prove that is a homomorphism and find ker ...

Elements Of Modern Algebra

In Exercises 27 and 28, let A=[2103] and B=[2312] Find the X satisfying the matrix equation 2A+X=3B

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding an Equation In Exercises 5560, find an equation for the function f that has the given derivative and wh...

Calculus: Early Transcendental Functions (MindTap Course List)

Solving a First-Order Linear Differential Equation In Exercises 53-58, find the general solution of the first-o...

Calculus of a Single Variable

Given: EFGOHMJK,withtransversalsFJandEK;FG=2,GH=8,HJ=5,EM=6 Find EO, EK

Elementary Geometry for College Students

In Exercise 110, determine whether E and F are mutually exclusive. Write a sentence justifying your answer. If ...

Mathematics: A Practical Odyssey

Reduce to halves. a. 2510 b. 1812 c. 12636 d. 22550

Mathematics For Machine Technology

In Figure 11.5, we show three combinations of main effects and interactions for a 2 2 factorial design. Using ...

Research Methods for the Behavioral Sciences (MindTap Course List)

How many second partial derivatives will there be for ? (Do not assume that they are continuous.)
5
10
20
25

Study Guide for Stewart's Multivariable Calculus, 8th

Assume a finite population has 350 elements. Using the last three digits of each of the following five-digit ra...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A stratified simple random sample is to be taken of a banks customers to learn about a variety of altitudinal a...

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

The paper Effect of a Nutritional Supplement on Hair Loss in Women (Journal of Cosmetic Dermatology [2015]: 76-...

Introduction To Statistics And Data Analysis

Graph each quadratic function given in standard form. Identify the vertex, intercepts and axis of symmetry. f(x...

College Algebra (MindTap Course List)

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

Identify the strengths and weaknesses of a multiple-baseline design and describe the circumstances in which it ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Using the Direct Comparison Test In Exercises 5-16, use the Direct Comparison Test to determine the convergence...

Calculus (MindTap Course List)