BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.3, Problem 27ES

Textbook Problem

33 views

Consider the weighted voting system

a. For what values of q is there **a dummy?**

b. For what values of q do all voters have the same power?

C. II a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas?

To determine

**(a)**

For what values of

**Given Information:**

Consider the weighted voting system

**Concept used:**

To determine

**(b)**

For what values of

To determine

**(c)**

If a voter is a dummy for a given quota, must the voter be a dummy for all larger quotas?

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 each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics

Factor each expression in Problems 7-18 as a product of binomials.
13.

Mathematical Applications for the Management, Life, and Social Sciences

Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had letter test scores...

Statistics for The Behavioral Sciences (MindTap Course List)

Stress is applied to a 20-in. steel bar that is clamped in a fixed position at each end. Let Y = the distance f...

Probability and Statistics for Engineering and the Sciences

For each of the following confidence levels, determine the corresponding Z score. Confidence Level Alpha Area B...

Essentials Of Statistics

Find all the second partial derivatives. 53. f(x, y) = x4y 2x3y2

Multivariable Calculus

(a) How is the graph of y = f (|x|) related to the graph of f? (b) Sketch the graph of y = sin |x|. (c) Sketch ...

Single Variable Calculus

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 2516

Applied Calculus

In Exercises 4449, find an equation of the line L that passes through the point (2, 4) and satisfies the condit...

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

Graph the function f(x)=cos2xsin3x and use the graph to guess the value of the integral 02f(x)dx. Then evaluate...

Calculus (MindTap Course List)

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample of n = 5 scores has a mean of M = 12. If one new score with a value of X 18 is added to the sample, t...

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

Terminology Which quantity is give by the expected value of a probability distribution? (a) the standard deviat...

Understanding Basic Statistics

A cell phone plan has a basic charge of 35 a month. The plan includes 400 free minutes and charges 10 cents for...

Calculus: Early Transcendentals

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joini...

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 6-8, sketch the graph of the equation and label the intercepts. y=x3

Calculus: An Applied Approach (MindTap Course List)

For Problems 1-14, state the property that justifies each of the statements. For example, 3+(4)=(4)+3 because o...

Intermediate Algebra

Determining Convergence or Divergence In Exercises 11-18, determine the convergence or divergence of the sequen...

Calculus: Early Transcendental Functions

U.S. Population The U.S. Constitution requires a census every 10 years. The census data for 17902010 are given ...

Precalculus: Mathematics for Calculus (Standalone Book)

Solve each equation and check: 5x6+13(6+x)=37

Elementary Technical Mathematics

Solve the following word problems. Round dollars to the nearest cent and percents to the nearest tenth of a per...

Contemporary Mathematics for Business & Consumers

Find the limit. limx0sin(x2)x

Single Variable Calculus: Early Transcendentals

4. Prove that the special linear group is a normal subgroup of the general linear group .

Elements Of Modern Algebra

Each of the following graphs shows at least one complete cycle of the graph of an equation containing a trigono...

Trigonometry (MindTap Course List)

Prove by the indirect method: Given: MPN is not isosceles Prove: PMPN

Elementary Geometry For College Students, 7e

DEMAND EQUATION FOR A COMPANY There is no demand for a certain commodity when the unit price is 200 or more, bu...

Finite Mathematics for the Managerial, Life, and Social Sciences

Which formula would you use to establish each of the following claims? a AC-DB- b AC-=DB- c DB- and AC- bisect ...

Elementary Geometry for College Students

Condensing a Logarithmic Expression In Exercises 99106, write the expression as the logarithm of a single quant...

Calculus: Early Transcendental Functions (MindTap Course List)

Using the Mean Value Theorem In Exercises 39-48, determine whether the Mean Value Theorem can be applied to f o...

Calculus of a Single Variable

Cast iron 10 cm in diameter is turned in a lathe at 350 rpm. Each length of cut is 65 cm and eight cuts are req...

Mathematics For Machine Technology

A study provided data on variables that may be related to the number of weeks a manufacturing worker has been j...

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

Solve each problem. Preparing seafood Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1000 shrim...

College Algebra (MindTap Course List)

What degree Taylor polynomial about a = 1 is needed to approximate e1.05 accurate to within 0.0001?
n = 2
n = 3...

Study Guide for Stewart's Multivariable Calculus, 8th

Describe the relationship between a sample and the population (both target and accessible) in a research study ...

Research Methods for the Behavioral Sciences (MindTap Course List)

limxx2+13x+2= a) 0 b) 1 c) 13 d) does not exist

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

The following data show the curb weight, horsepower, and 1/4-mile speed for 16 popular sports and GT cars. Supp...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Evaluating an Integral In Exercises 3 - 6, evaluate the integral. 0101+x(3x+2y)dydx

Multivariable Calculus

Describe how the cliche You can lead a horse to water, but you cant make it drink can be used to explain a pers...

Research Methods for the Behavioral Sciences (MindTap Course List)

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is s...

Introduction To Statistics And Data Analysis

Finding and Evaluating Partial DerivativesIn Exercises 2730, find all first partial derivatives, and evaluate e...

Calculus (MindTap Course List)

According to Example 11.3.6. the maximum number of comparisons needed to perform insertion sort on an array of ...

Discrete Mathematics With Applications

In Problems 1-18 solve each differential equation by variation of parameters. 6. y + y = sec2 x

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

In Exercises 27-56, use a calculator to find each value. Give the entire display of your calculator. a. eln3.2 ...

Mathematics: A Practical Odyssey

ReminderRound all answers to two decimal places unless otherwise indicated. Maximum Growth Rate for the Logisti...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

7. Three different methods for assembling a product were proposed by an industrial engineer. To investigate the...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Mixture Problem A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make ...

College Algebra

Machine Maintenance. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contrac...

Essentials Of Statistics For Business & Economics