Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 15.4, Problem 24E
To determine
The most disturbing impossibility of apportionment from given methods - quota rule violation, the Alabama paradox, the population paradox, or the new states paradox.
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Chapter 15 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
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- A travel agency is concerned with the accuracy and appearance of itineraries prepared for its clients Defects can include errors in times, airlines, flight numbers, prices, car rental information, lodging, charge card numbers, and reservation numbers, as well as typographical errors. As the possible number of errors is nearly infinite, the agency measures the number of errors that do occur. The current process results in an average of five errors per itinerary. a. What are the three-sigma control limits for these defects? The UCL, equals and the LCL, equals. (Enter your responses rounded to three decimal places. If your answer for LCL, is negative, enter this value as 0.) b. A client scheduled a trip to Dallas. Her itinerary contained five errors. Interpret this information. O A. The number of defects is within the control limits, so it is assumed that the process is not in control O B. The number of defects is within the control limits, so it is assumed that the process is in control…arrow_forwardSolve the problem. Which apportionment method may produce the Alabama paradox? Jefferson Webster Adams O Hamiltonarrow_forwardWhich of the following is a flaw in apportionment methods? Jefferson Plan Hare System Hamilton Plan Alabama Paradoxarrow_forward
- 9. A grant and a newly passed levy will allow a county to buy 13 new fire trucks for its fire precincts. The new trucks are going to be allotted to the precincts based on the number of times each precinct had to respond to calls in the last six months. Use the Hamilton Apportionment Plan and the table below to determine the number of fire trucks each precinct will receive. District Number of Calls D-1 45 D-2-1 73 D-2-2 100 D-3 67 D-4-1 179 D-4-2 95arrow_forwardSolve the problem. Which apportionment method may produce the Alabama paradox? Adams Hamilton Jefferson Websterarrow_forwardA travel agency is concerned with the accuracy and appearance of itineraries prepared for its clients. Defects can include errors in times, airlines, flight numbers, prices, car rental information, lodging, charge card numbers, and reservation numbers, as well as typographical errors. As the possible number of errors is nearly infinite, the agency measures the number of errors that do occur. The current process results in an average of three errors per itinerary.a. What are the two-sigma control limits for these defects?b. A client scheduled a trip to Dallas. Her itinerary contained six errors. Interpret this information.arrow_forward
- QUESTION 11 An apportionment method exists that satisfies the quota condition and is free from both the population paradox and the Alabama paradox. True Falsearrow_forwardShould religion be taught in all school? Propose a procedure to settle this issue.arrow_forward2. "Dalmatian Darnation," by Kathy SparlingA greedy dog breeder named Spreckles , Bred puppies with numerous frecklesThe Dalmatians he sought, Possessed spot upon spotThe more spots, he thought, the more shekels.His competitors did not agree, That freckles would increase the fee.They said, “Spots are quite nice, But they don't affect price;One should breed for improved pedigree.”The breeders decided to prove, This strategy was a wrong move.Breeding only for spots, Would wreak havoc, they thought.His theory they want to disprove.They proposed a contest to Spreckles, Comparing dog prices to freckles.In records they looked up, One hundred one pups:Dalmatians that fetched the most shekels.They asked Mr. Spreckles to name, An average spot count he'd claimTo bring in big bucks. Said Spreckles, “Well, shucks,It's for one hundred one that I aim.”Said an amateur statistician, Who wanted to help with this mission.“Twenty-one for the sample, Standard deviation's ample:They examined one hundred…arrow_forward
- 2. "Dalmatian Darnation," by Kathy SparlingA greedy dog breeder named Spreckles , Bred puppies with numerous frecklesThe Dalmatians he sought, Possessed spot upon spotThe more spots, he thought, the more shekels.His competitors did not agree, That freckles would increase the fee.They said, “Spots are quite nice, But they don't affect price;One should breed for improved pedigree.”The breeders decided to prove, This strategy was a wrong move.Breeding only for spots, Would wreak havoc, they thought.His theory they want to disprove.They proposed a contest to Spreckles, Comparing dog prices to freckles.In records they looked up, One hundred one pups:Dalmatians that fetched the most shekels.They asked Mr. Spreckles to name, An average spot count he'd claimTo bring in big bucks. Said Spreckles, “Well, shucks,It's for one hundred one that I aim.”Said an amateur statistician, Who wanted to help with this mission.“Twenty-one for the sample, Standard deviation's ample:They examined one hundred…arrow_forward2. "Dalmatian Darnation," by Kathy SparlingA greedy dog breeder named Spreckles , Bred puppies with numerous frecklesThe Dalmatians he sought, Possessed spot upon spotThe more spots, he thought, the more shekels.His competitors did not agree, That freckles would increase the fee.They said, “Spots are quite nice, But they don't affect price;One should breed for improved pedigree.”The breeders decided to prove, This strategy was a wrong move.Breeding only for spots, Would wreak havoc, they thought.His theory they want to disprove.They proposed a contest to Spreckles, Comparing dog prices to freckles.In records they looked up, One hundred one pups:Dalmatians that fetched the most shekels.They asked Mr. Spreckles to name, An average spot count he'd claimTo bring in big bucks. Said Spreckles, “Well, shucks,It's for one hundred one that I aim.”Said an amateur statistician, Who wanted to help with this mission.“Twenty-one for the sample, Standard deviation's ample:They examined one hundred…arrow_forwardState A has a population of 25,500 and has 15 representatives. State B has a population of 20,150 and has 13 representatives. Which state unfairness of this apportionment? more poorly represented? What is the absolute unfairness of this apportionment? What is the relative Which state is more poorly represented? Select the correct answer below and, if necessary, fill in the answer boxes within your choice. O A. State B is more poorly represented with an average constituency of. State A is represented better with an average constituency of. O B. State A is more poorly represented with an average constituency of State B is represented better with an average constituency of. (Type integers or decimals.)arrow_forward
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