Excursions in Modern Mathematics (9th E...9th EditionPeter Tannenbaum Publisher: PEARSONISBN: 9780134468372
Excursions in Modern Mathematics (9th E...
Solutions for Excursions in Modern Mathematics (9th Edition)
Problem 1E:
Five partners (P1,P2,P3,P4, andP5) jointly own the Gaussian Electric Company. P1 owns 15 shares of...Problem 2E:
Five partners (P1,P2,P3,P4, andP5) jointly own the Euler Moving Company. P1 owns 30, P2 owns 25, P3...Problem 5E:
In each of the following weighted voting systems, determine which players, if any, have veto power....Problem 6E:
In each of the following weighted voting systems, determine which players, if any, have veto power....Problem 7E:
Consider the weighted voting system[q:7,5,3]. Find the smallest value of q for which a. all three...Problem 8E:
Consider the weighted voting system [q:10,8,6,4,2]. Find the smallest value of q for which a. all...Problem 9E:
A committee has four members (P1,P2,P3,andP4). In this committee P1 has twice as many votes as P2;...Problem 10E:
A committee has six members (P1,P2,P3,P4,P5,andP6). In this committee P1 has twice as many votes as...Problem 11E:
Consider the weighted voting system [q:7,5,3]. a. What is the weight of the coalition formed by P1...Problem 12E:
Consider the weighted voting system [q:10,8,6,4,2]. a. What is the weight of the coalition formed by...Problem 13E:
Find the Banzhaf power distribution of a weighted voting system with four players in which the...Problem 14E:
Find the Banzhaf power distribution of a weighted voting system with five players in which the...Problem 15E:
Consider the weighted voting system [10:6,5,4,2]. a.Which players are critical in the winning...Problem 16E:
Consider the weighted voting system [5:3,2,1,1]. a.Which players are critical in the winning...Problem 17E:
a.Find the Banzhaf power distribution of this weighted voting system [6:5,2,1]. b.Find the Banzhaf...Problem 18E:
a. Find the Banzhaf power distribution of the weighted voting system [7:5,2,1]. b. Find the Banzhaf...Problem 19E:
Consider the weighted voting system [q:5,4,3,2,1]. Find the Banzaf power distribution of this...Problem 20E:
Consider the weighted voting system [q:8,4,2,1]. Find the Banzaf power distribution of this weighted...Problem 22E:
In a weighted voting system with four players the winning coalitions are: {P1,P2}, {P1,P2,P3},...Problem 23E:
The Nassau County N.Y. Board of Supervisors 1960s version. In the 1960s, the voting in the Nassau...Problem 24E:
The Nassau County N.Y. Board of Supervisors 1960s version. In the 1960s, the voting in the Nassau...Problem 25E:
A law firm is run by four partners (A,B,C,andD). Each partner has one vote and decisions are made by...Problem 26E:
A law firm is run by four partners (A,B,C,andD). Each partner has one vote and decisions are made by...Problem 27E:
Table 2-13 shows the 24 sequential coalitions with pivotal players underlined in a weighted voting...Problem 28E:
Table 2-14 shows the 24 sequential coalitions with pivotal players underlined in a weighted voting...Problem 29E:
Consider the weighted voting system [16:9,8,7]. a. Write down all the sequential coalitions, and in...Problem 30E:
Consider the weighted voting system [8:7,6,2]. a. Write down all the sequential coalitions, and in...Problem 31E:
Find the Shapley-Shubik power distribution of each of the following weighted voting systems. a....Problem 32E:
Find the Shapley-Shubik power distribution of each of the following weighted voting systems....Problem 33E:
Find the Shapley-Shubik power distribution of each of the following weighted voting systems....Problem 34E:
Find the Shapley-Shubik power distribution of each of the following weighted voting systems....Problem 35E:
In a weighted voting system with three players the winning coalitions are: {P1,P2}, {P1,P3}, and...Problem 36E:
In a weighted voting system with three players the winning coalitions are: {P1,P2}, and {P1,P2,P3}....Problem 37E:
Table 2-15 shows the 24 sequential coalitions in a weighted voting system with four players. In some...Problem 38E:
Table 2-16 shows the 24 sequential coalitions in a weighted voting system with four players. In some...Problem 39E:
Let A be a set with 10 elements. a. Find the number of subsets of A. b. Find the number of subsets...Problem 41E:
For a weighted voting system with 10 players. a. Find the total number of coalitions. b. Find the...Problem 42E:
Consider a weighted voting system with 12 players. a. Find the total number of coalitions in this...Problem 43E:
Consider a weighted voting system with six players P1 through P6. a. Find the total number of...Problem 44E:
Consider a weighted voting system with five players P1 through P5. a. Find the total number of...Problem 45E:
Use a calculator to compute each of the following. a. 13! b. 18! c. 25! d. Suppose that you have a...Problem 49E:
The purpose of Exercises 49 and 50 is for you to learn how to numerically manipulate factorials. If...Problem 50E:
The purpose of Exercises 49 and 50 is for you to learn how to numerically manipulate factorials. If...Problem 51E:
Consider a weighted voting system with seven players (P1throughP7). a. Find the number of sequential...Problem 52E:
Consider a weighted voting system with seven players (P1throughP6). a. Find the number of sequential...Problem 53E:
A law firm has seven partners: a senior partner (P1) with 6 votes and six junior partners...Problem 54E:
A law firm has six partners: a senior partner (P1) with 5 votes and five junior partners...Problem 57E:
Consider the weighted voting system [q:8,4,1]. a. What are the possible values of q? b. Which values...Problem 58E:
Consider the weighted voting system [9:w,5,2,1]. a. What are the possible values of w? b. Which...Problem 59E:
Equivalent voting systems. Two weighted voting systems are equivalent if they have the same number...Problem 60E:
Veto power. A player P with weight w is said to have veto power if and only if wq, and Vwq Where V...Problem 61E:
Consider the generic weighted voting system [q:w1,w2,...,wN]. Assume w1w2...wN. a. Find all the...Problem 64E:
The weighted voting system [27:10,8,6,4,2] represents a partnership among five people P1, P2, P3, P4...Problem 66E:
Mergers. Sometimes in a weighted voting system two or more players decide to merge-that is to say,...Problem 67E:
a.Verify that the weighted voting systems [12:7,4,3,2] and [24:14,8,6,4] result in exactly the same...Problem 78E:
Suppose that in a weighted voting system there is a player A who hates another player P so much that...Browse All Chapters of This Textbook
Chapter 1 - The Mathematics Of Elections The Paradoxes Of DemocracyChapter 2 - The Mathematics Of Power Weighted VotingChapter 3 - The Mathematics Of Sharing Fair-division GamesChapter 4 - The Mathematics Of Apportionment Making The RoundsChapter 5 - The Mathematics Of Getting Around Euler Paths And CircuitsChapter 6 - The Mathematics Of Touring Traveling Salesman ProblemsChapter 7 - The Mathematics Of Networks The Cost Of Being ConnectedChapter 8 - The Mathematics Of Scheduling Chasing The Critical PathChapter 9 - Population Growth Models There Is Strength In NumbersChapter 10 - Financial Mathematics Money Matters
Chapter 11 - The Mathematics Of Symmetry Beyond ReflectionChapter 12 - Fractal Geometry The Kinky Nature Of NatureChapter 13 - Fibonacci Numbers And The Golden Ratio Tales Of Rabbits And GnomonsChapter 14 - Censuses, Surveys, Polls, And Studies The Joys Of Collecting DataChapter 15 - Graphs, Charts And Numbers The Data Show And TellChapter 16 - Probabilities, Odds, And Expectations Measuring Uncertainty And RiskChapter 17 - The Mathematics Of Normality The Call Of The Bell
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