Explanation Given: A partnership has four partners ( P 1 , P 2 , P 3 , and P 4 ) . In this partnership P 1 has twice as many votes as P 2 , P 2 , has twice as many votes a P 3 ; P 3 has twice as many votes as P 4 . The quota is a simple majority of the votes. Approach: A given number of votes are controlled by each player in a formal voting arrangement, it is said to be weighted voting system. A player is a dictator if and only if the player’s weight is bigger than or equal to the quota. Calculation: Let the votes be represented as x then the number of votes P 4 has is x and P 3 has twice as many votes as P 4 . The number of votes P 3 has, P 3 = 2 × P 4 = 2 x The number of votes P 3 has is 2 x . Number of votes for P 2 is twice as many votes as P 3 , P 2 = 2 × P 3 = 2 × 2 x = 4 x The number of votes P 2 has is 4 x . Number of votes for P 1 is twice as many votes as P 2 , P 1 = 2 × P 2 = 2 × 4 x = 8 x The number of votes P 1 has is 8 x

Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

9th Edition

ISBN: 9780136208754

Author: Tannenbaum, Peter

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 2, Problem 71E

To determine

To show:

The player P1 is always a dictator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 70E

Chapter 2, Problem 72E

Students have asked these similar questions

24.4. For the function g(z) defined in (18.7), show that g(z) = j=0 z2j (−1)³ (2j+1)!" Hence, deduce that the function g(z) is entire. 2 E C.

Can you solve question 3,4,5 and 6 for this question

water at a rate of 2 m³/min. of the water height in this tank? 16) A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area). 17) A farmer wishes to

Chapter 2 Solutions

Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The player P 1 is always a dictator.

Solution Summary: The author explains that the player P_1 is always a dictator.

Concept explainers

Videos

To show:

The player P1 is always a dictator.

Want to see the full answer?

Chapter 2 Solutions

The player P 1 is always a dictator.

Solution Summary: The author explains that the player P_1 is always a dictator.

Concept explainers

Videos

To show: The player P1 is always a dictator.

Want to see the full answer?

Chapter 2 Solutions

To show:

The player P1 is always a dictator.