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1. You have two buckets: a 4-gallon bucket and 7-gallon bucket. There are no other containers. You have an infinite supply of water. How would you measure out exactly 5 gallon of water? Please bring these 5 gallons in one of the buckets.

1. You have two buckets: a 4-gallon bucket and 7-gallon bucket. There are no other containers. You have an infinite supply of water. How would you measure out exactly 5 gallon of water? Please bring these 5 gallons in one of the buckets.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. You have two buckets: a 4-gallon bucket and a 7-gallon bucket. There are no other containers. You have an infinite supply of water. How would you measure out exactly 5 gallons of water? Please bring these 5 gallons in one of the buckets. 2. Consider the following preference schedule for an election: | Number of voters | 4 | 5 | 6 | 2 | |------------------|---|---|---|---| | 1st choice | A | B | C | A | | 2nd choice | D | C | A | C | | 3rd choice | B | A | D | D | | 4th choice | C | D | B | B | (a) How many people voted in this election? (b) How many votes are needed for majority? (c) Use the following methods to find the winner. If there is a tie, suggest a reasonable tie-breaking rule and find the winner. i. vote-for-two ii. plurality voting iii. Borda count iv. plurality-with-elimination v. Is there a Condorcet candidate in this election? vi. In this election, does plurality vote violate Condorcet fairness criterion? vii. Suppose that the preference schedule above refers to a straw poll. Now we hold an official election - and everyone votes the same except for the two voters in the last column: they switch their votes and move C ahead of A in their ballots. Use plurality-with-elimination to find the winner of the official poll. viii. Do the results of (iv) and (vii) imply violation of which fairness criterion. 3. Give an example where a candidate may be ranked first by majority of voters, and still lose the election. 4. State Arrow’s impossibility theorem. 5. Vasya buys a brown bear who will teach Vasya to dance. Bear costs 111 rubles, and Vasya ends up paying 121 rubles and 21 kopeks. Compute the sales tax for the bear. Note that there are 100 kopeks in a ruble. 6. Over the course of five days, price P of Hoohle stock did the following: - Monday: P went up by 2.5% - Tuesday: P went up by 12.5% - Wednesday: P went down
Transcribed Image Text:1. You have two buckets: a 4-gallon bucket and a 7-gallon bucket. There are no other containers. You have an infinite supply of water. How would you measure out exactly 5 gallons of water? Please bring these 5 gallons in one of the buckets. 2. Consider the following preference schedule for an election: | Number of voters | 4 | 5 | 6 | 2 | |------------------|---|---|---|---| | 1st choice | A | B | C | A | | 2nd choice | D | C | A | C | | 3rd choice | B | A | D | D | | 4th choice | C | D | B | B | (a) How many people voted in this election? (b) How many votes are needed for majority? (c) Use the following methods to find the winner. If there is a tie, suggest a reasonable tie-breaking rule and find the winner. i. vote-for-two ii. plurality voting iii. Borda count iv. plurality-with-elimination v. Is there a Condorcet candidate in this election? vi. In this election, does plurality vote violate Condorcet fairness criterion? vii. Suppose that the preference schedule above refers to a straw poll. Now we hold an official election - and everyone votes the same except for the two voters in the last column: they switch their votes and move C ahead of A in their ballots. Use plurality-with-elimination to find the winner of the official poll. viii. Do the results of (iv) and (vii) imply violation of which fairness criterion. 3. Give an example where a candidate may be ranked first by majority of voters, and still lose the election. 4. State Arrow’s impossibility theorem. 5. Vasya buys a brown bear who will teach Vasya to dance. Bear costs 111 rubles, and Vasya ends up paying 121 rubles and 21 kopeks. Compute the sales tax for the bear. Note that there are 100 kopeks in a ruble. 6. Over the course of five days, price P of Hoohle stock did the following: - Monday: P went up by 2.5% - Tuesday: P went up by 12.5% - Wednesday: P went down
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