Mathematics Worksheet


1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

Math 1007-13
Homework 1.
R. Robinson
Due 2/7/2022 by 11:59pm
Please be sure to put your name on your submission, type your answers, and upload in PDF form
5 problems, 4 points each, total 20 points
Problem 1. Consider an election with 37 voters and two candidates A and B. In all of the
questions below show your work and explain. (a) How many votes (least number) would A need
to win with the simple majority method? (b) If B is the status quo candidate and the method is
2/3 majority with status quo, what is the least number of votes A would need to win? (c) Same
question for B? (d) In a weighted voting system, with simple majority, where 5 voters get 3
votes, 10 voters get 2 votes and the rest get 1 vote each, and where there is no status quo, what
is the smallest number of voters who need to vote for B in order for B to be the unique winner?
Problem 2. Consider a weighted voting method with 5 voters assigned weights 17, 15, 14, 12,
and 7, respectively, with a simple majority of the weighted votes sufficient for victory. Explain
why this method is, in effect the (unweighted) simple majority method. (Comment: This is
V(33;17,15,14,12,7) in the terminology of Chapter 19).
Problem 3. A small country of uses an Electoral College system (bloc method in language of
Chapter 1) to elect its leader. The chart below shows the population of each province, and each
province’s number of electoral votes. A simple majority of electoral votes is needed to win.
Assume that everyone votes. What is the smallest number of voters who can elect the leader?
What percentage of the total vote is this?
Hint: This problem is similar to part (d) of problem 1. It is also related to the following
“famous” problem: Look at the number of votes each state has in the actual US electoral college
(you can use the “microvotes” spreadsheet posted with class 5. Assume that everybody in each
state votes (of course in reality, not everybody is eligible, and the turnout even among eligible
voters is typically 40% – 60%). Assume winner (of the popular election in each state) takes all its
electoral votes. What is the smallest number of voters necessary to elect a president? What
percentage of the total (population of the US) is this? I will post this problem as an extra credit
Problem 4. Compute the Banzhaf power for (a) V(13;9,7,5,3,1), (b) V(14;9,7,5,3,1), and (c)
V(24;9,7,5,3,1). Compare. I would recommend the method of Alan Taylor.
Problem 5. Consider a “country” with five states A, B, C, D, E that conducts presidential
elections by a system that works like the US Electoral College. The five states have populations
9, 7, 5, 3, and 1, respectively. Compute the probability that a typical voter in each state is a
critical voter in a winning coalition. This is BCPv(1), BCPv(3), BCPv(5), BCPv(7), BCPv(9) in the
terminology of Class 5. There are two ways to do this calculation: (i) an approximate way using
Problem 6. In this problem reconsider Electoral College in the five state country from Problem
4. Use the answer to V(13;9,7,5,3,1) from Problem 4 above to find BCPs(A), BCPs(B), BCPs(C),
BCPs(D), BCPs(E) in the terminology of Class 5. Then combine this with the numbers from
Problem 4 to estimate the Banzhaf power of a voter in each state.

Purchase answer to see full


status quo

Winning Combination

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.
Khadija P.
Khadija P.
I have been searching for a custom book report help services for a while, and finally, I found the best of the best.
Regina Smith
Regina Smith
So amazed at how quickly they did my work!! very happy♥.