-Assignment consists of two part (part A and part B) -Do not use chat GPT for this assignment as it is generally inaccurate for this type of math -ignore any current answers as they may be incorrect

Part A

Question 14 pts

Given the weighted voting system [18: 11, 9, 5], which players have veto power?

Group of answer choices

Player 1

Player 1 and Player 2

Player 1, Player 2 and Player 3

There are no players with veto power.

Flag question: Question 2

Question 24 pts

Consider the following weighted voting system [13: 7, 4, 3, 3, 2, 1], what is the weight of P3?

Group of answer choices

7

4

2

3

Flag question: Question 3

Question 34 pts

In the weighted voting system [32: 12, 8, 6, 5, 5, 4, 2], what is the minimum percentage of the votes needed to pass a motion?

Group of answer choices

66.6%

76.19%

54.76%

32%

Flag question: Question 4

Question 44 pts

Consider the weighted voting system [5: 3, 2, 1, 1], what is the weight of the coalition formed by P1 and P2?

Group of answer choices

5

3

7

4

Flag question: Question 5

Question 54 pts

A student organization at Penn State is voting to pass its budget. Susan has 6 votes as the President, Joe has 4 votes as the Vice-President, Carol has 2 votes as an assistant and Margo has 1 vote as a committee member. The quota is 9. How is the weighted voting system represented mathematically?

Group of answer choices

[6: 4, 3, 2, 1]

[9]

[9: 4, 3, 2]

[9: 6, 4, 2, 1]

Flag question: Question 6

Question 64 pts

Consider the weighted voting system [21: 9, 8, 5, 3, 2], what is the total number of votes?

Group of answer choices

26

27

21

28

Flag question: Question 7

Question 74 pts

Consider the weighted voting system [15: 10, 6, 5, 3] and the Banzhaf Power distribution. How many winning coalitions will there be?

Group of answer choices

5

7

6

8

Flag question: Question 8

Question 84 pts

What equation is used to find the number of sequential coalitions in a Banzhaf Power System?

Group of answer choices

n2 + 1

n – 1

n!

2n – 1

Flag question: Question 9

Question 94 pts

If a graph has 26 edges, then the sum of the degrees of all of the vertices is

Group of answer choices

13

26

52

cannot be determined.

Flag question: Question 10

Question 104 pts

How many odd vertices are in the following graph?

Group of answer choices

5

4

2

1

Flag question: Question 11

Question 114 pts

Complete the following sentence so that it is a correct statement.
If a graph has _______________ , then it does not have an Euler _______________.

Group of answer choices

no odd vertices; circuit

any odd vertices; path

any odd vertices; circuit

Flag question: Question 12

Question 124 pts

From the information given below, how many vertices have a degree of 2?

Group of answer choices

1

2

3

4

Flag question: Question 13

Question 134 pts

Jane wants to show her parents 5 key places on campus: HUB, Nittany Lion Shrine, her dorm, Beaver Stadium, and her favorite restaurant. Below is a graph model indicating where the places are and the paths that connect them. If Jane starts her tour at her dorm, where will she end her tour considering that she wants to travel on each path just once and visit each of the 5 places

Group of answer choices

Dorm

Lion Shrine

HUB

Restaurant

Question 144 pts

If a connected graph has 4 odd vertices and 2 even vertices , then the graph has

Group of answer choices

an Euler circuit.

an Euler path.

neither an Euler circuit nor an Euler path.

Flag question: Question 15

Question 154 pts

In regard to obtaining the best answer, the Brute Force Method is _____________ while the Nearest Neighbor Algorithm is ____________________.

Group of answer choices

optimal, approximate

optimal, inefficient

approximate, optimal

approximate, inefficient

Flag question: Question 16

Question 164 pts

What is the weight of the optimal Hamilton path in this graph, starting at A?

Group of answer choices

18

12

13

23

Flag question: Question 17

Question 174 pts

How many edges are there in a K20 graph?

Group of answer choices

190

200

20

10

Flag question: Question 18

Question 184 pts

Which one of the following can be a Hamilton Circuit?

Group of answer choices

A, B, C, D, A

A, B, C, D

A, B, D, C, B, A

A, B, D, C, B

Flag question: Question 19

Question 194 pts

An election is to be decided using the Borda Count Method. There are 4 candidates (A, B, C, D) and 45 voters. If candidate A receives 90 points, candidate B receives 114 points and candidate C receives 110 points, how many points does candidate D receive?

Group of answer choices

36

450

314

136

Flag question: Question 20

Question 204 pts

Given the following preference schedule, rank the candidates using the extended plurality method. The answers are arranged from first to last.

Group of answer choices

A, B, C, D

B, C, A, D

C, D, A, B

Question 214 pts

A group of people were asked to vote for their favorite person among the candidates Alice (A), Bob (B), Cassie (C) and Dave (D) and the results are shown in the preference schedule below.   Using the plurality-with-elimination method, the winner is

Group of answer choices

Alice

Bob

Cassie

Dave

Question 224 pts

Which method of voting violates the Independence-of-Irrelevant-Alternatives Fairness Criterion?

Group of answer choices

Plurality Method

Borda Count Method

Plurality-with-Elimination Method

Pairwise Comparison Method

All of the above.

Flag question: Question 23

Question 234 pts

If there are 28 teams left in a round robin tournament. How many total matches will be played?

Group of answer choices

351

378

406

385

Flag question: Question 24

Question 244 pts

Given the preference schedule below, find the winner of the election under the method of pairwise comparisons.

Group of answer choices

A

B

C

D

Question 254 pts

Four players (A, B, C, D) agree to divide a cake fairly. The table below shows how each player values each of the four slices that have been cut by the divider.
Assuming all players play honestly, which player was the divider?

Group of answer choices

A

B

C

D

Flag question: Question 26

Question 264 pts

Three partners (Divine, Chase, Chandra) are dividing a plot of land among themselves using the lone-divider method. Using a map, divider (Divine) divides the property into 3 parcels s1, s2 and s3. When the choosers' bid lists are opened, Chase's bid list is (s2, s3) and Chandra's bid list is (s1, s3). Describe a fair division where Divine's fair share is s2?

Group of answer choices

Divine: s2; Chase: s1; Chandra: s3.

Divine: s2; Chase: s3; Chandra: s1.

Divine: s1; Chase: s3; Chandra: s2.

Question 274 pts

Did the divider do a good job in the example below of dividing a pizza?

Group of answer choices

The Divider did a good job

The Divider did not do a good job

More information is needed

Flag question: Question 28

Question 284 pts

Julie buys a chocolate-vanilla mousse cake for $16.00. Julie values vanilla 3 times as much as she values chocolate. What is the value of the vanilla half of the cake to Julie?

Group of answer choices

$12.00

$9.00

$8.00

$4.00

Flag question: Question 29

Question 294 pts

In this table of four shares, which slice will player A, the divider, never get?

Group of answer choices

S1

S2

S3

Question 304 pts

Jack, Ned and Paul are dividing 3 items and their bids are given in the table below.

What is Jack's Fair Share?

Group of answer choices

$566

$583.33

$900

$1750

Flag question: Question 31

Question 314 pts

If Bob, Ann and Joe have a flower shop and decide to have just one person keep the business. 
Bob bids $240,000 for it, Ann bids $210,000 and Jane bids $225,000 for the shop. 
What is the final settlement?

Group of answer choices

Ann and Jane both get $75,000 and Bob gets the business.

Jane gets the business.

Ann gets the business and pays $210,000.

Bob gets the business and pays $155,000. Jane gets $80,000 and Ann gets $75,000.

Flag question: Question 32

Question 324 pts

Three players (Alex, Allan, Mike) must divide a cake among them. The table below shows the value of each piece to each of the players.

Which of the following is a fair division of the cake?

Group of answer choices

Alex: S1; Allan: S2; Mike: S3

Alex: S3; Allan: S2; Mike: S1

Alex: S1; Allan: S3; Mike: S2

Question 334 pts

There are 4 states and 140 seats in congress. The population for state A is 2,500, state B is 8,082, state C is 3,013 and state D is 4,550. Using Hamilton's Method, which state has the correct apportionment?

Group of answer choices

State A is 20

State B is 63

State C is 24

State D is 36

Flag question: Question 34

Question 344 pts

Imagine you are a fashion designer marketing your new clothing line of 250 items. You must decide the number of items to give each store based on their flow of customers per week. How many items will Gap receive? In other words, find the standard quota for Gap.

Group of answer choices

2

25

1/2

75

Question 354 pts

Rule: If the sum of the initial quotas is too high, then choose a modified divisor that is higher than the standard divisor. 
This rule is used for

Group of answer choices

Jefferson's Method

Adam's Method

Hamilton's Method

Flag question: Question 36

Question 364 pts

The total population of several states is 205,000 and there are 148 seats to be apportioned to the House of Representatives for those states. What would be the standard quota of a state with a population of 19,947?

Group of answer choices

1385.14

10.28

134.78

14.40

Question 374 pts

The university apportions sections of Level 001 language classes based on last semester's course enrollment. In Fall 2008, 90 students enrolled in Mandarin, 80 enrolled in Japanese, 50 enrolled in Arabic, 45 enrolled in Russian, and 35 enrolled in Korean. If there are 20 teachers to be apportioned, find the standard divisor for determining the number of teachers per language in Spring 2009:

Group of answer choices

15

20

25