Maths Quiz

Question 13 pts

An election consists of four candidates A, B, C, and D. The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.

Using the Borda Count Method, how many “points” does candidate B have from the following election? 

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Question 23 pts

An election consists of four candidates A, B, C, and D. The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.

Using the Borda Count Method, rank the contestants. 

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Question 33 pts

According to the preference schedule of the following table, who is ranked third using the plurality with Elimination Method? 

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Question 43 pts

According to the preference schedule shown below, how many 1st place votes does candidate C have? 

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Question 53 pts

According to the preference schedule shown below, who is the winner of the election using the Plurality Method? 

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Question 63 pts

According to the preference schedule shown below, how many points does candidate C have using the Borda Count Method? 

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Question 73 pts

According to the preference schedule shown below, who is the winner of the election using the Plurality with Elimination Method? 

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Question 83 pts

According to the preference schedule shown below: 

 When you use the Method of Pairwise Comparisons, how many “pairwise” comparisons do you have?

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Question 93 pts

According to the preference schedule shown below:

 When you use the Method of Pairwise Comparisons, who is the winner?

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Question 103 pts

An election is held among five candidates (A, B, C, D, and E). There are 37 votes. Using the Method of Pairwise Comparison it is found that A, B, and C each win one pairwise comparison while D wins four. If E wins the remaining comparisons in this election, then which statement is true?

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Question 113 pts

A violation of the Monotonicity Criterion occurs when

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Question 123 pts

A violation of the Independence of Irrelevant Alternatives Criterion occurs when

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Question 133 pts

An election is held among five candidates (A, B, C, D, and E). There are 37 votes. Using the Method of Pairwise Comparison it is found that A, B, and C each win one pairwise comparison; D wins four and E wins the remaining comparisons in this election. How many “pairwise” comparisons did A lose?

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Question 143 pts

Tim and his three friends Beth, Jane, and Sam pool their money to buy a pizza. Tim gives $4; Beth gives $3; while both Jane and Sam each give $2. If there are two choices for pizza and each person gets to vote proportionally to the amount of money he or she gave, then which weighted voting system models scenario if the quota is a simple majority of votes?

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Question 153 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5]. 

What's the weight of P2?

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Question 163 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5].

In a coalition of {P2, P3, P4, P6, P5, P1} find all the pivotal players.

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Question 173 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5].

In a coalition of {P2, P3, P4, P5}, find all the critical players.

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Question 183 pts

An election with four candidates (A, B, C, and D) and 200 voters will use the Plurality Method to choose a winner. How many first-place votes are needed for a majority?

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Question 193 pts

Consider the weighted voting system [11: 7, 5, 2, 1]. Which player(s), if any, have veto power?

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Question 203 pts

A committee consists of four members. How many different coalitions are possible?

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Question 213 pts

In a weighted voting system, when the quota is too small, it’s possible for both YES’s and NO’s to have enough votes to a certain issue. For example, [10: 8, 7, 3, 2], one can see a mathematical version of ________________________. Fill the blank.

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Question 223 pts

On the other hand, if the quota is too big, you can never have enough votes to pass a motion. For example, [22: 8, 7, 3, 2], one can see a ________________________. Fill the blank.

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Question 233 pts

In the weighted voting system [13: 10, 6, 5], consider a sequential coalition <P2, P3, P1>. Who is the pivotal player?

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Question 243 pts

Consider the weighted voting system [13: 10, 6, 5]. What is the Shapely-Shubik Power of P1?

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Question 253 pts

Consider the weighted voting system [20: 13, 11, 8].

In a coalition of {P1, P2, P3} who is the critical player(s)?

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Question 263 pts

Consider the weighted voting system [20: 13, 11, 8]. What is the Banzhaf Power of P3?

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Question 273 pts

If there are 16 teams to play in a tournament, where each team will play every other team once. Then how many matches will take place?

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Question 283 pts

Consider the weighted voting system [q: 6, 4, 2, 2]. 

Find the smallest value that the quota q can take.

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Question 293 pts

Consider the weighted voting system [q: 6, 4, 2, 2].

What is the largest value that the quota q can take?

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Question 303 pts

Consider the weighted voting system [q: 8, 6, 4]. Find the smallest value of q for which all three players have veto power.

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Question 313 pts

Consider the weighted voting system [q: 8, 6, 4]. Find the smallest value of q for which P2 has veto power but P3 does not.

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Question 323 pts

Consider the weighted voting system [18: 12, 10, 6].

Consider a sequential coalition {P1, P3, P2}. Who is the pivotal player?

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Question 334 pts

Consider the weighted voting system [18: 12, 10, 6].

What is the Shapley-Shubik Power of P3?