Solve the problem. -Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to The following voter profile. $\begin{array} { c | l } \text { Number of Votes } & \text { Ranking } \\ \hline 5 & \mathrm {~A} > \mathrm { H } > \mathrm { F } > \mathrm { S } \\ 7 & \mathrm { H } > \mathrm { S } > \mathrm { A } > \mathrm { F } \\ 4 & \mathrm {~F} > \mathrm { S } > \mathrm { H } > \mathrm { A } \\ 7 & \mathrm {~A} > \mathrm { F } > \mathrm { S } > \mathrm { H } \\ 5 & \mathrm {~A} > \mathrm { H } > \mathrm { S } > \mathrm { F } \\ 6 & \mathrm { H } > \mathrm { F } > \mathrm { S } > \mathrm { A } \\ 8 & \mathrm {~F} > \mathrm { S } > \mathrm { A } > \mathrm { H } \end{array}$ Determine the winner using the plurality method and state whether the winner received a majority Of votes.

A) Hawaii; no B) Alaska; no C) Hawaii; yes D) Alaska; yes A) Hawaii; no B) Alaska; no C) Hawaii; yes D) Alaska; yes

A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use the Adams Method to apportion the seats. $\begin{array}{l|ccccc} \text { State } & \mathrm{a} & \mathrm{b} & \mathrm{c} & \mathrm{d} & \mathrm{e} \\ \hline \text { Population } & 912,000 & 1,117,000 & 4,537,000 & 739,000 & 695,000 \end{array}$

A) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 29 & 35 & 141 & 23 & 21 \end{array}$ B) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 28 & 35 & 143 & 23 & 21 \end{array}$ C) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 28 & 35 & 142 & 23 & 22 \end{array}$ D) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 29 & 35 & 141 & 23 & 22 \end{array}$ A) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 29 & 35 & 141 & 23 & 21 \end{array}$ B) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 28 & 35 & 143 & 23 & 21 \end{array}$ C) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 28 & 35 & 142 & 23 & 22 \end{array}$ D) $\begin{array}{l|ccccc} \text { State } & \text { a } & \text { b } & \text { c } & \text { d } & \text { e } \\ \hline \text { Number of Representatives } & 29 & 35 & 141 & 23 & 22 \end{array}$

Solve the problem. -Four members are running for president of the Greater New Orleans Stamp Club: Andy (a), Brett (b), Carol (c), and Denise (d). The voter profile is summarized in the table. $\begin{array} { c | l } \text { Number of Voters } & \text { Ranking } \\ \hline 15 & b > a > c > d \\ 11 & c > a > d > b \\ 9 & d > c > a > b \\ 5 & a > d > c > b \\ 1 & c > d > a > b \end{array}$ Use the Borda Method to determine the winner.

A) Denise B) Brett C) Carol D) Andy A) Denise B) Brett C) Carol D) Andy

Given the following voter profile, determine who has the majority of first place votes and then use the Borda Method to determine the outcome. Does the Borda method violate the majority criterion For the voter profile? $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 28 & \mathrm{~b}>\mathrm{a}>\mathrm{c}>\mathrm{d} \\ 11 & \mathrm{c}>\mathrm{a}>\mathrm{d}>\mathrm{b} \\ 9 & \mathrm{~d}>\mathrm{c}>\mathrm{a}>\mathrm{b} \\ 5 & \mathrm{a}>\mathrm{d}>\mathrm{c}>\mathrm{b} \\ 1 & \mathrm{c}>\mathrm{d}>\mathrm{a}>\mathrm{b} \end{array}$

A) b, a; yes B) $a$, a; no C) a, b;yes D) b, b; no A) b, a; yes B) $a$, a; no C) a, b;yes D) b, b; no

A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table. \[\begin{array} { l c c c c c c c c } \hline \text { Precinct } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Population } & 2115 & 3659 & 3117 & 1883 & 4912 & 4027 & 2776 & 3174 \\ \hline \end{array}\] Find the apportionment for the Seventh Precinct using Adams' method.

A) 7 B) 6 C) 5 D) 4 A) 7 B) 6 C) 5 D) 4

Suppose a legislative assembly is considering a new bill ( $\mathrm { n }$ ) to replace existing law (e), and two amendments $\left( a _ { x } , a _ { y } \right)$ are considered. The results of all pairwise comparisons are given in the table. $\begin{array}{c|c} \text { Pair } & \text { How Representatives Rank the Pair } \\ \hline \mathrm{n} \text { and } \mathrm{a}_{\mathrm{x}} & \mathrm{a}_{\mathrm{x}}>\mathrm{n} \\ \mathrm{n} \text { and } \mathrm{a}_{\mathrm{y}} & \mathrm{n}>\mathrm{a}_{\mathrm{y}} \\ \mathrm{n} \text { and } \mathrm{e} & \mathrm{n}>\mathrm{e} \\ \mathrm{a}_{\mathrm{X}} \text { and } \mathrm{a}_{\mathrm{y}} & \mathrm{a}_{\mathrm{y}}>\mathrm{a}_{\mathrm{x}} \\ \mathrm{a}_{\mathrm{x}} \text { and } \mathrm{e} & \mathrm{a}_{\mathrm{x}}>\mathrm{e} \\ \mathrm{a}_{\mathrm{y}} \text { and } \mathrm{e} & \mathrm{e}>\mathrm{a}_{\mathrm{y}} \end{array}$ If Amendment $\mathrm { a } _ { \mathrm { y } }$ is proposed and then Amendment $\mathrm { a } _ { \mathrm { x } }$, the order of the sequential pairwise comparisons needed to determine the legislative outcome is $n , a _ { y } , a _ { x } , e$. What is the choice of the representatives in this case?

A) $n$ B) $a _ { x }$ C) $a _ { y }$ D) e A) $n$ B) $a _ { x }$ C) $a _ { y }$ D) e

Exam 16: Voting and Apportionment

State Population 912,000 1,117,000 4,537,000 739,000 695,000 -Create a population profile for 5 states with a total population of 950 for which the Hamilton Method, Jefferson Method, and Webster Method apportionments of 16 legislative seats are all different.

(Essay)

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Question 81

Construct a voter profile of 41 voters and 5 candidates where the Majority Candidate wins 4 pairwise comparison points and another candidate wins 3 pairwise points.

(Essay)

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Question 82

Solve the problem. -Computer Specialists is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to The following voter profile. Number of Votes Ranking 5 >>> 7 >>> 4 >>> 7 >>> 5 >>> 6 >>> 8 >>> Determine the winner using the plurality method and state whether the winner received a majority Of votes.

(Multiple Choice)

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Question 83

A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use the Adams Method to apportion the seats. State Population 912,000 1,117,000 4,537,000 739,000 695,000

(Multiple Choice)

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Question 84

State Population 131 140 304 178 197 -If the Hamilton Method is used to apportion legislative seats to three states with the initial and revised populations given in the table, then one of the states loses a seat to another if the number of Seats being apportioned is 100. State Initial Population 7,557 20,545 71,898 Revised Population 7,652 20,710 71,898 Which state loses a seat to which state, and does the Population Paradox occur?

(Multiple Choice)

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Question 85

Solve the problem. -A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use the Jefferson Method to apportion the seats. State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

(Multiple Choice)

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Question 86

Find the quantity requested. Round to the nearest whole number. -A total of 280 seats were apportioned to 43 states in a certain country which has a total population of 24,853,749. Find the average number of seats assigned per state.

(Multiple Choice)

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Question 87

State Population 131 140 304 178 197 -If the Hamilton Method is used to apportion legislative seats to five states with the populations given in the table, then the Alabama Paradox occurs when the number of seats being apportioned Increases from 126 to 127. State Population 263 808 931 781 676 In which state does the paradox show up?

(Multiple Choice)

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Question 88

Solve the problem. -Four members are running for president of the Greater New Orleans Stamp Club: Andy (a), Brett (b), Carol (c), and Denise (d). The voter profile is summarized in the table. Number of Voters Ranking 15 b>a>c>d 11 c>a>d>b 9 d>c>a>b 5 a>d>c>b 1 c>d>a>b Use the Borda Method to determine the winner.

(Multiple Choice)

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Question 89

State Population 131 140 304 178 197 -If the Jefferson Method is used to apportion 200 legislative seats to four states with the populations given in the table, then a violation of the Quota Rule occurs. State a b c d e Population 4590 1515 2015 1120 1110 The apportionment for which state violates the Quota Rule?

(Multiple Choice)

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Question 90

Given the following voter profile, determine who has the majority of first place votes and then use the Borda Method to determine the outcome. Does the Borda method violate the majority criterion For the voter profile? Number of Voters Ranking 28 >>> 11 >>> 9 >>> 5 >>> 1 >>>

(Multiple Choice)

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Question 91

A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table. Precinct 1 2 3 4 5 6 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the apportionment for the Seventh Precinct using Adams' method.

(Multiple Choice)

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Question 92

In the following voter profile, use the Hare Method to determine the winner. If candidate d drops out, and a second election is held, who is the winner if the Hare Method is again used? Does the Hare Method violate the Independence of Irrelevant Alternatives Criterion in this election process?

(Multiple Choice)

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Question 93

Suppose a legislative assembly is considering a new bill ( $\mathrm { n }$ ) to replace existing law (e), and two amendments $\left( a _ { x } , a _ { y } \right)$ are considered. The results of all pairwise comparisons are given in the table. Pair How Representatives Rank the Pair and > and > and > and > and > and > If Amendment $\mathrm { a } _ { \mathrm { y } }$ is proposed and then Amendment $\mathrm { a } _ { \mathrm { x } }$ , the order of the sequential pairwise comparisons needed to determine the legislative outcome is $n , a _ { y } , a _ { x } , e$ . What is the choice of the representatives in this case?

(Multiple Choice)

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Question 94

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Hare Method. Does the Hare Method violate the Condorcet criterion For the voter profile? Number of Voters Ranking 7 a>b>c 10 b>a>c 4 a>c>b 8 c>b>a

(Multiple Choice)

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Question 95

Twenty-five voters are using the Borda method to select one of five candidates: a, b, c, d, or e. If Candidate a receives 32 Borda points, Candidate b receives 58 Borda points, Candidate c receives 46 Borda points, and Candidate d receives 55 Borda points, how many Borda points does Candidate e Receive? Who wins the Borda election?

(Multiple Choice)

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Question 96

Which fairness criterion may be violated by any of the voting methods?

(Multiple Choice)

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Question 97

Solve the problem. -West End school district is purchasing 50 new computers to be distributed among the five schools in the district. The computers will be apportioned based on the school population of each school as Given in the table below. Use the Jefferson Method to apportion the computers. School a b c d e Population 210 165 160 175 190

(Multiple Choice)

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Question 98

How many different pairwise comparisons are needed to learn the outcome of an election involving n = 5 candidates?

(Multiple Choice)

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Question 99

State Population 912,000 1,117,000 4,537,000 739,000 695,000 -Create a population profile for 5 states with a total population of 950 for which the Hamilton Method, Jefferson Method, and Webster Method apportionments of 16 legislative seats are all different.

Construct a voter profile of 41 voters and 5 candidates where the Majority Candidate wins 4 pairwise comparison points and another candidate wins 3 pairwise points.

A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use the Adams Method to apportion the seats. State Population 912,000 1,117,000 4,537,000 739,000 695,000

Solve the problem. -A country has five states with populations as given in the table below and needs to apportion 250 seats in the legislature. Use the Jefferson Method to apportion the seats. State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

Find the quantity requested. Round to the nearest whole number. -A total of 280 seats were apportioned to 43 states in a certain country which has a total population of 24,853,749. Find the average number of seats assigned per state.

Given the following voter profile, determine who has the majority of first place votes and then use the Borda Method to determine the outcome. Does the Borda method violate the majority criterion For the voter profile? Number of Voters Ranking 28 >>> 11 >>> 9 >>> 5 >>> 1 >>>

In the following voter profile, use the Hare Method to determine the winner. If candidate d drops out, and a second election is held, who is the winner if the Hare Method is again used? Does the Hare Method violate the Independence of Irrelevant Alternatives Criterion in this election process?

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Hare Method. Does the Hare Method violate the Condorcet criterion For the voter profile? Number of Voters Ranking 7 a>b>c 10 b>a>c 4 a>c>b 8 c>b>a

Which fairness criterion may be violated by any of the voting methods?

How many different pairwise comparisons are needed to learn the outcome of an election involving n = 5 candidates?

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