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? $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 8 & \mathrm{a}>\mathrm{b}>\mathrm{c}>\mathrm{d} \\ 7 & \mathrm{~b}>\mathrm{c}>\mathrm{d}>\mathrm{a} \\ 4 & \mathrm{~b}>\mathrm{d}>\mathrm{c}>\mathrm{a} \\ 10 & \mathrm{a}>\mathrm{b}>\mathrm{d}>\mathrm{c} \\ 8 & \mathrm{a}>\mathrm{c}>\mathrm{d}>\mathrm{b} \\ 6 & \mathrm{c}>\mathrm{b}>\mathrm{d}>\mathrm{a} \\ 8 & \mathrm{~b}>\mathrm{d}>\mathrm{a}>\mathrm{c} \end{array}$

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

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

A) $a _ { X }$ B) $\mathrm { e }$ C) $n$ D) $a _ { y }$ A) $a _ { X }$ B) $\mathrm { e }$ C) $n$ D) $a _ { y }$ B

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: $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 5 & \mathrm{~A}>\mathrm{H}>\mathrm{F}>\mathrm{S} \\ 7 & \mathrm{H}>\mathrm{S}>\mathrm{A}>\mathrm{F} \\ 4 & \mathrm{~F}>\mathrm{S}>\mathrm{H}>\mathrm{A} \\ 7 & \mathrm{~A}>\mathrm{F}>\mathrm{H}>\mathrm{S} \\ 5 & \mathrm{~A}>\mathrm{H}>\mathrm{S}>\mathrm{F} \\ 6 & \mathrm{H}>\mathrm{F}>\mathrm{S}>\mathrm{A} \\ 8 & \mathrm{~F}>\mathrm{A}>\mathrm{S}>\mathrm{H} \end{array}$ Use the Borda method to determine the winner of a preliminary nonbinding election based on the above voter profile. Suppose that after the preliminary election, the eight voters who voted $F > A > S > H$, in that order, change their votes to $\mathrm { A } > \mathrm { H } > \mathrm { F } > \mathrm { S }$. The official vote is then held. If the Borda Method is used to determine the winner, who is the winner and is the Monotonicity Criterion violated?

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

Solve the problem. -A small country consists of 7 provinces with the following populations: $\begin{array}{lccccccc} \hline \text { Province } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Population } & 25,312 & 19,734 & 33,407 & 29,591 & 13,288 & 22,751 & 31,992 \end{array}$ There are 300 federal judges to be apportioned according to the population of each province. Find the apportionment for province $G$ using Webster's method.

A) 54 B) 56 C) 55 D) 53 A) 54 B) 56 C) 55 D) 53

Write a voter profile for the voting situation. -Eight voters are asked to rank 4 brands of ice cream: A, B, C, and D. The eight voters turn in the following ballots showing their preferences in order: $\begin{array}{l|lllllllll} \text { Voter } & \# 1 & \# 2 & \# 3 & \# 4 & \# 5 & \# 6 & \# & \# 8 \\ \hline \text { 1st place } & \text { B } & \text { C } & \text { C } & \text { C } & \text { B } & \text { C } & \text { B } & \text { C } \\ \hline \text { 2nd place } & \text { C } & \text { A } & \text { D } & \text { D } & \text { C } & \text { D } & \text { A } & \text { A } \\ \hline \text { 3rd place } & \text { A } & \text { D } & \text { A } & \text { A } & \text { A } & \text { A } & \text { C } & \text { D } \\ \hline \text { 4th nlace } & \text { D } & \text { B } & \text { B } & \text { B } & \text { D } & \text { B } & \text { D } & \text { B } \end{array}$ Write a voter profile for these ballots.

A) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & \mathrm{~B}>\mathrm{A}>\mathrm{C}>\mathrm{D} \\ 2 & \mathrm{~B}>\mathrm{C}>\mathrm{A}>\mathrm{D} \\ 3 & \mathrm{C}>\mathrm{A}>\mathrm{D}>\mathrm{B} \\ 2 & \mathrm{C}>\mathrm{D}>\mathrm{A}>\mathrm{B} \end{array}$ B) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & B>A>C>D \\ 2 & B>C>A>D \\ 2 & C>B>D>A \\ 3 & C>D>A>B \end{array}$ C) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & \mathrm{~B}>\mathrm{A}>\mathrm{C}>\mathrm{D} \\ 2 & \mathrm{~B}>\mathrm{C}>\mathrm{A}>\mathrm{D} \\ 3 & \mathrm{C}>\mathrm{B}>\mathrm{D}>\mathrm{A} \\ 2 & \mathrm{C}>\mathrm{D}>\mathrm{A}>\mathrm{B} \end{array}$ D) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & B>A>C>D \\ 2 & B>C>A>D \\ 2 & C>A>D>B \\ 3 & C>D>A>B \end{array}$ A) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & \mathrm{~B}>\mathrm{A}>\mathrm{C}>\mathrm{D} \\ 2 & \mathrm{~B}>\mathrm{C}>\mathrm{A}>\mathrm{D} \\ 3 & \mathrm{C}>\mathrm{A}>\mathrm{D}>\mathrm{B} \\ 2 & \mathrm{C}>\mathrm{D}>\mathrm{A}>\mathrm{B} \end{array}$ B) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & B>A>C>D \\ 2 & B>C>A>D \\ 2 & C>B>D>A \\ 3 & C>D>A>B \end{array}$ C) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & \mathrm{~B}>\mathrm{A}>\mathrm{C}>\mathrm{D} \\ 2 & \mathrm{~B}>\mathrm{C}>\mathrm{A}>\mathrm{D} \\ 3 & \mathrm{C}>\mathrm{B}>\mathrm{D}>\mathrm{A} \\ 2 & \mathrm{C}>\mathrm{D}>\mathrm{A}>\mathrm{B} \end{array}$ D) $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 1 & B>A>C>D \\ 2 & B>C>A>D \\ 2 & C>A>D>B \\ 3 & C>D>A>B \end{array}$

Solve the problem. -A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. $\begin{array}{lccccccc} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Population } & 1283 & 2374 & 2725 & 2155 & 1592 & 2511 & 2017 \\ \hline \end{array}$ Find the apportionment for state $\mathrm { D }$ using Webster's method.

A) 26 B) 25 C) 23 D) 24 A) 26 B) 25 C) 23 D) 24

For the voter profile given below, who (or what) is selected if a second runoff election is held between the two candidates with the most first place votes? $\begin{array}{c|l} \text { Number of Voters } & \text { Ranking } \\ \hline 2 & \mathrm{c}>\mathrm{j}>\mathrm{t} \\ 3 & \mathrm{c}>\mathrm{t}>\mathrm{j} \\ 3 & \mathrm{j}>\mathrm{c}>\mathrm{t} \\ 1 & \mathrm{j}>\mathrm{t}>\mathrm{c} \\ 5 & \mathrm{t}>\mathrm{c}>\mathrm{j} \\ 1 & \mathrm{t}>\mathrm{j}>\mathrm{c} \end{array}$

A) $\mathrm { j }$ B) $c$ C) $\mathrm { t }$ A) $\mathrm { j }$ B) $c$ C) $\mathrm { t }$

Write a voter profile for the voting situation. -Ten voters are asked to rank 3 brands of shoes: A, B, and C. The ten voters turn in the following ballots showing their preferences in order: $\begin{array}{l|lllllllllll} \text { Voter } & \# 1 & \# 2 & \# 3 & \# 4 & \# 5 & & \# 6 & \# 7 & \# 8 & \# 9 & \# 10 \\ \hline \text { 1st place } & \mathrm{C} & \mathrm{B} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{C} & \mathrm{B} \\ \hline \text { 2nd place } & \mathrm{B} & \mathrm{C} & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{B} & \mathrm{C} \\ \hline \text { 3rd place } & \mathrm{A} & \mathrm{A} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{C} & \mathrm{A} & \mathrm{A} & \mathrm{A} & \mathrm{A} \end{array}$ Write a voter profile for these ballots.

A) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 3 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{B}>\mathrm{A} \\ 1 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ B) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 4 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ C) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 3 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 3 & \mathrm{C}>\mathrm{B}>\mathrm{A} \\ 2 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ D) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 4 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{B}>\mathrm{A} \end{array}$ A) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 3 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{B}>\mathrm{A} \\ 1 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ B) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 4 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ C) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 3 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 3 & \mathrm{C}>\mathrm{B}>\mathrm{A} \\ 2 & \mathrm{C}>\mathrm{A}>\mathrm{B} \end{array}$ D) $\begin{array}{c|l} \text { Number of Votes } & \text { Ranking } \\ \hline 2 & \mathrm{~B}>\mathrm{A}>\mathrm{C} \\ 4 & \mathrm{~B}>\mathrm{C}>\mathrm{A} \\ 4 & \mathrm{C}>\mathrm{B}>\mathrm{A} \end{array}$

A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. \[\begin{array} { l c c c c c c c } \hline \text { State } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } \\ \hline \text { Population } & 1283 & 2374 & 2725 & 2155 & 1592 & 2511 & 2017 \end{array}\] Find the apportionment for state D using Adams' method.

A) 26 B) 25 C) 23 D) 24 A) 26 B) 25 C) 23 D) 24

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Plurality Method. Does the Plurality Method violate the Condorcet Criterion for the voter profile? $\begin{array}{c|c} \text { Number of Voters } & \text { Ranking } \\ \hline 15 & \mathrm{~b}>\mathrm{a}>\mathrm{c}>\mathrm{d} \\ 11 & \mathrm{c}>\mathrm{a}>\mathrm{d}>\mathrm{b} \\ 9 & \mathrm{~d}>\mathrm{c}>\mathrm{a}>\mathrm{b} \\ 5 & \mathrm{a}>\mathrm{d}>\mathrm{c}>\mathrm{b} \\ 1 & \mathrm{c}>\mathrm{d}>\mathrm{a}>\mathrm{b} \end{array}$

A) c, c; no B) b, b; no C) c, b; yes D) b, c; yes A) c, c; no B) b, b; no C) c, b; yes D) b, c; yes

Exam 16: Voting and Apportionment

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 8 >>> 7 >>> 4 >>> 10 >>> 8 >>> 6 >>> 8 >>>

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

B

Suppose a legislative assembly is considering a new bill ( $\mathrm { n }$ ) to replace existing law (e), and two amendments $\left( \mathrm { a } _ { \mathrm { x } } , \mathrm { a } _ { \mathrm { y } } \right)$ 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 $\mathrm { a } _ { \mathrm { X } }$ is proposed and then Amendment $\mathrm { a } _ { \mathrm { y } }$ , the order of the sequential pairwise comparisons needed to determine the legislative outcome is $n , a _ { x } , a _ { y } , e$ . What is the choice of the representatives in this case?

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

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 Voters Ranking 5 >>> 7 >>> 4 >>> 7 >>> 5 >>> 6 >>> 8 >>> Use the Borda method to determine the winner of a preliminary nonbinding election based on the above voter profile. Suppose that after the preliminary election, the eight voters who voted $F > A > S > H$ , in that order, change their votes to $\mathrm { A } > \mathrm { H } > \mathrm { F } > \mathrm { S }$ . The official vote is then held. If the Borda Method is used to determine the winner, who is the winner and is the Monotonicity Criterion violated?

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

A

Solve the problem. -A small country consists of 7 provinces with the following populations: Province A B C D E F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 300 federal judges to be apportioned according to the population of each province. Find the apportionment for province $G$ using Webster's method.

(Multiple Choice)

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Question 4

Write a voter profile for the voting situation. -Eight voters are asked to rank 4 brands of ice cream: A, B, C, and D. The eight voters turn in the following ballots showing their preferences in order: Voter \#1 \#2 \#3 \#4 \#5 \#6 \# \#8 1st place B C C C B C B C 2nd place C A D D C D A A 3rd place A D A A A A C D 4th nlace D B B B D B D B Write a voter profile for these ballots.

(Multiple Choice)

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Question 5

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 Hamilton 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 6

Solve the problem. -A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. State A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state $\mathrm { D }$ using Webster's method.

(Multiple Choice)

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Question 7

For the voter profile given below, who (or what) is selected if a second runoff election is held between the two candidates with the most first place votes? Number of Voters Ranking 2 >> 3 >> 3 >> 1 >> 5 >> 1 >>

(Multiple Choice)

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Question 8

The preference table shows the results of an election among three candidates, A, B, and C. Number of Voters Ranking 10 >> 4 >> 2 >> (a)Using the plurality method, who is the winner? (b)The voters in the two columns on the right move their last-place candidates from last place to First place. Construct a new preference table for the election. Using the table and the plurality Method, who is the winner? (c)Suppose that candidate C drops out of the new table, but the winner is still chosen by the Plurality method. Is the irrelevant alternatives criterion satisfied?

(Multiple Choice)

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Question 9

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 (in thousands), then one of the states loses a seat to another if The number of seats being apportioned is 13. State Initial Population 930 738 415 Revised Population 975 752 422 Which state loses a seat to which state, and does the Population Paradox occur?

(Multiple Choice)

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Question 10

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 Webster Method to apportion the computers. School a b c d e Population 210 165 160 175 190

(Multiple Choice)

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Question 11

Write a voter profile for the voting situation. -Ten voters are asked to rank 3 brands of shoes: A, B, and C. The ten voters turn in the following ballots showing their preferences in order: Voter \#1 \#2 \#3 \#4 \#5 \#6 \#7 \#8 \#9 \#10 1st place 2nd place 3rd place Write a voter profile for these ballots.

(Multiple Choice)

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Question 12

A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. State Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Adams' method.

(Multiple Choice)

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Question 13

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Plurality Method. Does the Plurality Method violate the Condorcet Criterion for the voter profile? Number of Voters Ranking 15 >>> 11 >>> 9 >>> 5 >>> 1 >>>

(Multiple Choice)

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Question 14

State Population 131 140 304 178 197 -If the Hamilton Method is used to apportion legislative seats to two original states and a new state with the populations given in the table (in thousands), then one of the states loses a seat to another If the original number of seats being apportioned is 100. State Original State a Original State b New State c Population 2145 7855 625 Which state loses a seat to which state, and does the New States paradox occur?

(Multiple Choice)

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Question 15

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 (in thousands), then one of the states loses a seat to another if The number of seats being apportioned is 11. State a b c Initial Population 55 125 190 Revised Population 61 148 215 Which state loses a seat to which state, and does the Population Paradox occur?

(Multiple Choice)

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Question 16

Find the Hill-Huntington cutoff point for rounding up a modified quota of 14.465.

(Multiple Choice)

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Question 17

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

(Multiple Choice)

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Question 18

If there are $\mathrm { n } = 6$ candidates, how many different rankings of the candidates are there?

(Multiple Choice)

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Question 19

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. School Population 210 165 160 175 190 Use the Adams Method to apportion the computers.

(Multiple Choice)

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Question 20

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 8 >>> 7 >>> 4 >>> 10 >>> 8 >>> 6 >>> 8 >>>

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 Hamilton Method to apportion the seats. State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

For the voter profile given below, who (or what) is selected if a second runoff election is held between the two candidates with the most first place votes? Number of Voters Ranking 2 >> 3 >> 3 >> 1 >> 5 >> 1 >>

A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. State Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Adams' method.

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Plurality Method. Does the Plurality Method violate the Condorcet Criterion for the voter profile? Number of Voters Ranking 15 >>> 11 >>> 9 >>> 5 >>> 1 >>>

Find the Hill-Huntington cutoff point for rounding up a modified quota of 14.465.

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

If there are $\mathrm { n } = 6$ candidates, how many different rankings of the candidates are there?

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Exam 16: Voting and Apportionment

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 8 >>> 7 >>> 4 >>> 10 >>> 8 >>> 6 >>> 8 >>>

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 Hamilton Method to apportion the seats. State a b c d e Population 912,000 1,117,000 4,537,000 739,000 695,000

For the voter profile given below, who (or what) is selected if a second runoff election is held between the two candidates with the most first place votes? Number of Voters Ranking 2 >> 3 >> 3 >> 1 >> 5 >> 1 >>

A small country consists of seven states; there are 160 seats in the legislature that need to be apportioned among the seven states; and the population of each state is shown in the table. State Population 1283 2374 2725 2155 1592 2511 2017 Find the apportionment for state D using Adams' method.

Given the following voter profile, determine which candidate (if any)is a Condorcet Candidate and who will be selected using the Plurality Method. Does the Plurality Method violate the Condorcet Criterion for the voter profile? Number of Voters Ranking 15 >>> 11 >>> 9 >>> 5 >>> 1 >>>

Find the Hill-Huntington cutoff point for rounding up a modified quota of 14.465.

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

If there are n=6\mathrm { n } = 6n=6 candidates, how many different rankings of the candidates are there?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Filters

If there are $\mathrm { n } = 6$ candidates, how many different rankings of the candidates are there?