Exam 14: Voting and Apportionment

Determine whether the specified paradox occurs. -A country with two states has 75 seats in the legislature. The population of each state (in Thousands) is given by: State A B Total Population 3184 8475 11659 A third state is added with 2 additional seats as shown below. State A B C Total Population 3184 8475 330 11989 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

Find the apportionment asked for. -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 D using Adamsʹ method.

Find the standard divisor for the given situation. Round your answer to two decimals. -A small country consists of 7 provinces with the following populations: Province F G Population 25,312 19,734 33,407 29,591 13,288 22,751 31,992 There are 200 federal judges to be apportioned according to the population of each province.

Make a preference table for the given voting situation. -A condominium association is holding an election for president of the board of directors. Each Member ranks the candidates from first to third. The preference table below shows the results of The ballots with candidates Abbott(A), Blake (B), Cleary (C), and Downs (D). Number of Votes 3 7 5 8 7 4 6 6 4 First A B A A C B D C C Second C A B C D D B B A Third B C C D A A A D D Fourth D D D B B C C A B Determine the winner using the plurality method and if the winner received a majority of first Place votes.

Determine whether the specified paradox occurs. -A country with two states has 16 seats in the legislature. The population of each state is given by: State A B Total Population 86,342 77,312 163,654 A third state is added with 5 additional seats as shown below. State A B C Total Population 86,342 77,312 53,792 217,446 Does the new-states paradox occur using Hamiltonʹs method of apportionment?

Find the standard divisor for the given situation. Round your answer to two decimals. -The faculty senate of a university has 45 senators to be apportioned among its four colleges based On the number of faculty in each college. The colleges are Liberal Arts (L), Sciences (S), Business (B), and Engineering (E). The number of faculty in each college is shown in the following table. College L S B E Number of Faculty 279 355 312 423

Find the apportionment asked for. -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 Hamiltonʹs method.

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. -A condominium association is holding an election for president of the board of directors. Each Member ranks the candidates from first to third. The preference table below shows the results of The ballots with candidates Abbott(A), Blake (B), Cleary (C), and Downs (D). Determine the winner using the Borda count method and if the winner received a majority of first Place votes.

The Mathematics Department is holding an election for department chair. Each member ranks the Candidates from first to third. The preference table below shows the results of the ballots with Candidates Clark (C), Jones (J), and Smith (S). A second election is then held resulting in the following preference table: If the plurality with elimination method is used to determine the winner, is the montonicity Criterion satisfied?

Find the standard divisor for the given situation. Round your answer to two decimals. -A small country consists of seven states; there are 158 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

Make a preference table for the given 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: $\text { C B B C B B C B C B}$ $\text { B C A B C A B C B C }$ $\text { A A C A A C A A A A}$ Make a preference table for these ballots.

Solve the problem. -Which apportionment method may produce the Alabama paradox?

Find the standard divisor for the given situation. Round your answer to two decimals. -A school district receives a grant to purchase 55 new computers to be apportioned among the 6 Schools in the district based on the student population of each school. The student populations are Given in the following table. School A B C D E F Population 314 211 197 243 279 325 Find the modified quota for school B using the divisor 28.5.

Solve the problem. -Which fairness criterion is always satisfied by the plurality with elimination method?

Solve the problem. -Which apportionment method never violates the quota rule?

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. -The Mathematics Department is holding an election for department chair. Each member ranks the Candidates from first to third. The preference table below shows the results of the ballots with Candidates Clark (C), Jones (J), and Smith (S). Determine the winner using the plurality with elimination method and if the winner received a Majority of first place votes.

Find the standard divisor for the given situation. Round your answer to two decimals. -The faculty senate of a university has 40 senators to be apportioned among its four colleges based On the number of faculty in each college. The colleges are Liberal Arts (L), Sciences (S), Business (B), and Engineering (E). The number of faculty in each college is shown in the following table. College L S B E Number of Faculty 279 355312 423 Find the standard quota for the College of Sciences.

Find the standard divisor for the given situation. Round your answer to two decimals. -A school district receives a grant to purchase 66 new computers to be apportioned among the 6 Schools in the district based on the student population of each school. The student populations are Given in the following table. School A B C D E F Population 314 211 197 243 279 325

The Mathematics Department is holding an election for department chair. Each member ranks the Candidates from first to third. The preference table below shows the results of the ballots with Candidates Clark (C), Jones (J), and Smith (S). If the Borda count method is used to determine the winner, is the head-to-head criterion satisfied?

Solve the problem. -Which voting method always satisfies the head-to-head criterion?