1. Find the standard divisor (to two decimal places) for the given population and number of representative seats. Population 130,000 a. b. c. d. e. # seats 8 14,750.00 16,250.00 13,750.00 17,750.00 16,750.00 25 points Question 2 1. For the year 1840, find the standard quotas for the city districts given in table that shows the population (in thousands) over the years. Assume there are eight council seats. a . b . c . d . e . 25 points Question 3 1. Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding down for the standard quotas. 10 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 35,000 21,000 12,000 48,000 116,000 a. 10,600 b. 9,400 c. 10,900 d. 9,900 e. 9,600 25 points Question 4 1. Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding up for the standard quotas. 12 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 37,000 22,000 13,000 46,000 118,000 a. 12,733 b. 11,400 c. 11,200 d. 12,433 e. 11,700 estion 1 1. Find the standard divisor (to two decimal places) for the given population and number of representative seats. Population 135,000 a. b. c. d. e. # seats 10 15,000.00 12,000.00 13,500.00 14,000.00 11,000.00 25 points Question 2 1. For the year 1840, find the standard quotas for the city districts given in table that shows the population (in thousands) over the years. Assume there are eight council seats. a . b . c . d . e . 25 points Question 3 1. Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding down for the standard quotas. 10 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 35,000 22,000 15,000 46,000 118,000 a. 11,100 b. 11,400 c. 9,000 d. 9,200 e. 9,500 25 points Question 4 1. Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding up for the standard quotas. 12 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 36,000 21,000 14,000 49,000 120,000 a. 12,200 b. 12,349 c. 11,700 d. 11,900 e. 12,649 1. The Adobe School District is hiring a vice principal and has interviewed four candidates: Alicia (A), Ben (B), Carmelia (C), and Diana (D). The hiring committee has indicated their preferences. (ACDB) 8 (CBAD) 5 (BCDA) 1 (DBCA) 4 Determine who is the winner using the plurality method. Then suppose that Diana drops out of the running before the vote is taken. Do the results you obtain violate the irrelevant alternatives criterion? a . Ye s b No . 10 points Question 2 1. A focus group of 47 people for ABC TV were asked to rank the government spending priorities of education (E), military spending (M), health care (H), immigration (I), and lowering taxes (T). Here are the preferences: (IEHMT) 20 (TEIHM) 9 (HTIME) 9 (MTIEH) 9 Suppose that the losing issues of health care, military spending, and education are removed from the table. Now, who is the winner using the Borda count method? aI . bT . c No . winner. 10 points Question 3 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) 6 (CBA) 10 (BCA) 9 Who wins using the Borda count method? Does this violate the Condorcet criterion? a . Connie, Yes b Alice, Yes . c . Alice, No d Betty, . e Betty, . No Yes 10 points Question 4 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) 10 (ACB) 4 (CAB) 5 Who wins the election using the Hare method? Does this violate the Condorcet criterion? a Betty, No . b Alice, Yes . c Connie, . No d Betty, . Yes e Connie, . Yes 10 points Question 5 1. The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (CADB) 93 (CABD) 113 (DABC) 123 (BADC) 143 Who wins the election using the Hare method? Does this violate any of the fairness criteria? Dave. Yes. Condorcet criterion. b Carl. No. a . . c . Carl. Yes. Condorcet criterion. d Bate. No. . e . Bate. Yes. Condorcet criterion. 10 points Question 6 1. The Adobe School District is hiring a vice principal and has interviewed four candidates: Anna (A), Bono (B), Clark (C), and David (D). The hiring committee has indicated their preferences. (ACDB) 8 (CBAD) 1 (BCDA) 3 (DBCA) 6 Who is the winner using the plurality method? Answer A, B, C, or D. Suppose that Bono drops out of the running before the vote is taken. Who is the winner using the plurality method? Answer A, B, C, or D. Do the results of the previous questions violate the irrelevant alternatives criterion? Answer yes or no. A; A; No A; B; No A; A; Yes B; C; Yes 10 points Question 7 1. A focus group of 46 people for ABC TV were asked to rank the government spending priorities of education (E), military spending (M), health care (H), immigration (I), and lowering taxes (T). Here are the preferences: (EIHTM) 16 (MIEHT) 10 (HMETI) 10 (TMEIH) 10 Suppose that the losing issues of health care, lowering taxes, and immigration are removed from the table. Now, who is the winner using the Borda count method? Answer E, H, M, I, or T. Does the Borda count method violate the irrelevant alternatives criterion? Answer yes or no. E;Yes H;Yes M; Yes T;Yes 10 points Question 8 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) 4 (ACB) 8 (CAB) 6 Who wins the election using the Hare method? Answer Alice, Betty, or Connie. Does this violate the Condorcet criterion? Answer yes or no. Betty;No Connie; Yes Betty;Yes Connie;No 10 points Question 9 1. The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (CADB) 110 (CABD) 130 (DABC) 140 (BADC) 160 Who wins the election using the Hare method? Answer Alberto, Bate, Carl, or Dave. Does this violate any of the fairness criteria? Answer Yes. Irrelevant alternative criterion.; Yes. Condition of decisiveness.; Yes. Condorcet criterion.; or No. Alberto;No. Condorcet criterion. Carl; Yes. Condition of decisiveness Bate; Yes. Condorcet criterion. Bate; Yes. Condorcet criterion. 10 points Question 10 1. Consider an election with three candidates with the results: (CBA) 2 (ACB) 6 (BAC) 5 (BCA) 2 Is there a majority winner? If not, who is the plurality winner? Answer No, B; Yes, A; No, A; No, C; or Yes, B. Who wins the election using the Borda count method? Answer B; A; C and B tie; C; or A and B tie. Who wins if they first eliminate the one with the most last-place votes and then have a runoff between the other two? Answer B; A; C and B tie; C; or A and B tie. Could the two voters with preference (BCA) change the outcome of the election in previous question if they voted insincerely and pretended to have the preference (BAC)? Answer yes or no. No, B; A; A; Yes Yes, B; A; A; No No, A; B; B; Yes No, B; B; A; Yes 1. The Adobe School District is hiring a vice principal and has interviewed four candidates: Alicia (A), Ben (B), Carmelia (C), and Diana (D). The hiring committee has indicated their preferences. (ACDB) 8 (CBAD) 5 (BCDA) 1 (DBCA) 4 Determine who is the winner using the plurality method. Then suppose that Diana drops out of the running before the vote is taken. Do the results you obtain violate the irrelevant alternatives criterion? a No . b Ye . s 10 points Question 2 1. A focus group of 47 people for ABC TV were asked to rank the government spending priorities of education (E), military spending (M), health care (H), immigration (I), and lowering taxes (T). Here are the preferences: (TEIHM) 17 (METIH) 10 (IMTHE) 10 (HMTEI) 10 Suppose that the losing issues of immigration, health care, and education are removed from the table. Now, who is the winner using the Borda count method? aT . bM . c No . winner. 10 points Question 3 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) 10 (CBA) 20 (BCA) 5 Who wins using the Borda count method? Does this violate the Condorcet criterion? Connie, No b Betty, No a . . c Alice, Yes . d Connie, . Yes e Betty, . Yes 10 points Question 4 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) 8 (ACB) 4 (CAB) 6 Who wins the election using the Hare method? Does this violate the Condorcet criterion? a Alice, Yes . b Connie, . Yes c Connie, . No d Betty, . Yes e Alice, No . 10 points Question 5 1. The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (CADB) 110 (CABD) 130 (DABC) 140 (BADC) 160 Who wins the election using the Hare method? Does this violate any of the fairness criteria? Dave. Yes. Condorcet criterion. b Carl. No. a . . c . Carl. Yes. Condorcet criterion. d Bate. Yes. Condorcet . criterion. e Bate. No. . 10 points Question 6 1. The Adobe School District is hiring a vice principal and has interviewed four candidates: Anna (A), Bono (B), Clark (C), and David (D). The hiring committee has indicated their preferences. (ACDB) 8 (CBAD) 1 (BCDA) 3 (DBCA) 6 Who is the winner using the plurality method? Answer A, B, C, or D. Suppose that Bono drops out of the running before the vote is taken. Who is the winner using the plurality method? Answer A, B, C, or D. Do the results of the previous questions violate the irrelevant alternatives criterion? Answer yes or no. a A; A; No . b A; A; Yes . c A; B; Yes . d A; B; No . 10 points Question 7 1. A focus group of 37 people for ABC TV were asked to rank the government spending priorities of education (E), military spending (M), health care (H), immigration (I), and lowering taxes (T). Here are the preferences: (MEIHT) 16 (TEMIH) 7 (ITMHE) 7 (HTMEI) 7 Suppose that the losing issues of immigration, health care, and education are removed from the table. Now, who is the winner using the Borda count method? Answer E, H, M, I, or T. Does the Borda count method violate the irrelevant alternatives criterion? Answer yes or no a T; Yes . b T; No . c H; Yes . d H; No . 10 points Question 8 1. A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (CAB) 10 (BAC) 5 (ABC) 8 Who wins the election using the Hare method? Answer Alice, Betty, or Connie. Does this violate the Condorcet criterion? Answer yes or no. a Connie;Y . es b Betty;No . c Alice; Yes . d Alice; No . 10 points Question 9 1. The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (DBAC) 98 (DBCA) 118 (ABCD) 128 (CBAD) 148 Who wins the election using the Hare method? Answer Alberto, Bate, Carl, or Dave. Does this violate any of the fairness criteria? Answer Yes. Irrelevant alternative criterion.; Yes. Condition of decisiveness.; Yes. Condorcet criterion.; or No. Carl; Yes. Condorcet criterion. Carl; No. Condorcet criterion. Bate; Yes. Condorcet criterion. Dave; No. Condorcet criterion. 10 points Question 10 1. Consider an election with three candidates with the results: (CBA) 2 (ACB) 6 (BAC) 5 (BCA) 2 Is there a majority winner? If not, who is the plurality winner? Answer No, B; Yes, A; No, A; No, C; or Yes, B. Who wins the election using the Borda count method? Answer B; A; C and B tie; C; or A and B tie. Who wins if they first eliminate the one with the most last-place votes and then have a runoff between the other two? Answer B; A; C and B tie; C; or A and B tie. Could the two voters with preference (BCA) change the outcome of the election in previous question if they voted insincerely and pretended to have the preference (BAC)? Answer yes or no. Yes, B; A; A; Yes No, A; A; A; Yes No, B; A; A; Yes No, B; A; A; No Consider the populations given in problems 31 and 36 ( page 857) of your textbook. Please post your solution to one of the problems indicated: #31) 10 seats #36) 12 seats Population Population 1st 135,000 1st 135,000 nd nd 2 231,000 2 231,000 3rd 118,000 3rd 118,000 th th 4 316,000 4 316,000 Total 800,000 Total 800,000 a. b. c. d. Find the standard divisor. Find the standard quota for each precinct. For # 31, total rounding the standard quotas down. For # 36, total rounding the standard quotas up. Find a modified divisor that will give modified quotas to produce the desire number of seats