4. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What is the minimum number of votes required to pass a bill?

5. PLACE YOUR BET

6. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What is the minimum number of votes required to pass a bill?

7. ANSWER: 6

8. Given the scenario previously mentioned, how many coalitions are possible?

9. PLACE YOUR BET

10. Given the scenario previously mentioned, how many coalitions are possible?

12. Given the same scenario, list all possible coalitions with voting bodies A, B, C and D. Be sure to include their point totals! Try and do this in an orderly fashion!

13. PLACE YOUR BET

14. Given the same scenario, list all possible coalitions with voting bodies A, B, C and D. Be sure to include their point totals! Try and do this in an orderly fashion!

15. { }AB;5ABC;6ABCD;10 A;3AC;4ABD;9 B;2AD;7ACD;8 C;1BC;3BCD;7 D;4BD;6 CD;5

16. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What are the winning coalitions? Write you answers like { A,B,D;10}

17. PLACE YOUR BET

18. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What are the winning coalitions? Write you answers like { A,B,D;10}

19. ANSWER: { A,B,C;6} {A,B,C,D;10} {B,C,D;7} {A,C,D;8} {A,B,D;9} {B,D;6} {A,D;7}

20. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Find the power index for each province.

21. PLACE YOUR BET

22. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Find the power index for each province.

23. ANSWER: A = 3 B = 3 C = 1 D = 5

24. What % of the vote does D have? What % of the power does D have?

25. PLACE YOUR BET

26. What % of the vote does D have? What % of the power does D have?

28. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Name the dummies and/or dictators.

29. PLACE YOUR BET

30. A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Name the dummies and/or dictators.

31. ANSWER: There are no dummies or dictators

32. Determine whether any voter is a dictator and whether any is a dummy. A – 10 votes B – 8 votes C – 6 votes D – 3 votes 20 votes are needed to pass an issue

33. Place your bet!

34. Determine whether any voter is a dictator and whether any is a dummy. A – 10 votes B – 8 votes C – 6 votes D – 3 votes 20 votes are needed to pass an issue

35. No one is a dictator because no one has 20 or more votes AND No dummies because each voter is essential in at least one winning coalition

36. Determine whether any voter is a dictator and whether any is a dummy. A – 20 votes B – 10 votes C – 8 votes D – 1 votes 20 votes are needed to pass an issue

37. Place your bet!

38. Determine whether any voter is a dictator and whether any is a dummy. A – 20 votes B – 10 votes C – 8 votes D – 1 votes 20 votes are needed to pass an issue

39. A is a dictator because it has 20 votes and 20 votes are needed to pass the issue AND B, C and D dummies because they don’t have enough points to pass and issue

40. A corporation has 4 shareholders and a total of 60 shares. Each share is worth one vote. The # of votes needed to pass an issue is a simple majority. The # of shares are as follows: A – 27 B - 15 C - 12 and D - 6 The winning coalitions are [A,B; 42] [A,B,C; 54] [A,B,C,D; 60] [A,C; 39] [A,B,D; 48] [A,D; 33] [A,C,D; 45] [B,C,D; 33] The power indexes are as follows: A = 6 B = 2 C = 2 D = 2 B owns 25% of the shares. What fraction of the power does B have?

41. Place your bet!

42. A corporation has 4 shareholders and a total of 60 shares. Each share is worth one vote. The # of votes needed to pass an issue is a simple majority. The # of shares are as follows: A – 27 B - 15 C - 12 and D - 6 The winning coalitions are [A,B; 42] [A,B,C; 54] [A,B,C,D; 60] [A,C; 39] [A,B,D; 48] [A,D; 33] [A,C,D; 45] [B,C,D; 33] The power indexes are as follows: A = 6 B = 2 C = 2 D = 2 B owns 25% of the shares. What fraction of the power does B have?

43. 2/12 = 1/6

44. Question #:

45. Place your bet!

46. If each person approves of their first 3 choices, who is the winner using the approval method?