MATH 11008 Lecture 3: Mathematics of Powers
23 Sep 2016
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Imagine a situation where the senate has 100 members. 49 of those members are republicans, 48 are democrats, and 3 are independents. Imagine that, for passing a bill, 51 affirmative votes are required (simple majority) [51;49, 48, 3] dealing with the blocks of votes. Coalition: a set of players who join forces to vote the same way. If the set is all the players, then we will say that it is the grand coalition. In a winning coalition, a player is a critical player if his/her votes are required to win, that is, if without his/her votes the coalition loses. The critical count of a player is the number of times this player is a critical player. Compute the banhaf power: quota- [6: 4(p1), 3(p2), 2(p3), 1(p4)] Step 2: determine on each winning coalition which of the players are critical. Step 3: find the critical counts for each of the critical players.
