1. Homework Collection Homework Discussion Page 35: 35, 38, 63, 64

2. Nassau County Board of Supervisors in 1960:
District
Weight
Hemstead #1 31
Hemstead #2
Oyster Bay 28
North Hempstead 21
Long Beach 2
Glen Cove

3. WEIGHTED VOTING (page 50)
weighted voting system - Any formal voting arrangement in which the voters are not necessarily equal in terms of the number of votes they control is called a weighted voting system.
The players are the voters. We call them voters in the case of one-person-one vote and players in the case of a weighted voting system.
N is the number of players and are the names of the players.
The player’s weight is the number of votes he/she controls.
are the weights of respectively.
A vote involving only two choices is generally referred to as a motion.

4. The quota is the minimum number of votes necessary to pass a motion
The quota is the minimum number of votes necessary to pass a motion. q denotes the quota.
describes a weighted voting system where q is the quota and are the respective votes of the players. The weights are normally written in numerical order from the highest to the lowest.
Example 1.

5. Example 2.
Anarchy - quota too low - this is not a legal weighted voting system
Example 3.
Quota too high - no motion could ever pass - this is not a legal weighted voting system

6. Definitions (page 54)
coalition - Any set of players that might join forces to vote together is called a coalition. (single player coalitions are allowed)
weight of the coalition - The total number of votes controlled by a coalition is called the weight of the coalition.
A coalition with enough votes to win is called a winning coalition. A coalition without enough votes to win is called a losing coalition.
The coalition consisting of all the players is called the grand coalition.

7. Goal: Construct an algorithm to determine the “power” of each player.
critical player - A player whose desertion turns a winning coalition into a losing coalition is said to be a critical player for that coalition.

8. Homework Read Pages 48 – 62 Page 72: 1 – 4, 6
TEST 1 ON THURSDAY FEBRUARY 8
The test will cover sections 1.1 – 1.6, and 2.1 – 2.3 in the textbook as well as any other items covered in the class notes and homework assignments.