Math 103, Section 11, Friday, February 4, 2011
1. Submitted Homework for Chapter 2 is at Sakai.
It is in the Assignments section and is called:
Assignment Chapter 2A
Please do Exercises 18b,18c,20 and 24 on page 68 and upload to
Homework is due by Friday, February 11 at midnight
The Exercises are at Sakai, Resources, Chapter 2 Exercises from
Homework to be discussed on Tuesday, February 8:
Page 68 in the text, Exercises 17a,17b,17c, 19,23
Setup and terminology:
A weighted voting system has some number of
These are, essentially, the voters, i.e. the entities
which cast votes.
They may be individual people, or states in the electoral college, or nations sitting on
the UN Security Council, etc.
We will call them "player 1, player 2, player 3.
.." and use the shorthand
The players vote on a
, which can be thought of as a proposal, or a legislative bill, or a UN
Each player votes either "yes" or "no".
Each player casts a certain number of votes.
This number is the player's "
" in the system.
The minimum number of "yes" votes required to pass a motion is called the
of the weighted
This could be a simple majority of the total number of votes cast (more than 50%), or a
60% majority, or a two thirds majority, etc.
The quota could even equal 100% of the total number of
[quota: weight of
, weight of
, weight of
[12: 7, 5, 3, 2] describes a
weighted voting systems with 4 players whose weights are 7, 5, 3, and 2 respectively, and with a quota of
12 votes needed to pass a motion.
is a set of players who all vote the same way on a specific motion.
We usually think of a
coalition as a set of players who are all voting "yes", since the quota is defined in terms of how may "yes"
votes are needed to pass a motion.
The coalition consisting of all the players is called the
When all players unanimously vote "yes" for the motion, they are forming the grand coalition.
A coalition with enough votes to win is called a
A coalition without enough votes to
win is called a
A player is called a
for a specific winning coalition if that player's departure from the
coalition would change it from a winning to a losing coalition.
In other words, the decision of the player
to stay or leave is
to whether the motion will pass.
"Critical" makes sense only in relation to a