**TERMINOLOGY**

**Motion**

A __ motion __is any vote involving only two alternatives.

**Player
**A

*The N players are: P*_{1}, P_{2}, P_{3},…, P_{N}.

**Weight
**The

*The weights of the N players are (in order): w*_{1}, w_{2}, w_{3},…, w_{N}.

**Quota
**The

*We will use the letter***q**to stand for quota.**q**must be__at least__a majority but not more than the total number of votes.

**Dictator
**A

*A dictator’s weight is always greater than or equal to the quota .**Whenever there is a dictator, all other players have NO power.*

**Dummy
**A

**Veto Power
**A player that is not a dictator but can single-handedly prevent any group of
players from passing a motion is said to have

**Coalition
**A

- The total number of votes controlled by a coalition is
called the
*weight of the coalition*. - A
*winning coalition*is one with enough votes to win. - A
*losing coalition*is one without enough votes to win. - A coalition consisting of all players is often called a
*grand coalition.* - With N players, there are 2
^{N}-1 possible coalitions.

**Critical Player
**A player whose desertion of a winning coalition turns it into a losing one is
called a c

**Sequential Coalition
**A

**Pivotal Player
**A

**N!
**N! = N(N-1)(N-2) ...(2)(1)

*Examples:*

*6! = 6(5)(4)(3)(2)(1) = 720*

*4! = 4(3)(2)(1) = 24*

*and, by definition,*

*0! = 1*