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Chapter 2: The Mathematics of Power
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Gravity
Weighted Voting Systems Vocabulary
Terms in this set (15)
Dictator
A player whose weight is larger than or equal to the quota.
Electoral College
A body of people representing the states of the US, who formally cast votes for Presidential Election.
Quota
The minimum number of votes needed to pass a motion.
Critical Player
In a winning coalition, a player without whom the coalition would be a losing coalition.
Pivotal Player
In a sequential coalition, as the votes are tallied from left to right, the first player whose votes make the total equal to or higher than the quota.
Grand Coalition
The coalition consisting of all the players.
N!
The factorial is used to find the number of sequential coalitions.
Sequential Coalition
A coalition in which order matters.
Motion
A yes/no vote, or a vote involving only two choices.
Dummy
A player with no power.
Weight
The number of votes that a player controls.
Veto Power
The power of a player to single-handedly prevent the rest of the players from passing a motion.
Coalition
A set of one or more players that join forces to vote together.
Banzhaf Power Index
For each player, the fraction B/T, in which B is the player's critical count and T is the total critical count for all the players.
Shapley-Shubik Power Index
For each player, the fraction SS/N!, where SS is the player's pivotal count and N! is the number of sequential coalitions (or total number of pivotal players).
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Verified questions
DISCRETE MATH
Let R be a relation on a set A. Prove or disprove: If R is antisymmetric, then R is irreflexive.
DISCRETE MATH
In how many ways can a family of four (mother, father, and two children) be seated at a round table, with eight other people, so that the parents are seated next to each other and there is one child on a side of each parent? (Two seatings are considered the same if one can be rotated to look like the other.)
QUESTION
An inheritance of $25,000 is to be paid in equal amounts over a 5-year period at the end of each year. If the$25,000 can be invested at 5% per annum, what is the annual payment?
DISCRETE MATH
Show that a three-dimensional 2ⁿ × 2ⁿ × 2ⁿ checkerboard with one 1 × 1 × 1 cube missing can be completely covered by 2 × 2 × 2 cubes with one 1 × 1 × 1 cube removed.