Unit 3 Test Flashcards

1
Q

Winning coalition/combination

A

A coalition is winning if they have enough weight to meet the quota

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2
Q

Minimal winning coalition

A

Winning coalitions where every voter is critical

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3
Q

Banzhaf power index steps

A

List out all winning coalitions (all combinations), identify each coalition’s critical players, count how many times each player is critical, and the power of a player is the # of times they’re critical

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4
Q

Extra votes principle

A

The critical voters in a winning voting combination are the “yes” voters whose weights are greater than the number of extra votes in the combination

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5
Q

Equivalent voting systems

A

When two voting systems have the same power indices

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6
Q

Combination formula

A

The number of ways to choose k outcomes, without regard to order, from n possibilities is nCk (on calculator) = “n choose k”= n!/k!(n-k)!

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7
Q

Permutation

A

A specific ordering from first to last of all elements of a set. AB =/BA

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8
Q

Voting permutation/sequential coalition

A

A coalition where we record the order that players joined

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9
Q

Pivotal player/voter

A

A player is called pivotal if the coalition goes from losing to winning when they joined

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10
Q

Shapley-Shubik power index steps

A

List out all sequential coalitions (n! for n players), determine the pivotal player in each, count how many times each player is pivotal, and divide each of these #s by n!

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11
Q

Fair division method

A

Step-by-step procedure that results in a division of items in a way so that each party feels that they have received what they deem to be fair

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12
Q

Continuous division

A

Occurs with objects which can be divided into parts as small as we’d like, such as money or cake

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13
Q

Discrete division

A

Occurs with objects which cannot be divided into smaller parts, like a car or house

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14
Q

Fair share

A

In Knaster inheritance, the amount for each party when the values of all items are totaled and divided by the number of parties

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15
Q

Adjusted winner procedure steps

A

Each person is assigned 100 points and distributes these points to the items on the list based on their valuations of the items and the highest bidder of an items gets that item. Ties are broken by giving the items to the person with the most leftover points. After all the points are distributed, total the value of the items awarded to each person by their own point estimations, calculate the point ratio for the initial winner, and transfer the item with the smallest point ratio to the person with the fewest points. Continue until the values of awarded items are equal between the two persons, usually with an algebraic equation

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16
Q

Initial winner

A

The person after the initial distribution of items with more points according to their own estimation in adjusted winner procedure

17
Q

Initial loser

A

The person after the initial distribution of items with fewer points according to their own estimation in adjusted winner procedure

18
Q

Point ratio

A

Calculated for each item the initial winner receives initially in adjusted winner procedure. Found as (higher valuation of the item) / (lower valuation of the item)

19
Q

Equitable

A

If each player believes they received the same fractional part of the total value

20
Q

Proportional

A

If each party believes they received at least 1/n of the total value. Most basic notion of fairness

21
Q

Envy-free

A

If no party would prefer another party’s share over their own

22
Q

Pareto optimal

A

If no other division would make a party better off without making another party worse off

23
Q

Sealed bids method/Knaster inheritance procedure steps

A

Each party assigns each item a bid, the values of all items are totaled and divided by the number of parties, and each item is awarded to the highest bidder. For each party, the value of all items received is totaled, and they pay/get the difference from the fair share to/from a holding pile, then any money left over in the holding pile is divided evenly

24
Q

Bids

A

The secret dollar amount each party assigns to each item in a Knaster inheritance procedure

25
Q

Critical voter/player

A

If a player is in a winning coalition and them leaving the coalition would cause the coalition to change to a losing one

26
Q

Dummy voter

A

A player whose vote is never essential to reach the quota, so have no say in the outcome.

27
Q

Dictator

A

A player whose weight is equal to or greater than the quota. Have enough say to always pass, so the election id entirely decided by their vote.

28
Q

Veto power

A

A player whose support is necessary to reach the quota. Have enough say to always fail. Possible to have multiple voters with veto power.

29
Q

Minimal quota

A

Must be larger than half the number of voters

30
Q

Maximal quota

A

Can’t be larger than the number of voters

31
Q

Taking Turns

A

Strategy for dividing items by alternately selecting objects with no knowledge of each other’s preferences, so sincere choices

32
Q

Bottom-Up strategy

A

A systematic way to choose when both players know the other’s preferences, so they will not willingly choose their least-preferred object available, and won’t waste a choice on an object they know will remain available

33
Q

Weight

A

How many votes a player gets. Denoted W1, W2, …

34
Q

Quota

A

Minimum weight needed to pass a proposal. Denoted q

35
Q

Player

A

Individual/entity casting a vote. Denoted P1, P2,…

36
Q

Coalition

A

A group of players voting the same way

37
Q

Notation for weighted voting systems

A

[q: W1, …., Wn]

38
Q

How many possible sequential coalitions for n players?

A

n!