Chapter 3: The Mathematics of Sharing

A cake valued at $35 is to be divided among five players (P1, P2, P3, P4 and P5) using the last-diminisher method. P1 makes the first cut and makes a claim on a C-piece. For each remaining player, the value of the current C-piece at the time it is his turn to play is given in the table.
              S₁    S₂    S₃    S₄
Value    $10    $9    $6   $7
What is the value of a fair share of the cake? 

• $7
• $8.75
• $8
• $6

Tags

CCSS.7.RP.A.2

CCSS.7.RP.A.3

CCSS.7.EE.B.3

CCSS.7.NS.A.3

What are the 4 basic assumptions in fair division?

• Rationality, Privacy, Symmetry, and Kindness
• Respect, Privacy, Kindness, and Symmetry
• Rationality, Cooperation, Privacy, and 
  Symmetry
• Cooperation, Respect, Privacy, Symmetry

How many dividers are there in the divider chooser method ?

• 5
• 3
• 1
• 2

What is the Method of Markers?

• count 100 markers and divide
• discrete fair-division method proposed by William F. Lucas
• A man named charlie brown dropped his markers , and he picked them up to count 
• A division method used to help in school

What is the first step for the method of markers?

• Bidding
• Allocations
• Distribution
• Dividing

How do you distribute the surplus in Method of Sealed Bids?

• Divide by 4
• Let the oldest and richest person keep all of the surplus, because they deserve it
• Let everyone pick what they want  
• Divided fairly among players depending on what they got

Four partners , A, B, C, D, jointly own a piece of land with a market value of 480,000. The four partners are dividing the land among themselves. The value of each piece of land in the eyes of the partners are in the table below. Some values are missing, find the value of S3 in the eyes of Partner D.  

       S₁          S₂          S₃          S₄
A 80,000   85,000                195,000
B              100,000 135,000 120,000
C                    120,000
D 95,000  100,000              110,000

• 65,000
• 100,000
• 120,000
• None of these

How do you distribute surplus in the Method of Markers?

• Give one to each player and keep the rest 
• Divide by number of players
• Players are chosen to pick one item at a time until all surplus is gone
• none of these 

Consider the weighted voting system { 10: 6 , 5, 4, 2 } what is the weight of the coalition formed by by P1 and P3 ?

• 10
• 27
• 17
• 12

The Lone Chooser was introduced in what year?

• 1917
• 1955
• 1899
• 1964