Question

Exercises Fair Division

Score: 16.88/20 8/10 answered
Question 4
Juan Martín and Hailey want to split a bag of candy, and decide to use the divider-chooser method. The bag
contains 100 Snickers, 100 Milky Ways, and 100 Reese's, which Juan Martín values at $2, $1, and $4
respectively.
If Juan Martín is the divider, find a possible division that is consistent with his value system.
In this division, one half contains:

Answer 1

A fair division of candies for Juan Martín using the divider-chooser method, considering his value system, would involve splitting the candies so that each half has an equal total value of $350. One possible division is: Half A contains 50 Snickers, 50 Milky Ways, and 50 Reese's, and Half B contains the same.

Step-by-step explanation:

To find a possible division of candies that is fair according to Juan Martín's value system using the divider-chooser method, we need to consider the values he assigns to each type of candy. Juan Martín values Snickers at $2, Milky Ways at $1, and Reese's at $4. The bag contains 100 of each, so in total, the Snickers are worth $200, Milky Ways are worth $100, and Reese's are worth $400. To ensure a fair division that is as equal in value as possible, Juan Martín should aim to have each half of the division as close to the same total value as possible ($350 each, since the total value is $700).

One possible division could be:

• Half A: 50 Snickers + 50 Milky Ways + 50 Reese's (Value: $100 + $50 + $200 = $350)
• Half B: 50 Snickers + 50 Milky Ways + 50 Reese's (Value: $100 + $50 + $200 = $350)

This division ensures that both halves are equal in total value, which aligns with Juan Martín's value system, making it a fair division. This strategy in the divider-chooser method allows for a fair share that takes individual preferences into account.