Fair Division Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem. By nature, they are more...

Fair Division
Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem.  By nature, they are more difficult than the regular exercises. 
Adjusted Winner Method:  For discrete division between two players, there is a method called Adjusted Winner that produces an outcome that is always equitable and envy-free.  It does require, that items can be split or shared.  The method works like this. 
1. Each player gets 100 points that they assign to the items to be divided based on their relative worth.
2. In the initial allocation, each item is given to the party that assigns it more points.  If there are any times that both parties are assigned the same number of points, they go to the person with the fewest points so far.
3. If the assigned point values are not equal, then begin transfe
ing items from the person with  more points.Start with the items that have the smallest point ratio (higher person's value/lower person's value)
4. If transfe
ing an entire item would move too many points only transfer a portion of the item. 
Example: A couple is trying to settle a contentious divorce.  They assign their 100 points as possible. 
     
    Mike
    Carol
    Custody of Children
    25
    65
    Alimony
    60
    25
    House
    15
    10
In the initial allocation MIke gets his way on alimony and the house and Carol gets custody of the children.  That means Mike has 75 points and Carol has 65 points.  To decide what to transfer do the point ratio. 
     
    Mike
    Carol
    Point ratio
    Custody of Children
    25
    65
    65/25 = 2.6
    Alimony
    60
    25
    60/25 = 2.4
    House
    15
    10
    15/10 = 1.5
The house has the smallest ratio, but if we transfer all the house to Carol she has too many points. so instead we transfer a fraction of the house (called p) because we want Carol and Mike to have the same point value.  So Mike has 1 - p value of the house and Carol has p value of the house (total of 1) 
So we do each of their points   
Mike 60 (alimony XXXXXXXXXXp) (house) and Carol 65 (children) + 10p (house) 
Set these equal to one another to find p  
XXXXXXXXXXp) = XXXXXXXXXXp   solved give p to be 0.4  which is 40% so Carol gets custody and 40% of house and Mike gets alimony decision and 60% of house. 
Using this method find the division settlement for Sandra and Kenny 
     
    Sandra
    Kenny
    Home
    20
    30
    Summer Cottage
    15
    10
    Retirement Acct
    50
    40
    Investments
    10
    10
    Othe
    5
    10
Submit using an attachment by the due date listed in the class schedule.  
Type project as much as possible.