Warm Up – 2/18 - Tuesday

A companies assets are split into four shares. How eachpartner values each share is listed above. A) List the shares that each partner would consider to be a fair share.B) List a possible way that you could divide the sharesfairly among the four partners.

Basic Assumptions

• S – is the total to be divided – the “goodies”• s - Fair Share – A fair share is determined by

the individual player. • Example: Say there are five players. fair share

would be 1/5 of the total, S, in opinion. • We call something fairly divided if every player

gets a perceived fair share.

Fair Division CW

Damian cuts the cake like so…

• Damian is the “Divider” which means Cleo is the “chooser.”

• Which piece will Cleo choose and is this a fair division?

Divider-Chooser

• It is always better to be the chooser over the divider.

• The divider’s goal is to ensure they get at least 50% of the goodies.

• The chooser may get well more than 50% in their opinion.

Eat Fresh

• We are going to Label every inch of the sub with a value of ‘x’ according to Bill’s liking.

Bill and Claudia are going to split the sub to the right. Half of the sub is Vegetarian and half of the sub is Meatball. Bill likes Meatball three times as much as vegetarian while Claudia does not like Meatball at all.

1. Suppose Bill is going to divide the sub into two. How can he divide the sub so he guarantees he gets a fair share?

Label the ruler

• We make X = an inch of whatever Bill likes the least. In this case Bill likes Vegetarian the least. That means each vegetarian inch is worth 1X.

The vegetarian side has 6x’s total.

1x 1x 1x 1x 1x 1x

Meatball Side

• Since Bill likes the Vegetarian Side 3 times as much as the vegetarian side, every inch of meatball will be worth 3x.

The vegetarian side has 18x’s total.

3x3x3x3x3x3x

Overall

• Overall there are a total of 24x’s across the whole sub. How many x’s would Bill want to get 50%?

Bill will split the sub at exactly 50% to guarantee he gets a fair share.

3x3x3x3x3x3x1x 1x 1x 1x 1x 1x

Overall

• 12x’s is exactly half, so we count from the left until we get to 12x.

Bill will split the sub at the 8 inch mark creating two shares: Which share will Claudia decide to take?

3x3x3x3x3x3x1x 1x 1x 1x 1x 1x

Claudia’s Decision

• We will use Y for Claudia, since she is a vegetarian each Meatball inch is worth 0Y.

We can say the Vegetarian side is 1Y. In total the left side is worth 6y and the right side 0y. Claudia will pick the side worth more to her, .

3x3x3x3x3x3x1x 1x 1x 1x 1x 1x

0y0y0y0y0y0y1y 1y 1y 1y 1y 1y

Claudia’s Percentage

• The percentage of the left side is the weight of the left side divided by the whole sub.

• Left Side = Total: • Percentage

3x3x3x3x3x3x1x 1x 1x 1x 1x 1x

0y0y0y0y0y0y1y 1y 1y 1y 1y 1y

M = Matt G = Gabe

• Matt likes Ham twice as much as Turkey.• Matt likes Turkey and Roast Beef the same.• Gabe likes Roast Beef twice as much as Turkey.• Gabe likes Turkey and Ham the same.