Lucy, Porter, and Arnold will share 15 ounces of chocolate ice cream and 15 ounces of st...

Lucy, Porter, and Arnold will share 15 ounces of chocolate ice cream and 15 ounces of strawberry ice cream. Lucy prefers chocolate in a 3-to-1 ratio over strawberry, Porter prefers it in a 1-to-2 ratio, and Arnold prefers it in a 3-to-2 ratio. The division will be made using the continuous envy-free division method.

a. Suppose Lucy is the divider, and she creates the following servings:

Serving I: 4 ounces chocolate and 8 ounces strawberry

Serving II: 6 ounces chocolate and 2 ounces strawberry

Serving III: 5 ounces chocolate and 5 ounces strawberry

Verify that each serving represents one-third of the value of the ice cream according to Lucy’s values.

b. Porter will be the chooser, so he evaluates the servings from part (a). Which serving will he think has the greatest value? Which serving will have the second-greatest value?

c. Porter trims the greatest-valued serving to match the second-greatest-valued serving. One way he could do it is to trim 1 ounce of the chocolate ice cream and 2 ounces of the strawberry. Verify that this trimming yields two pieces of equal value, and find one other way in which he could trim the serving.

d. Suppose Porter trims the serving as described in the beginning of part (c). Arnold, Porter, and Lucy will take turns selecting servings. Which serving will each one pick and why?

e. Who will the new divider and the new chooser be?

f. Suppose the new divider creates the following three servings from the excess.

Which piece will the chooser choose, and how will the remaining pieces be chosen?

g. Describe the final division of the ice cream, and explain why it is both proportional and envy-free.