A pastry bar, half chocolate and half maple, is to be shared by Madeline and Graham....

A pastry bar, half chocolate and half maple, is to be shared by Madeline and Graham.

Madeline likes chocolate and maple equally, while Graham prefers chocolate to maple. Using the divide-and-choose method for two players, consider three possible divisions of the pastry bar made by Madeline.

a. Visually inspect the two pieces in (I), and explain which half Graham would select and why. You need not assign numerical values to the pieces.

b. Visually inspect the two pieces in (II), and explain which half Graham would select and why. You need not assign numerical values to the pieces.

c. Visually inspect the two pieces in (III), and explain which half Graham would select and why. You need not assign numerical values to the pieces.

d. Suppose in division (I), Graham selects the chocolate half, leaving the maple half for Madeline. How would each judge the fairness of the portion they received compared with the value of the entire pastry bar?