Framing effects and prospect theory: Life and Death •
The Asian Disease Problem: Imagine that the United States is preparing for an outbreak of an unusual Asian disease that is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Scientific estimates of the programs are as follows: – A: If program A is adopted, 200 people will be saved – B: If program B is adopted, there is a 1 in 3 chance that 600 people will be saved and a 2 in 3 chance that no people will be saved – Result: 72% choose A •
Now consider a choice between C and D: – C: If program C is adopted, 400 people will die – D: If program D is adopted, there is a 1 in 3 chance that nobody will die and a 2 in 3 chance that 600 will die – Result: 78% choose D
What is the expected value of the number of deaths?
A: 600 +(-200) = 400 deaths
B: 600 +0.333*(-600) = 400 deaths
C: 400 + 0 = 400 deaths
D: 0.333*0 + 0.667*600 = 400 deaths
For this assignment, you are asked to create TWO of your own sets of dual problems illustrating the framing effect discussed in class, for a total of four “choose A or B” problems. Be creative. Your problems may involve decisions about money, life and death situations, or anything else for which the outcome is quantifiable (the Asian Disease problem discussed in class is an example of one set of dual problems; you must create two sets of problems like this one for this assignment). For each of your framing problem pairs, you must do two analyses:
1) Demonstrate mathematically the equivalence of the paired prospects using probability theory. In other words, the expected value of all 4 alternatives for each problem pair should be the same. Use the lecture notes as a model for how to do this. If the pairs are not mathematically equivalent, you will be asked to revise and resubmit them for partial credit.
2) Demonstrate mathematically, using the prospect theory equations presented in class, what the predicted human choices are. Use the lecture notes as a model for how to do this.