Question: Making decisions. Exercise reported the results of a study by the psychologist Amos Tversky on the effect of wording on people's decisions about chance outcomes. His subjects were college students. Repeat Tversky's study at your school. Prepare two typed cards.
One says: You are responsible for treating 600 people who have been exposed to a fatal virus. Treatment A has probability 1/2 of saving all 600 and probability 1/2 that all 600 will die. Treatment B is guaranteed to save exactly 400 of the 600 people. Which treatment will you give?
The second card says: You are responsible for treating 600 people who have been exposed to a fatal virus. Treatment A has probability 1/2 of saving all 600 and probability 1/2 that all 600 will die. Treatment B will definitely lose exactly 200 of the lives. Which treatment will you give?
Show each card to at least 25 people (25 different people for each, chosen as randomly as you can conveniently manage, and chosen from people who have not studied probability). Record the choices. Tversky claims that people shown the first card tend to choose B, while those shown the second card tend to choose A. Do your results agree with this claim? Write a brief summary of your findings: Do people use expected values in their decisions? Does the frame in which a decision is presented (the wording, for example) influence choices?
Exercise: Making decisions. The psychologist Amos Tversky did many studies of our perception of chance behavior. In its obituary of Tversky, the New York Times cited the following example.
(a) Tversky asked subjects to choose between two public health programs that affect 600 people. One has probability 1/2 of saving all 600 and probability 1/2 that all 600 will die. The other is guaranteed to save exactly 400 of the 600 people. Find the expected number of people saved by the first program.
(b) Tversky then offered a different choice. One program has probability 1/2 of saving all 600 and probability 1/2 of losing all 600, while the other will definitely lose exactly 200 lives. What is the difference between this choice and that in (a)?
(c) Given option (a), most subjects choose the second program. Given option (b), most subjects choose the first program. Do the subjects appear to use expected values in their choice? Why do you think the choices differ in the two cases?