Transcribed image text: 15.25 A policy maker in the Occupational Safety and Health Administration is under pressure from industry to permit the use of certain chemicals in a newly developed industrial process. Two different versions of the process use two different chemicals, A and B. The risks associated with these chemicals are not known with certainty, but the available in- formation indicates that they may affect two groups of people in the following ways: Chemical A There is a 50% chance that Group 1 will be adversely affected, while Group 2 is unaffected; and a 50% chance that Group 2 is adversely affected, while Group 1 is unaffected. Chemical B There is a 50% chance that both groups will be adversely affected, and a 50% chance that neither group will be affected. Assume that "adversely affected" means the same in every case--an expected increase of one death in the affected group over the next two years. The decision maker's problem looks like the decision tree in Figure 15.16. a Calculate the expected number of deaths for each chemical. Figure 15.16 Deciding between alternative chemicals in Problem 15.25 Expected deaths in: Group 1 Group 2 (0.5) Chemical (0.5) 0 0 (0.5) (0.5) 0 1 b A decision maker who values consequences using an overall utility might calculate the utility for each consequence as U(Chemical) = k, U,(Group 1 Deaths) + kqU(Group 2 Deaths) For both U, and Uy, the best and worst possible outcomes are 0 deaths and 1 death, re. spectively. Thus, U (1 Death) = 0 U (1 Death) = 1 U (1 Death) = 0 Uz(1 Death) = 1 Explain why k, and 1-k, may not be equal. c Assume that k, = 0.4. Show that the decision maker who evaluates the two chemicals in terms of their expected overall utilities (as defined above) would be indifferent be- tween them. Does the value of k, matter? d Why might the decision maker not be indifferent between the two programs? (Most people think about the decision maker's risk attitude toward the number of deaths or lives saved. Besides this, think about the following: Suppose you are a member of Group 1, and the decision maker has chosen Chemical A. It turned out that Group 1 was affected. How would you feel? What would you do? What does this imply for the decision maker?) Transcribed image text: 15.25 A policy maker in the Occupational Safety and Health Administration is under pressure from industry to permit the use of certain chemicals in a newly developed industrial process. Two different versions of the process use two different chemicals, A and B. The risks associated with these chemicals are not known with certainty, but the available in- formation indicates that they may affect two groups of people in the following ways: Chemical A There is a 50% chance that Group 1 will be adversely affected, while Group 2 is unaffected; and a 50% chance that Group 2 is adversely affected, while Group 1 is unaffected. Chemical B There is a 50% chance that both groups will be adversely affected, and a 50% chance that neither group will be affected. Assume that "adversely affected" means the same in every case--an expected increase of one death in the affected group over the next two years. The decision maker's problem looks like the decision tree in Figure 15.16. a Calculate the expected number of deaths for each chemical. Figure 15.16 Deciding between alternative chemicals in Problem 15.25 Expected deaths in: Group 1 Group 2 (0.5) Chemical (0.5) 0 0 (0.5) (0.5) 0 1 b A decision maker who values consequences using an overall utility might calculate the utility for each consequence as U(Chemical) = k, U,(Group 1 Deaths) + kqU(Group 2 Deaths) For both U, and Uy, the best and worst possible outcomes are 0 deaths and 1 death, re. spectively. Thus, U (1 Death) = 0 U (1 Death) = 1 U (1 Death) = 0 Uz(1 Death) = 1 Explain why k, and 1-k, may not be equal. c Assume that k, = 0.4. Show that the decision maker who evaluates the two chemicals in terms of their expected overall utilities (as defined above) would be indifferent be- tween them. Does the value of k, matter? d Why might the decision maker not be indifferent between the two programs? (Most people think about the decision maker's risk attitude toward the number of deaths or lives saved. Besides this, think about the following: Suppose you are a member of Group 1, and the decision maker has chosen Chemical A. It turned out that Group 1 was affected. How would you feel? What would you do? What does this imply for the decision maker?)