## Question 1, short answers are ok, but be sure to show or explain your work and c

Question 1, short answers are ok, but be sure to show or explain your work and calculations:
You want to go see a movie and decide to apply your Multi-attribute Decision Making knowledge to this decision. For the four movies that you are considering, you decide upon your personal (but mostly uninformed) preference for the movie and also look up the movie reviews. As with many people, your choice of movie relies on a combination of your basic preferences and the reviews of the movie. Your rating is on a 0-100 scale, while the movie reviews are on a 0-5 star scale (higher is better in both cases). The scores are:
Movie A B C D
Your rating 95 65 45 40
Movie review 2 4 2 5
– What is the “non-dominated set” in this case?
– Assuming proportional scoring (linear utility) and additive utility, which of the four movies would the best choice be if you were indifferent between A and a hypothetical movie (H) that has a score of 75 in your personal rating and 3 from the movie reviews?
Question 2, short answers plus some drawn out decision trees are expected (you can draw them on paper and send me a picture):
a. Draw out the decision tree for the decision described below. Make sure to label the outcomes and any probabilities that you can:
After finishing the City Sciences program, you apply to several jobs while continuing to work in your current position (Job A). You get several rejection letters and do two interviews. From these interviews, you have one job offer (call this Job B), and haven’t heard either way from the other job (Job C). Your preference for these jobs is that you like Job C the best, Job B second best, and Job A (your current position) the least. Because you like Job C the best, you would like to hold off on making a decision until they contact you. But Job B insists that you accept or decline their offer right away. Job A is your current position, so continuing to work at Job A is always an option.
So your choices are basically: You could accept the offer from Job B, or you could reject it and maybe get Job C. If you do this and don’t get Job C, you can always keep working at Job A but that is your least favorite alternative. You figure that there is a 60% chance that you are offered Job C.
b. Once you have set up the decision tree, I want you to assume that you rate the three outcomes like this: Utility(Job A) = 3, Utility(Job B) = 5, Utility(Job C) = 8. If you also assume that you are risk-neutral, what is the best choice/strategy?
c. If the utility of Job A was 3 and the utility of Job B was 5, how much would you have to change the utility of Job C to switch your answer just above? (This is like part b above, except imagine that Utility(Job C) is unknown and we want to do some breakeven analysis on how high or low it needs to be to change the answer).
– Please find attached a sample of how the answers should be like.
– Decision Trees Chapter from Making Hard Decisions – This reading explains how to set up and solve a decision tree, which is a useful tool for problems where there are lots of decisions and lots of uncertain outcomes in between