Tutorial Exercise - Week 10 Question 1: Imagine that you are betting on a race between two athletes, Smith and Jones. You can place one bet of R100 on either athlete. Smith is the underdog, so if you bet R100 on him, you will get R400 if he wins. On the other hand, Jones is a well established and respected athlete - if you bet R100 on him, you will only get R150 if he wins. You estimate that there is an 80% chance that Jones will win the race, and only a 20% chance that Smith will win. a.Draw up a decision matrix of this scenario, including the values and probabilities for each outcome b.Calculate the expected value of each choice that you have available to you c.Which one of these choices is the dominant choice? Smith winsJones wins Bet on Smith400 x 0.2 = 80-100 x 0.8 = -80 Bet on Jones-100 x 0.2 = -20150 x 0.8 = 120 Bet on SmithEV: 80 + (-80) = 0 Bet on JonesEV: (-20) + 120 = 100 Question 2: Imagine that I am throwing a birthday party for my partner. I am trying to decide whether I should make the party a surprise party, or a regular party. I know that my partner hates surprises in general, but I think there is a chance that she will have a lot of fun if I throw her a surprise party. Having a normal party is safer, since she is more likely to have a good time, but I think that regular parties are quite boring compared to a good surprise party. I draw up the following decision matrix to assess my options: My partner loves itMy partner hates it Surprise party100 x 0.5 = 50-20 x 0.5 = -10 Regular party60 x 0.7 = 42-20 x 0.3 = -6 a.What are the expected values for my choices?
Surprise party50 + (-10) = 40 Regular party42 + (-6) = 38 b.Which one of these choices is the dominant choice? Surprise party dominates, according to the matrix c.Basedonthestoryabove,identifythepotentialproblemswiththevaluesand probabilities assigned to the outcomes. The probability of my partner loving a surprise party is 50% according to the matrix. This seems unlikely, since I have stated that she hates surprises in general. Even if there is some chance that she will love the surprise party, it is probably lower than 50%. We might also question the values of her hating the parties. Since she hates surprises so much, she will probably hate a bad surprise party much more than she would hate a bad regular party. Assigning both of these as -20 in the matrix seems like a problem. It is also possible that I am over-estimating how much my partner would enjoy a good surprise party. It seems possible that she might enjoy a surprise party less than a regular party, even if she likes the party. A value of 100 for a surprise party that she loves seems very optimistic, especially since the value for a regular party that she loves is only 60. Question 3: One problem with decision matrices is that they can require us to assign numbers to abstract things, such as happiness and unhappiness. Is this a fatal flaw for decision theory? Why/Why not? You can answer either way here! If you think that assigning numbers to things like happiness and unhappiness means that decision theory is useless, you might argue any of the following points: -Itisimpossible to assign a non-arbitrary value to things like happiness or unhappiness. It is absurd to think that we could assign a number to the feeling of seeing a loved one, or to the feeling of losing a parent. -If we are assigning values arbitrarily, we can game the system, by assigning more points to things that we want to do, and less points to things we don't. For example, in question 2, it could be the case that I really want to throw a surprise party, and have provided values for the outcomes that could justify my decision. If you think that this is not useless, you might argue: -The numbers are arbitrary, but that doesn't mean that they are meaningless. They are supposed to be a rough approximation of the value (or negative value) of the outcomes we are examining. They can never be completely accurate - but they don't need to be. They just need to be close enough to help us make decisions
-It is possible to game the system, but that doesn't mean that the system is bad. Instead, it means that the person gaming it is using it incorrectly or misleadingly. If someone misuses any other mathematical formula to get a weird result, we don't blame the formula, but the person. -The decision matrix is not a hard and fast guide to action. Instead, we should view it as a tool that can be used to help us in our decision making.
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