Subjective Expected Utility Theory
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What is subjective expected utility theory?
- Savage (1954)
- EU assumes probability information is available to people (a coin has landed on heads 600 out of 1000 times)
- Savage argues that, because we do not always know the probability of occurrences, we should allow subjective probabilities to substitute for objective ones
What problems do subjective expected utility face?
- Are the probabilities confined by the same rules that govern objective ones?
- Even if they do, they are still not accurate enough to be used prescriptively
How is subjective EU used for decision analysis?
- Raiffa (1968)
- First your problems are structured, and the possible events that could occur are determined, this prevents
- Probabilities and utilities are estimated, this can occur directly or through the choice between wagers (failure to include some of the possible events biases subjective probabilities given to those remaining - Fischhoff, Slovic & Lichtenstein, 1978)
- Finally, each outcome’s product of utility & probability is calculated and the option with the largest sum of these products is chosen
Give an example of decision analysis using EU
- Subjective probability for the weather the next day:
- Sunny: sp=.2,
- Rain: sp=.4
- Overcast: sp=.1
- Showers: sp=.3
- Utilities for option A (go for a picnic) for the weather conditions: U=100 U=-90 U=0 U=50
- Utilities for option B (revise) for the weather conditions: (U=-50 U=80 U=50 U=30)
- Subjective expected utilities for:
- Picnic: .2(100) +.4 (-90) +.1(0) + .3(50) = -1
- Revision: .2(-50) + .4(80) = .1 (50) = .3 (30) = 36
- The option with the largest subjective expected utility is to revise
What is the subadditivity effect?
- Tversky & Koehler (1994)
- When people estimate the probability of something and the probability of the single alternative to it, experiments show these estimates do sum to one.
- But if the single alternative is broken down into several sub-alternatives, they sum to more than one
- P's judged the probability of death from cancer in the United States was 18%, the probability from heart attack was 22%, and the probability of death from "other natural causes" was 33%.
- Other participants judged the probability of death from a natural cause was 58%.
- Natural causes are made up of precisely cancer, heart attack, and "other natural causes," however, the sum of the latter three probabilities was 73%, and not 58%.
What is the conjunction fallacy?
- Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.
- Which is more likely:
- Linda is a bank teller
- Linda is a bank teller and an active member of the feminist movement
- People choose both despite the fact that the probability of them happening together is much smaller than the first choice
- It is argued that they are heuristically biased by the representativeness heuristic (option 2 seems more representative of Linda despite its mathematical unlikelihood
Are probability estimates accurate?
- For experts, yes- Murphy & Winkler (1984)
- People give weather predictions as percentage probabilities
- Plotted the predictions against the actual weather and it was found that there was a very close match on the calibration curve
- No, for non experts- Christensen–Szalanski & Busheyhead (1981)
- Asked doctors to estimate the probability of patients having pneumonia and compared these with medical tests for the disease
- Data on the calibration curve fell way below the indicated optimal judgments, with doctors overestimating the probability of the patients having the disease
Are the general public accurate at predicting probability?
- No- Russo & Shoemaker (1989)
- P's given 10 items of questions they were very unlikely to possess accurate knowledge of, and asked to make a high and low estimate about their values in which they are 90% sure the answer falls in
- E.g. number of books in the old testament or MLK's age at death
- Found that p's usually showed overconfidence despite inaccurate predictions, regardless of training, intelligence or the way confidence is elicited (Lichtenstein, Fischhoff & Phillips, 1982)
- This has been interpreted as a tendency to be overoptimistic (optimism bias- Weinstein, 1980)
- Argued by some psychologists such as Juslin that this is an artefact and there were too many questions with which common sensical answers were garnered, leading to a high optimism as this overconfidence is not present when people make perceptual judgments
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