Expected Utility Evaluation
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Who created the Allais paradox?
What does the Allais paradox entail?
- Choose between 2 for 2 bets:
- 1A) 100% chance of £1 million OR
- 1B) 89% of £1 million, 10% chance of £5 million and 1% chance of nothing
- 2A) 11% chance of £1 million and 89% chance of nothing OR
- 2B) 10% chance of £5 million and 90% chance of nothing
What does the Allais Paradox show?
- When broken down, 1A & 1B both offer 89% probabolity of £1 million an 2A & 2B offer 89% probability of nothing, under the cancellation axiom these should be ignored meaning the choice is the same
- Both 2A & 2B also have a 1% chance of nothing and a 10% chance of £5 million
- The fact that these bets are the same means that any reasoning for 1 should be carried over with P's choosing 1A and 2A or 1B and 2B
- This doesn't happen though, meaning people violate the independence axiom and do not reason using EU
Who created the Ellsberg Paradox?
What does the Ellsberg Paradox entail?
- P's told there is an urn containing 30 red balls and 60 that are either black of yellow (quantities unknown) and the probability of selection is equally likely
- 1A) £100 for drawing a red ball
- 1B) £100 for drawing a black ball
- 2A) £100 for red and yellow
- 2B) £100 for yellow and black
What does the Ellsberg Paradox show?
- If p's choose 1A over 1B they assume that the probability of choosing red is greater than that for black
- This means the probability of red and yellow should be higher than black and yellow so they should choose 1A and 2A
- But they don't, this breaches the invariance axiom showing that people do not behave rationally as predicted by EU
Who investigated preference reversal?
Lichtenstein & Fischhoff (1977)
What does preference reversal entail?
- A) 80% chance of winning £2; 20% chance of losing £1
- B) 20% chance of winning £9; 80% chance of losing 50p
- P's then told they had tickets for each gamble and asked how much they would sell them for
What does preference reversal show?
- People tended to choose A but 81% of p's valued B as higher
- This violates the invariance principle
Who created the asian disease problem? (not literally)
Kahneman & Tversky (1981)
What does the Asian Disease problem entail?
Preparing for an outbreak of disease that will kill 600
- Programme A) 200 are saved
- Programme B) 1/3 probability that all are saved but 2/3 probability that nobody is saved
- Or choose between
- Programme C) 400 will die
- Programme D) 1/3 probability that nobody will die
- 72% chose A and 78% chose D
- This shows that simply framing something as a loss changes decisions and people are more interested in averting loss. By doing this they are violating the invariance principle
Who supported the Asian disease problem?
- McNeil et al 1982
- P's given info about surgery and radiation therapy for cancer and told in terms of mortality or survival rates
- 78% preferred radiation in the survival frame
- 58% preferred it in the mortality frame
How do credit cards support the Asian Disease problem?
People are much less likely to use a credit card if they are told there is to be a surcharge than if they are told they will forgo a cash discount
Who investigated psychological accounting?
Tversky & Kahneman (1981)
What does the psychological accounting study entail?
- You have decided to see a play. Admission is £10. On entering the theatre, you find you
- have lost a £10 note. Would you still pay £10 for your ticket? 88% say YES
- You have decided to see a play and have paid £10 for a ticket. On entering the theatre,
- you find that you have lost it. Would you pay £10 for another ticket? 46% say YES
- Study 2:
- You are going to buy a calculator for £15 and a jacket for £125. A salesperson tells you
- the calculator is on sale in another branch of the store 20 minutes drive away. Would
- you make the trip? 68% say YES
- You are going to by a calculator for £125 and a jacket for £15. A salesperson tells you the
- calculator is on sale for £120 in another branch of the store 20 minutes away. Would
- you make the trip? 29% say YES
How can we explain the fact that humans don't reason as expected by EU?
- EU assumes that people have the mental resources acquired to reason rationally at all times, this is not the case though
- People might be tired or distracted and are acting in a reasonable way given their mental capacity
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