1. Psychology 485 March 23, 2010

2.  Intro & Definitions Why learn about probabilities and risk?  What is learned? Expected Utility Prospect Theory Scalar Utility Theory

3.  In the lab, reinforcement is often uniform Choose correct  reinforcement Choose incorrect  no reinforcement

4.  In real life, different choices lead to varying outcomes Different probability of rewards Trade-offs

5. -Good size (preferred) -Fast & Vigilant (harder to catch) -Smaller (less preferred) -Slower & less Vigilant (easier to catch) What to hunt??

6.  Utility Economic term: relative satisfaction gained from consumption of goods & services Relative benefit gained from a given choice  Lion hunt Impala: high utility, high risk Warthog: low utility, low risk  How is utility balanced with risk and probability?

8. OR? 100% chance for $100 50% chance for $200

9.  The “correct” answer  Expected Value = Value * Probability Choice 1 = 1.0 * $100 = $100 Choice 2 = 0.5 * $200 = $100  But, people and animals don’t act this way!

10.  Choice: Guaranteed $1 OR 1/80 chance at $100 1.0 * $1 = $10.0125 * $100 = $1.25  But, there is no $1.25 payout $0, $1 or $100

11.  Change in utility is not linear The more you have of a resource, the less valuable it becomes You may not take the $1 because it doesn’t make much difference to you... But homeless?

12.  Expected Utility Expected Utility = Probability * Utility  Large gains are devalued $200 ≠ 2 * $100 4 pellets ≠ 4 * 1 pellet Value Utility

13.  Requires a ‘rational’ decision maker  Must understand the following: Completeness  be able to evaluate options; A>B, A<B or A=B Transitivity  If A>B and B>C, then A>C Independence  Probabilities are independent of each other Continuity  If A>B and B>C, there should be some combination where A+C=B  But people often act irrationally

14.  Birthday problem: What are the chance 2 people in a room have the same birthday?  Calculate probability of not being born on the same day: First person – born any day – 365/365 (1.0) Second person – born any other day – 364/365 Third person – born any day except those 2 – 363/365 (365 * 364 * 363) / (365 * 365 * 365) = 0.992 probably that those 3 people won’t be born on the same day  In a room or 25 people, drops to 0.43 Better than 50/50 chance that 2 people share the same birthday!

15.  Birthday paradox shows reliance on heuristics We don’t estimate probability accurately  e.g. Availability heuristic More frequent: words that start with ‘r’ or have ‘r’ as 3 rd letter? Words that start with ‘r’ jump to mind more easily!

16. OR? 100% chance for $100 80% chance for $140

17. OR? 25% chance for $100 20% chance for $140  Results: 1. Most people (78%) choose $100 II. Most people (58%) choose $140

19.  Models real-life decision making  Prospect = subjective probability  Expected Utility = prospect * utility Concave for gains Convex for losses Gains Losses Value

20.  1% risk of $1000 loss, or buy insurance for $15 1.0 * $15OR 0.01 * $1000  People tend to be: Risk averse for gains (i.e. Take the guaranteed payoff) Risk prone for losses (i.e. More likely to chance it and not by insurance)

21.  Does this pattern apply to animals?  Bateson & Kacelnik (1995) Amount:  Red key = 100% * 3 grains  Green key = 50/50 * 1 or 5 grains Delay  Red key = 100% * 20s delay  Green key = 50/50 * 5s or 60s delay

22.  Results show starlings are: Risk-seeking for delay Risk-averse for amount  Not gains and losses like humans

23.  What other factors can affect subjective probability (prospect)? Reference Points Framing

24.  From the perspective of expected utility Important to determine whether something is seen as gain or loss Anchor point  e.g. Tickets to Olympic gold medal hockey game

25.  Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people.  Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: If Program A is adopted, 200 people will be saved. If Program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved.  Which of the two programs would you favor?

26.  Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people.  Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: If Program C is adopted, 400 people will die. If Program D is adopted, there is 1/3 probability that no one will die, and 2/3 probability that 600 people will die.  Which of the two programs would you favor?

27.  First problem: A: 72%. B: 28%  Second problem: C: 22%. D:72%  Framing of the problem as gain or loss affects risk sensitivity

28. -Good size (preferred) -Fast & Vigilant (harder to catch) -Smaller (less preferred) -Slower & less Vigilant (easier to catch) What to hunt??

29. -Wet season, lots of vegetation so easy to sneak up on prey -Assume for now, impala only available during wet season -Lions are well-fed during wet season -Dry season, little vegetation so hard to sneak up on prey -Lions are not well-fed during wet season -Assume warthog only available during dry season Hunger

30.  Now assume a lion came upon an impala and warthog at the same time... Based on utility, which one should it prefer?

32.  Based on animal data  Includes information about timing Based on Scalar Expectancy Theory  Temporal Discounting: $100 todayOR$110 next year? Based on utility, should choose later Later rewards

33.  Scalar Expectancy Theory Pacemaker (Pulse Generator) Accumulator Working Memory Reference Memory Ratio Comparator Decision or Response

34.  Internal representation of probability i.e. How variable/risky is a particular choice?  Compare to expectations What are you used to getting? Is a choice worth the risk (i.e. Is possibility greater than expected reward?)

36. Time of day Energy reserves Option 1 = low risk, low payoff Option 2 = high risk, high payoff Option 1 Option 2

37.  Black-eyed Juncos tested on risk sensitivity under two outside temperatures Risk averse when warm Risk prone when cold  In cold temps, need more food to survive