Prospect Theory

Prospect TheoryPsychology 485March 23, 20101OutlineIntro & DefinitionsWhy learn about probabilities and risk?What is learned?Expected UtilityProspect TheoryScalar Utility Theory2

Choices, choices, choices...In the lab, reinforcement is often uniformChoose correct reinforcementChoose incorrect no reinforcement

3Choices and RiskIn real life, different choices lead to varying outcomesDifferent probability of rewardsTrade-offs

4In the wild...

Good size (preferred)Fast & Vigilant (harder to catch)

Smaller (less preferred)Slower & less Vigilant (easier to catch)What to hunt??5UtilityUtilityEconomic term: relative satisfaction gained from consumption of goods & servicesRelative benefit gained from a given choiceLion huntImpala: high utility, high riskWarthog: low utility, low riskHow is utility balanced with risk and probability?6Expected Utility Theory7Risky Decisions

OR?100% chance for $10050% chance for $2008Expected ValueThe correct answer

Expected Value = Value * ProbabilityChoice 1 = 1.0 * $100 = $100Choice 2 = 0.5 * $200 = $100

But, people and animals dont act this way!9Expected Values: exampleChoice:Guaranteed $1 OR 1/80 chance at $1001.0 * $1 = $10.0125 * $100 = $1.25

But, there is no $1.25 payout$0, $1 or $100

10Marginal UtilityChange in utility is not linearThe more you have of a resource, the less valuable it becomesYou may not take the $1 because it doesnt make much difference to you... But homeless?

11Expected UtilityExpected UtilityExpected Utility = Probability * Utility

Large gains are devalued$200 2 * $1004 pellets 4 * 1 pelletValueUtility12Expected Utility TheoryRequires a rational decision makerMust understand the following:Completeness be able to evaluate options; A>B, AB and B>C, then A>CIndependenceProbabilities are independent of each otherContinuityIf A>B and B>C, there should be some combination where A+C=BBut people often act irrationally13Understanding ProbabilityBirthday 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 364/365Third person born any day except those 2 363/365(365 * 364 * 363) / (365 * 365 * 365) = 0.992 probably that those 3 people wont be born on the same dayIn a room or 25 people, drops to 0.43Better than 50/50 chance that 2 people share the same birthday!14Understanding ProbabilityBirthday paradox shows reliance on heuristicsWe dont estimate probability accuratelye.g. Availability heuristicMore frequent: words that start with r or have r as 3rd letter?Words that start with r jump to mind more easily!15Allais ParadoxOR?100% chance for $10080% chance for $14016Allais ParadoxOR?25% chance for $10020% chance for $140Results:1. Most people (78%) choose $100II. Most people (58%) choose $14017Prospect Theory18Prospect TheoryModels real-life decision makingProspect = subjective probabilityExpected Utility = prospect * utilityConcave for gainsConvex for lossesGainsLossesValue19Losses: Insurance example1% risk of $1000 loss, or buy insurance for $151.0 * $15OR 0.01 * $1000People 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)20Animals?Does this pattern apply to animals?Bateson & Kacelnik (1995)Amount:Red key = 100% * 3 grainsGreen key = 50/50 * 1 or 5 grainsDelayRed key = 100% * 20s delayGreen key = 50/50 * 5s or 60s delay21Bateson & Kacelnik (1995)Results show starlings are:Risk-seeking for delayRisk-averse for amountNot gains and losses like humans22Subjective ProbabilityWhat other factors can affect subjective probability (prospect)?Reference PointsFraming23Reference PointFrom the perspective of expected utilityImportant to determine whether something is seen as gain or lossAnchor pointe.g. Tickets to Olympic gold medal hockey game 24Framing in HumansImagine 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?25Framing in HumansImagine 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?26Framing in HumansFirst problem:A: 72%. B: 28%Second problem:C: 22%. D:72%Framing of the problem as gain or loss affects risk sensitivity27Framing in Animals?Good size (preferred)Fast & Vigilant (harder to catch)Smaller (less preferred)Slower & less Vigilant (easier to catch)What to hunt??28In the wild...Wet season, lots of vegetation so easy to sneak up on preyAssume for now, impala only available during wet seasonLions are well-fed during wet seasonDry season, little vegetation so hard to sneak up on preyLions are not well-fed during wet seasonAssume warthog only available during dry seasonHungerHunger29FramingNow assume a lion came upon an impala and warthog at the same time...Based on utility, which one should it prefer?30Scalar Utility Theory31Scalar Utility TheoryBased on animal dataIncludes information about timingBased on Scalar Expectancy TheoryTemporal Discounting:$100 todayOR$110 next year?Based on utility, should choose laterLater rewards 32Scalar Utility TheoryScalar Expectancy TheoryPacemaker(Pulse Generator)AccumulatorWorking MemoryReference MemoryRatio ComparatorDecision or Response33Scalar Utility TheoryInternal representation of probabilityi.e. How variable/risky is a particular choice?Compare to expectationsWhat are you used to getting?Is a choice worth the risk (i.e. Is possibility greater than expected reward?)34What affects risk-sensitivity?35Risk and food storesTime of dayEnergy reservesOption 1 = low risk, low payoffOption 2 = high risk, high payoffOption 1Option 236Risk and food storesBlack-eyed Juncos tested on risk sensitivity under two outside temperaturesRisk averse when warmRisk prone when coldIn cold temps, need more food to survive37