Decision-making II choosing between gambles neural basis of decision-makingDo we always make the best possible decisions?What are rational decisions?ExampleClassic Expected Utility ModelSlide 6Example (1)Example (2)Limitations of the Classic Expected Utility ModelViolations of TransitivityFraming effectExample: CheeseburgersSlide 13Slide 14Slide 15Prospect TheorySlide 17Slide 18Risk Aversion for GainsSlide 20Slide 21Individual DifferencesSubjective ProbabilityRationality up to a pointNeural Basis of Decision-Making & Role of EmotionsNeural Bases Of Expected Utility CalculationsSlide 27Anticipation of reward for same neuronsInvolvement of Emotional Areas in DecisionsThe Iowa Gambling TaskSlide 31Slide 32Behavioral Results with Normals and Patients with Ventromedial Prefrontal DamageSkin conductance results in same experimentResultsOne interpretation (controversial)Decision-making IIchoosing between gamblesneural basis of decision-makingDo we always make the best possible decisions?•Normative (or prescriptive) theories: tell us how we should make rational decisions–E.g. optimize financial gain•Descriptive theories: tell us how we actually make decisions, not on how we should make them.•Behavior can deviate from normative account in systematic waysWhat are rational decisions?•Decisions that are internally consistent–E.g., •if A>B, then B<A•if A>B, B>C, then A>C (transitivity) •Decisions that optimize some criterion–E.g. financial gain (classic expected utility theory)Example•What is the best choice?A) .50 chance of winning $20B) .25 chance of winning $48Classic Expected Utility Model•The utility of an outcome is a numerical score to measure how attractive the value associated with an outcome is to the decision-maker.•In classic expected utility model, we assume that utility = valueClassic Expected Utility Model•The expected utility is the summed utility of a each outcome, weighted by the probability of the outcome occurring.•A rational decision-maker should always choose the alternative that has the maximum expected utility.Expected Utility ( ) ( )i ip x u x=�probability utilityExample (1)•Gamble: if you roll a 6 with a die, you get $4. Otherwise, you give me $1.•Take the gamble?•Expected utility = p(win)*u(win) + p(lose)*u(lose)=(1/6)*(4)+ (5/6)*(-1)=-1/6•So...do not take betExample (2)•Which job would you accept:Job A:50% chance of a 20% salary increase in the first yearJob B:90% chance of a 10% salary increase in the first year•The classic expected utility model predicts Job A to be better (0.5 x 0.2 > 0.9 x 0.1)Limitations of the Classic Expected Utility Model•We can make “bad decisions”—that is, decisions that are do not make sense according to the expected utility model–Violations of transitivity–Framing effectsViolations of Transitivity•Transitivity: If you prefer A to B and B to C then you should prefer A to C.•Experiment included the following gambles (expected values were not shown):•Result: subjects preferred:–A>B, B>C, C>D, D>E, but also E > A(Tversky, 1969)Framing effect•Problem 1:–Select one of two prizes(36%) An elegant Cross pen(64%) $6•Problem 2:–Select one of three prizes(46%) An elegant Cross pen(52%) $6 (2%) An inferior pen(Shafir & Tversky 1995)Example: Cheeseburgers 50% 50%Example: Cheeseburgers 50% 50% 10%30% 60%Framing effect•Version A: Imagine that you have decided to see a play where admission is $10 per ticket. As you enter the theater you discover that you have lost a $10 bill. Would you still pay $10 for a ticket for the play? •Version B: Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theater you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $10 for another ticket? (Tversky & Kahneman, 1981)Yes 46%No 54%Yes 88%No 12%Framing effect•Problem 1Suppose I give you $300, but you also have to select one of these two options:(A) 1.0 chance of gaining $100(B) .50 chance of gaining $200 and a .50 chance of gaining nothing•Problem 2Suppose I give you $500, but you also have to select one of these two options:(A) 1.0 chance of losing $100(B) .50 chance of losing $200 and a .50 chance of losing nothing(72%)(28%)(Tversky & Kahneman, 1986)(36%)(64%)Prospect Theory•For most people, the utility of an amount of money is not equivalent to the monetary value, it is based on the subjective utility•Example:What is the best choice? (A) .10 chance of winning $10 million dollars(B) .99 chance of winning $1 million dollars•Each additional dollar added to wealth brings less utility(“diminishing marginal utility effect”)Prospect TheoryDiminishing marginal utility: additional gains (or losses) are not valued as much as early gains (or losses)A hypothetical function relating subjective utility to valueProspect Theory Loss-aversionthe negative effect of a loss is larger than the positive effect of a gainRisk Aversion for GainsExampleGamble 1: win $20 with 50% chance or $60 with 50% chanceGamble 2:win $40 with 100% chanceRisk Aversion for GainsMonetary Value ($)Utility0 20 40 60 80 100100 60 40 20 80ExampleGamble 1: win $20 with 50% chance or $60 with 50% chanceGamble 2:win $40 with 100% chanceWhat would a person choose with the subjective utility function shown on left?Gamble 1: 74x0.5+100x0.5=87< Gamble 2: 92x1=92Prospect Theory concave utility function for gains: Risk-aversion for gainsconvex utility function for losses: Risk seeking for lossesIndividual DifferencesDecision Maker I(risk avoider)Decision Maker II(risk taker)Monetary ValueUtility0 20 40 60 80 100100 60 40 20 80Subjective Probability•The probability of an event might not be based on objective statistical calculations but might be based on a subjective estimate•Overweighting of small probabilities and underweighting of likely outcomesRationality up to a point•People have limitations in memory and time•Simon (1957)–Bounded rationality•we are rational, but within limits of human processing capabilities–Satisficing•We choose the first option that meets our minimum requirementspeople might satisfice when making decisions such as buying a carNeural Basis of Decision-Making & Role of EmotionsNeural Bases Of Expected Utility CalculationsGlimcher (2003)Fiorillo, Tobler, and Schultz. Science. (2003)Reward