2 What is Rational: Normative. 4 Lottery & Gambling


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1 1 Decision Making 2 What is Rational: Normative Key Question: Are you Rational? Deviations from rationality: Value is subjective (utility, and more..). Value is multidimensional (multiple budgets, not one). Loss aversion: we don t like to lose. Thought aversion: don t like to think (shortcuts instead). Representativeness, Availability, Anchoring Heuristics. Don t use base rates, sample sizes, statistical trends. Normative theory = what you should do. (Descriptive theory = what you actually do). Consistency: same decision each.. time, version of question, etc.. Transitive: same ordering across multiple choices: Chicken Fish; Tofu; Therefore: Chicken Tofu Expected value: multiply odds of thing happening by value: a).10 (10%) chance of winning $10 million dollars. Expected value (EV) =.1 * 10 = $1 mil. b).99 chance of winning $1 million dollars. Expected value (EV) =.99 * 1 = $.99 mil. 3 Utility and Value Utility is more relevant than value.. You re broke and hungry.. a).85 chance of winning $8 (EV = $6.80) b).25 chance of winning $28 (EV = $7.00) Yeah, but I want to have a better chance of eating: a) please! Certainty has utility: a).10 chance of winning $10 million dollars (EV = $1 mil). b).99 chance of winning $1 million dollars (EV = $.99 mil). You ll take the certain mil over the uncertain 10 mil.. 4 Lottery & Gambling Lottery: utility of $3 million is much higher than $1. a) 1.0 chance of winning $1 (EV $1) b) chance of winning $3 million (EV = $.42) Gambling is the same deal: you put in small change (nickel slots) for the chance of winning big, even though on average you re a loser. Problem: Utility is inherently subjective (what would Bill Gates do??) can t have a normative theory based on subjective judgments.
2 5 Loss Aversion (and Violation of Rationality!) 1. I give you $300, and you must select one of these options: a) (72%) 1.0 chance of gaining $100 (EV $400). b) (28%).50 chance of gaining $200,.50 of gaining $0 (EV $400). 6 Problem Framing Previous example shows that answers depend on how the problem is framed (i.e., framing effects). The normative, rational view of decision making says that framing effects should not exist, but clearly they do. 2. I give you $500, and you must select one of these options: a) (36%) 1.0 chance of losing $100 (EV $400). b) (64%).50 chance of losing $200,.50 of losing $0 (EV $400). (xx%) shows people choose a) in choice 1, but b) in choice 2.. We want certain gains but are willing to take a risk if it means we might lose less: we are averse to loss! 7 We are Accountants with Different Balance Sheets 1. You lose $100 play tickets on way to theatre, but can buy new ones at box office, do you? (46%) 2. You lose $100 cash on way to theatre, and can refund tickets to cover $100 loss, do you? (98%) 3. You lose $100 cash on way to theatre, and haven t paid for $100 tickets yet, do you buy? (??%) In 1, you will have spent $200 in the theatre account, but in 2, 3 you spent only $100 (other $100 was just in cash account.) We keep track of where $ is spent and don t want pay too much out of a given account $ is not just $ (psychic budgets). 8 Relativity Effects Another version of $ is not just $: Dealer 1 has car for $15,000, dealer 2 for $14,975 who cares? Store 1 has briefcase for $75, store 2 for $50 such a deal! $25 relative to $15,000 is.167%, but relative to $75 its 33% Other examples?? Anyone bought a house? Choose one: a) (36%) An elegant Cross pen. b) (64%) $6. a) (46%) An elegant Cross pen. b) (52%) $6. c) (02%) An inferior pen (makes Cross pen look relatively better).
3 9 Sunk Costs Anybody walk out of a bad movie? (which one?) Once you ve invested that $7.50 into a movie, by gum you re going to get your $ s worth.. I have this problem with finishing food on my plate.. The thing is, once you ve paid, you can t get your $ back (sunk costs), so you might as well do whatever makes you happiest.. 10 Procedure Invariance Previous examples are violations of description invariance. Procedure invariance is when we vary how you make your bet. a) (71%) 8/9 chance to win $4 (EV=$3.56). b) (29%) 1/9 chance to win $40 (EV=$4.45). What is minimum price you would sell your right to this choice? Now, 67% give a higher price to b) over a)! (don t want the other guy to make it big..) 11 Transitivity Gamble Odds Payoff EV A 7/ B 8/ C 9/ D 10/ E 11/ For all neighbor pairs,,, etc cuz payoff increase looked bigger than odds decrease (odds = colored portion of a wheel of fortune ). 12 Shortcuts (Heuristics) We re obviously not rational; we re lazy and we take shortcuts. Psychologists are wordy & use heuristics (rules of thumb). Heuristics are usually effective they get the job done. but we can trick people (just as with visual illusions) to find out what heuristics are being used.. But because now the odds looked substantially different! This is a violation of transitivity..
4 13 Representativeness 14 Representativeness Linda is a classic: Linda is 31 yrs 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 of these is more likely: a) Linda is a bank teller. b) Linda is a bank teller and is active in the feminist movement. The laws of probability say that it is impossible for b) to be more likely than a) because b) is more restrictive than a). (I personally think Linda is unlikely to be satisfied with herself if she were just a bank teller b) is more likely!) It all comes back to chickens vs. canaries: we reason based on prototypes. Things are judged to be more likely if they are more like our prototypes (representativeness = more like prototype). Another example: which is more likely sequence of coin tosses: a) HHHHH b) HTTHT b) looks more representative of random, so we choose it (but odds are actually identical!) 15 Availability 16 Availability & Selffulfilling Prophesy The more events you can recall that fit the description, the more probable you think this thing is. Are there more words in English that start with R, or have R as the 3rd letter? Words are organized by first letter in our minds easy to recall R words.. How many committees of size X can be formed among 10 people? X = 2? X = 5? X = 8? We often end up noticing more the things that fit with our existing beliefs. Professors are all nerdy.. You notice the nerdy professors more, and think they are all that way.. (illusory correlation) Other examples? A s & B s: 2/3 positive facts & 1/3 negative for each. but B s had only 12 statements vs. 24 for A s S s overestimated negative aspects of B s: very rare and thus noticeable.. (rare or common = available; middle = ignored..).
5 17 Anchoring Anyone good at bargaining here? I had an experience in Morocco... Key principle: seller starts high, buyer starts low. This anchors the estimate of worth we then reason in adjustments to this anchor. Damage assessments by fake juries: Cancer patient initially seeks $100, $20,000, $5M, or $1G; influences size of compensation awarded.. 18 Stuff we Ignore We ignore lots of statistical information that is actually useful for making better decisions.. Sample size: accuracy of estimate goes up with sample size. Base rate: overall probability of events is important! Regression to the mean: slumps and streaks are natural. 19 Base Rate Neglect Lots of ink has been spilled over this issue.. Classic example: Blue cabs are 85% of cabs; Green are 15% (these are base rates). Cab is involved in hitandrun. Eyewitness thinks it was Green; but only 80% correct in judging this in tests. What are odds it was green? What if there wasn t an eyewitness?? Think about it.. What are chances of seeing a Penguin in Paris, France? 20 Regression to the Mean If you do above average one day, you re likely to do worse next time. If you do worse than average, you re likely to do better. You see, you are just very likely to be around your average.. If the Broncos win one week, likely to lose (badly) the next, because w/out Eddie Mac, their avg isn t so hot.. Many, many examples.. If evidence is strong, you should ignore base rate If base rate is strong, you should ignore evidence..
6 21 Other Approaches Read Alternative Concepts of Optimality for your own edification.. Frequency vs. probability vs. conditional probability vs. whatever.
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