Descriptive Decision Theory. Logic and Decision Making Unit 3

Transcription

1 Descriptive Decision Theory Logic and Decision Making Unit 3

2 How do we really decide?

3 Anatomy of decisions De?ine the problem Identify the criteria Gather information, analyze the situation Weight the criteria Generate alternatives Evaluate alternatives Compute optimal decision Act on the decision Posterior evaluation

4 Do we really behave in this way? Video

5 System 1 and System 2 System 1: fast, automatic, effortless, emotional Interpreting verbal language or visual information System 2: slower, conscious, effortful, logical Most people (and most managers) often rely on System 1 thinking because they trust on their intuitions When should they trust it? When they should not? Also if people are intelligent and generally successful, their judgments systematically deviate from rationality The objective is to improve your judgment

6 Longer! Larger!

7 Bounded rationality H. Simon: individual judgment is bounded in its rationality and decision making can be better understood by explaining actual decision (not by prescriptive methods) We satis?ice : in complex situations, rather than examining all possible alternatives we simply search for a satisfactory solution (and then, usually, we stop) The descriptive approach helps clarifying recurrent mistakes when better strategies are needed what other abilities should be trained

8 Heuristics When making decisions, people rely on heuristics, i.e. simplifying strategies, or rules of thumb, or shortcuts, that help with coping in complex environments heuristics are helpful (they often lead to adequate decisions), but they may also lead to severe errors The logic of using them is that, on average, any loss in decision quality is outweighted by time saved People use a variety of heuristics; for example availability, representativeness, positive hypothesis testing, affect heuristics

9 Availability heuristics Our minds generally recall instances of events of greater frequency more easily than rare events But the availability of information is also affected by other factors unrelated to the objective frequencies (such as vividness, easiness of imagination, evoking of emotional reactions) As a consequence, we too easily assume that available recollections are representative of the events existing outside our range of experience

10 Consider P1. Your answers: Ease of recall

11 Ease of recall (cont d) Consider P2 and P35. Your answers: 100% gave answers so that the sum of causes in P35 exceeds the percentage given in P2 In P1: vivid deaths tend to get a lot of press coverage The availability of vivid stories in the media biases our perception of the frequency of events In P2/P35: when no suggestions are given estimation are lower but more real; with suggestions, estimation are emphasized (more time spent, and no time devoted to opposite events) hence, thinking more isn t (always) thinking better Thus, managerial decisions may be heavily affected by distorted frequencies

12 Retrievability Consider P3 and P36. Analysis done on < words contained (of?icial italian) 1) italian words beginning with R : 6334 (6.8%) 2) Italian words with R in 3rd pos.: 8882 (9.6%, i.e. +40%) Your answers (22 respondents): some of you gave strange answers: 8 said (1) + (2) is greater than 50% (?); anyway, 9 said (1) is higher than (2), 11 said the opposite

13 Retrievability (cont d) In P3/P36: we are better at retrieving words from memory using the word s initial letter than the word s 3rd letter (and so we overestimate them) Sometimes the world structures itself according to our search strategies Multiple restaurants or gas station at the same intersection, biggest bookstores located close to each other (so they maxmize their customer traf?ic)

14 Representativeness Heuristics People often base their predictions/decisions on the base of an established category of situations that the problem somehow represents predicting a person s performance, or the success of a new business, based on the similarity with past performances This simplifying heuristic can serve us well, because the likelihood of a speci?ic occurrence is usually related to that of similar types, but people rely on that also with insuf?icient information people tend to overuse it when making decisions it can work at an unconscious level (for example in discrimination: race, social classes, etc.)

15 Insensitivity to Base Rates Consider P4. The correct answer, using Bayes, is 7.9% (answer A) Your answers: only 4 (18%) answered correctly, 61% answered D or E People tend to ignore the base rates For example, in P4 people ignore that the base rate of Down syndrome is only 1/1000 When prenuptial agreement is avoided, individuals approach marriage with the false belief that the high base rate for divorce does not apply to them People use base rate data correctly when no other information is provided

16 Insensitivity to Sample Size Consider P5. The correct answer is B Your answers: only 9 (41%) answered correctly, 59% answered A or C Born/day 50% 40% - 60% Larger Contrary to what statistics tells, most individuals expect the hospitals to record a similar number of days on which more than 60% are boys (answ. C) Sample size is fundamental in statistics, but rarely part of our intuition: people think only about how representative it would be for 60% babies born to be boys in a random event Smaller

17 Misconception of Chance Consider P6. The correct answer is B Your answers (22 respondents): 11 of you (50%) misjudged the probabilityrelying on representativeness, intuition suggests that having 4 girls in a row is unlikely (but the gender determination has got no memory) You have to estimate p(4 girls 3 girls), not p(4 girls) In tossing a coin: what is more likely, THHTTHTH or TTTTHHHH? The logic concerning misconception explain the gambler s fallacy (take to be dependent what isn t) The hot hand in sport does not exist: we see patterns everywhere, but it is a combination of skills and luck

18 Regression to the Mean Consider P7. These are statistical data of the Blue Jay s players , ,275 0, , , , (68%) of you maintained the positions, just shifting the averages

19 Regression to the Mean (cont d) This concept is counterintuitive because the representativeness heuristic suggests individuals that future outcomes (this year s sales) are directly predictable from past outcomes (last year s sales), i.e. assuming perfect correlation It becomes intuitive when the performance is very extreme (so that it is dif?icult it lasts)

20 Kahneman on regression to the mean I had the most satisfying Eureka experience of my career while attempting to teach 9light instructors that praise is more effective than punishment for promoting skill- learning. When I had 9inished my enthusiastic speech, one of the most seasoned instructors in the audience raised his hand and made his own short speech, which began by conceding that positive reinforcement might be good for the birds, but went on to deny that it was optimal for 9light cadets. He said, On many occasions I have praised 9light cadets for clean execution of some aerobatic maneuver, and in general when they try it again, they do worse. On the other hand, I have often screamed at cadets for bad execution, and in general they do better the next time. So please don t tell us that reinforcement works and punishment does not, because the opposite is the case. This was a joyous moment, in which I understood an important truth about the world: because we tend to reward others when they do well and punish them when they do badly, and because there is regression to the mean, it is part of the human condition that we are statistically punished for rewarding others and rewarded for punishing them. I immediately arranged a demonstration in which each participant tossed two coins at a target behind his back, without any feedback. We measured the distances from the target and could see that those who had done best the 9irst time had mostly deteriorated on their second try, and vice versa. But I knew that this demonstration would not undo the effects of lifelong exposure to a perverse contingency.

21 Conjunction Fallacy Consider P8. Your answers (22 resp.): 19 (86%) said bank+fem is more likely than bank alone 4 (18%) said bank+fem is more likely than fem

22 Conjunction Fallacy (cont d) Linda s pro?ile is taken to be more representative of a feminist, then of a feminist bank teller, then of a bank teller, but B = Linda is a bank teller F = Linda is a feminist Then p(f) p(f and B) and p(b) p(f and B)

23 Positive Hypothesis Testing When assessing the association between two events, people usually do not recall all the situation Example: in assessing if marijuana is related to delinquency, people typically try to remember whether marijuana users were delinquents This leads to a series of biases (con?irmation, hindsight) and in?luencing phenomena (anchoring, overcon?idence)

24 Con?irmation trap Consider P9. Your answers: A0empts # Resp. Perc. All numbers % All posihve numbers % Including the sequence % All 2- increasing sequences 8 36% At least two 2- increasing sequences 10 45% All sequences with a final sum 2 9% All with a fixed increment 11 50% Three different choices (OK!) 3 14% well done! J (but not perfect: a 2- increasing sequence is anyway included L

25 Con?irmation trap (cont d) If you want to guess the rule, given that satis?ies it, you should?irst understand which properties can be positive numbers, numbers, numbers within a certain range increasing by 2, increasing by a?ixed number, summed to a constant number, multiples of 2, increasing the?irst is the sum of the?irst two it opens the door to more complex rules: the third is the product of the?irst two minus 2, the third is the product of the?irst two minus the?irst, and so on Or strange ones, like number 2 is in or the third number is 6 A lot (but not all) of these properties can be mixed Rational attempts: try to submit sequences where properties are missing. For example, I should start with - 9, - 6, - 3 or with - 25, - 6, 13, and so on

26 Con?irmation trap (cont d) People naturally tend to seek information that con?irms their expectations and hypothesis, even when discon?irming and falsifying information is more useful Two main causes: the way we retrieve information from memory (mere hypothesis makes information accessible), and the selective search for information where we think it can be more likely found (giving special credence to information that allows to reach a desired conclusion) It pervades our decision- making processes, where discon?irming evidence provide the most useful insights (buying, hiring an employee, starting a new business, and so on)

27 Anchoring Consider P10. The correct answer is Consider P11 and P37. Your answers: In P11, 59% says the salary is higher than in P37, 0% says it is smaller

28 Anchoring (cont d) We pay attention to irrelevant anchors for at least 2 reasons: We often develop estimates starting form an initial anchor, then we adjust it to yield a?inal answer When anchors are subliminal, they lead us to think information that is consistent with it, rather than inconsistent with it The power of anchoring can be explained by con?irmation heuristic and the selective accessibility to hypothesis- consistent information

29 Anchoring (cont d) Other examples: In education, teachers tend to expect little from children assigned to the lowest group, more from the others We all fall victim of the?irst- impression syndrome when meeting someone for the?irst time A person s race anchors our expectations of their behavior In a restaurant, more expensive wines anchor us to higher expenditures The classical example of subscriptions to the Economist review

30 Without the only print option 68% 32%

31 Conjunctive- and Disjunctive- Events Bias Consider P12. Your average answers: 12 (55%) said B is more probable than C Most common ordering: B A C Correct answer: C A B Disjunctive event Conjunctive event

32 Conjunctive- and Disjunctive- Events Bias (cont d) There is a general tendency to overestimate the probability of conjunctive events, and to underestimate the probability of disjunctive events or that occur independently This explains why projects with multistage planning have problems (timing, budgets), why we are too optimistic in our assessment of a project s cost and time frame Even when the likelihood of failure is slight, an overall failure can be high if many components are involved

33 Overcon?indence Consider P13. Your answers: Ques;on MarHn Luther King Nile River OPEC Old Testament Moon diameter 747 weight Mozart Elephant Tokyo- London Ocean depth Correct Answer KM KM KG KM M # good es;mates 14 (67%) 3 (14%) 12 (57%) 3 (14%) 4 (19%) 0 (0%) 8 (38%) 0 (0%) 5 (24%) 10 (47%) # exact/student 10 (0%) 9 (0%) 8 (0%) 7 (0%) 6 (5%) 5 (0%) 4 (19%) 3 (33%) 2 (38%) 1 (0%) 0 (5%) The smart (1Q) (2Q) (3Q) (4Q) (5Q) (6Q) and so on 2 are wrong! (1 and 6) Most people surround only between 3 and 7

34 Overcon?indence Most of us are overcon?ident in the precision of our beliefs and do not acknowledge our true uncertainty While con?idence in our abilities are necessary for achievements in life, overcon?idence can be a barrier in decision making Unwarranted con?idence can be bene?icial in some situation, for example can increase the social status, give greater power to sway others and make achieve higher success but the downside is that the overcon?ident person may convince themselves that they are more skilled and capable than they really are

35 Hindsight The Hindsight bias is when, after an event occurs, we feel we already knew what was going to happen Last seconds of a game your team is loosing; after the error you shout I knew that was a bad play After a six- month study on customers behavior, someone tells you I could have told what the results were going to be We are typically not good at reconstructing the way an uncertain situation appeared to us before?inding out the results of the decision Knowledge of the outcome works as an anchor by which individuals interpret their prior judgments of the event s likelihood It reduces our ability to learn from the past

36 Blindness Video

37 Inattentional Blindness By focusing on one task, most people miss very obvious information, thus violating assumptions about our visual awareness People have the tendency not to see what they are not looking for, even when they are looking directly at it Inattentional blindness provides evidence that we may overlook a wide array of information that is available in the environment

38 Change Blindness Video

39 Focalism and Focusing Illusion Focalism is the common tendency to focus too much on a particular event and too little on other events that are likely to occur concurrently Focusing illusion is the tendency of people to make judgments based on their attention to only a subset of the available information, to overweight it and underweight unattended information What is the probability that Italy will win the World Cup? Have you considered the probability that other teams will win? Many decision makers err by limiting their analysis to only some data, rather than looking at all the data

40 Bounded Awareness in groups While individuals awareness is bounded by the information they mentally consider, the awareness of groups is bounded by the information that becomes part of the discussion Groups tend to focus and discuss more shared information (previously known to all group members) than unshared information (previously known by only one group member), although groups are usually brought together to share unique or individual information

41 Bounded Awareness Monty Hall (a switch is always offered) You have to switch Mean Monty (If a switch is offered with the goal of minimizing the likelihood that you get the prize) You do not have to switch Minor changes can make a huge difference in the optimal strategy. Games like this show that people miss these little changes