Cognitive and computational limitations and bounded rationality

Transcription

1 and bounded April 12, /54

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3 Ambiguous objects 3/54

4 Kanisza s triangle 4/54

5 Muller s arrows 5/54

6 Size from context 6/54

7 Shepard s tables 7/54

8 Beau Deeley s illusions 8/54

9 Esher s waterfall 9/54

10 summary is among the most (if not the most) valuable cognitive system. Nature had a long evolutionary horizon to perfect it. The brain interprets and gives meaning to ambiguous visual inputs and fills in the gaps of visual experience. Contextual information is crucial for generating meaning and can change the way we see things. Experienced visual illusions can be very persistent, suggesting that such a perfected instrument such as the visual system can lead to consistent biases. These biases were known and exploited by artists and architects, in the same way that marketing people exploit choice biases. 10 / 54

11 Reasoning: Wason s selection task What card or cards do you need to turn over to test the rule If there is a K on one side there is a 2 on the other, to see if it is violated? 11 / 54

12 Reasoning: Wason s selection task The problem can be solved by choosing the cards using modus ponens and modus tollens. 12 / 54

13 Heuristics and bias 13 / 54

14 Cognitive biases 14 / 54

15 Anchoring and adjustment What is the freezing point of Vodka? How long is Mars orbit around the sun? 15 / 54

16 Anchoring and adjustment Cognitive load, time pressure and alcohol reduce adjustment (Epley and Gilovich, 2006). Bias increases with anchor extremity (Russo and Shoemaker, 1989). Uncertainty increases anchoring Jacowitz and Kahneman, 1995). 16 / 54

17 Availability of extreme events Making judgements about the frequency of likelihood of an event based on the ease with which evidence or example come to mind. 17 / 54

18 Representativeness A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80 % of the time and failed 20% of the time. What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue? 18 / 54

19 Representativeness Most subjects gave probabilities over 50%, and some gave answers over 80%. The correct answer, found using Bayes theorem, is lower than these estimates: There is a 12% chance (15% times 80%) of the witness correctly identifying a blue cab. There is a 17% chance (85% times 20%) of the witness incorrectly identifying a green cab as blue. There is therefore a 29% chance (12% plus 17%) the witness will identify the cab as blue. This results in a 41% chance (12% divided by 29%) that the cab identified as blue is actually blue. 19 / 54

20 Representativeness 20 / 54

21 Conjunction fallacy Linda is 31 years 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 anti-nuclear demonstrations. Which is more probable? Linda is a bank teller. Linda is a bank teller and is active in the feminist movement. 21 / 54

22 Hindsight bias The hindsight bias is an shortcoming of the availability and representativeness heuristics. It was initially studied by Baruch Fischhof and Ruth Beyth. In the first experiments participants were asked to judge the likelihood of US president Richard Nixon s upcoming visit to Beijing and Moscow, such as whether Nixon with meet the Chinese president Mao, whether he will declare the visit a success, etc. Some time after president Nixon s return, participants were asked to recall (or reconstruct) the probabilities they had assigned to each possible outcome, and their perceptions of likelihood of each outcome was greater or overestimated for events that actually had occurred. 22 / 54

23 The hot hand fallacy 23 / 54

24 Sunk cost fallacy As president of an airline company, you have received a suggestion from one of your employees. The suggestion is to use the last 1 million dollars of your research funds to develop a plane that would not be detected by conventional radar, in other words, a radar-blank plane. However, another firm has just begun marketing a plane that cannot be detected by radar. Also, it is apparent that their plane is much faster and far more economical than the plane your company could build. The question is: should you invest the last million dollars of your research funds to build the radar-blank plane proposed by your employee? 24 / 54

25 Sunk cost fallacy As the president of an airline company, you have invested 10 million dollars of the company?s money into a research project. The purpose was to build a plane that would not be detected by conventional radar, in other words, a radar-blank plane. When the project is 90% completed, another firm begins marketing a plane that cannot be detected by radar. Also, it is apparent that their plane is much faster and far more economical than the plane your company is building. The question is: should you invest the last 10% of the research funds to finish your radar-blank plane? 25 / 54

26 Gambler s fallacy At the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, with a probability of around 1 in million. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red. I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls. Pierre Simon Laplace, / 54

27 Regression fallacy On many occasions I have praised flight 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. 27 / 54

28 The endowment e ect 28 / 54

29 Framing 29 / 54

30 Default e ects (Johnson and Goldstein, 2003) 30 / 54

31 Nudges Thaler and Sunstein A nudge, as we will use the term, is any aspect of the choice architecture that alters people s behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not. 31 / 54

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33 Decoy e ects 33 / 54

34 Decoy e ects 34 / 54

35 Overconfidence People judgments are often miscalibrated, people overestimate the chances of events when their own competences have an e ect on the outcome. Wishful thinking: overestimate the likelihood of an event because of its desirability (see Krizan and Windschitl, 2007). Illusion of control: People may behave as if they have control when they have none (Langer, 1975). 93% of American drivers rate themselves as better than the median (Svenson, 1981). People tend to overestimate their rate of work or to underestimate how long it will take them to get things done (Buehler et al., 1994). 35 / 54

36 Unskilled but unaware of it 36 / 54

37 Availability of extreme events revisited Estimate the expected utility of an action. Generate samples of the possible outcomes of the actions. Drawing these samples is costly. 37 / 54

38 Importance sampling Lieder, Gri ths and Hsu (2018) 38 / 54

39 Importance sampling Lieder, Gri ths and Hsu (2018) 39 / 54

40 Anchoring and adjustment revisited Estimate a quantity based on memory and other cues. Draw samples using the Metropolis-Hastings algorithm. The cost increases linearly as a function of time. 40 / 54

41 Drawing information from memory Lieder, Gri ths, Huys and Goodman (2017). 41 / 54

42 Drawing information from memory Lieder, Gri ths, Huys and Goodman (2017). 42 / 54

43 The evolution of cooperation Originally framed by Flood and Dresher and formalized by Tucker. Axelrod asked game theorist to submit strategies which were translated to computer coded paired randomly against each other in a 200 round competition. 43 / 54

44 The evolution of cooperation Tic-for-tat a simple strategy that retaliated when the opponent did not cooperate dominated the competition. 44 / 54

45 Ultimatum game 45 / 54

46 The public good game In the basic game, subjects secretly choose how many of their private tokens to put into a public pot. The tokens in this pot are multiplied by a factor (greater than one and less than the number of players, N) and this public good payo is evenly divided among players. Each subject also keeps the tokens they do not contribute. The group s total payo is maximized when everyone contributes all of their tokens to the public pool. Yet the Nash equilibrium in this game is simply zero contributions by all. The actual levels of contribution found varies widely, and depend on the multiplication factor. 46 / 54

47 Altruistic punishment People are willing to forego profits to punish people that defect from cooperation, although this is irrational (Fehr and Gaechter 47 / 54

48 Roger s paradox 48 / 54

49 Why copy others? Rendell et. al armed multi-armed bandit with exponentially distributed pay-o s. The environment was non-stationary and there was a small probability that they pay-o s would change. Submitted strategies could either innovate, observe or exploit. Evolutionary dynamics were realized by killing 1/50 of the agents and replacing them with o spring rounds in total. 49 / 54

50 Ulysses and the sirens 50 / 54

51 Cognitive dissonance and sour grapes 51 / 54

52 Probing our memory Nickerson and Adams (1979) 52 / 54

53 Remembering too much [I]n my country, when they would say a man has no sense, they say, such an one has no memory; and when I complain of the defect of mine, they do not believe me, and reprove me, as though I accused myself for a fool: not discerning the di erence betwixt memory and understanding, which is to make matters still worse for me. But they do me wrong; for experience, rather, daily shows us, on the contrary, that a strong memory is commonly coupled with infirm judgment. Montaigne essays. 53 / 54

54 More is less in memory: the recognition heuristic Which German city is larger in population, Leipzig or Jena? 54 / 54