PSYCH 240 1st Edition Lecture 19Outline of Last Lecture: Problem SolvingI. Skill AcquisitionII. Motor Program RepresentationsOutline of Current Lecture: Judgement and Decision MakingLecture 18 (continued)II.Expertise in Problem SolvingLecture 19I. Reasoning TaxonomyII. Normative Theories of Probabilistic ReasoningIII. Descriptive Theories of Probabilistic ReasoningCurrent Lecture: Lecture 18: Problem Solving (continued)1. Means-ends analysisi. Identify the largest difference btwn current state and goal stateii. Set as a subgoalreducing the differenceiii. Find and apply an operatorto reduce the difference iv. (if operator can’t be applied, new subgoal= remove obstacle that prevents applying the operator)v.a. Air Travel Examplevi. Goal: get to CaliforniaThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.vii. Operator: Fly in a plane1. Subgoal: get to airport2. Operator: driving cara. Subgoal: get to carb. Operator: walkingc. Apply walking operation to achieve subgoal3. Apply driving car operator to achieve sub-goalviii. Apply flying in plane operator to achieve goalb. Basic Logic of Means-end Analysisix.c. Productions for Tower of Hanoix. IFthe peg 3 is clear and the largest disk is free THENmove the largest disk to peg 3xi. IFthe largest disk is not free, THENset a subgoal to free itxii. IF a subgoal is to free the largest disk and a smaller disk is on it THENmove the smaller disk off2. Working Backwardsa. Transform goal state so it is more similar to the initial stateb. Useful if too many paths leading from initial statec. Examplesi. Useful for mazesii. Geometry Problem1.iii. The Water Lilies Problem1.d. Means-ends analysis can involve working backwardsi. Airport example1. Largest difference was the final step2. We solved the entire problem from the end backward before even taking our first step3. Gives impression that a problem-solver is contemplative, doing everything in head before taking action4. Probably not accurate for many problemsII. Expertise in Problem Solvingi. Expertiseusually helps ability to solve problems1. More experience2. Better representations3. More practice solving problemsii. But can sometimes harm:1. Functional fixedness2. Water jug “mental set”b. Very domain specific (chess study)i.1. In chess study, experts memory was no better than beginners2. Memory for meaningful configurations much better3. Memory for random configurations slightly worse (probably hindered byschemas)4. Chess masters know 50,000 chess patterns5. Chess masters intentionally study these patterns6. For any non-trivial domain, true expertise develops after 10,000 hours ofpractice (or about ten years)c. Power law of practicei. Talent or Motivation?1. Study compared 18 year old violinists:a. Some were international-level soloistsb. Others were very good (but at a level below)c. Estimated the number of hours spent practicing2. Best: 7,410 hours of practice3. Good: 5,301 hoursa. What makes someone an incredible athlete, musician, writer, chef, etc.? i. Nature or Nurture?4. Results: improvement follows a proper law:a. Improvement diminishes w/ timeb. It takes VERY long to gain the small amount of improvement that separates really good from greatc.d. Characteristics of expertisei. ACT-R Knowledge Compilation1. ACT-R predicts power law of practice because of: a. Proceduralization: take declarative knowledge and turn into productionsb. Composition: take several productions and join them together into oneii. More on expertise1. Rich, organized schemasa. Lots of well-organized declarative and procedural knowledgeb. More sophisticated representations2. Spends more time on representationa. Experts take longer to start solution, but let time to complete it3. Recognize subcomponents4. Less Means-End analysisa. Pre-stored solutions in long term memoryb. Fewer demands on working memory5. Move forward, not backwardLecture 19: Judgement and Decision Making (April 8, 2015)I. Reasoning Taxonomya. Kinds of Reasoningi. Deterministic: deductiveii. Probabilistic: inductive1. Drawing conclusions from evidencea. Client reports hearing voices – schizophrenic?b. Bleeding gums – gingivitis?c. Mammogram yields positive result – breast cancer?i. Current evidence: Patient A.C. has a positive mammogramii. Base Rate: 80% of all women with breast cancer have a positive mammogram result1. What’s the probability patient A.C. has cancer?b. Theories of Reasoningi. Normative: how one ought to reason1. Rules of logicii. Descriptive: how people actually reason1. Biases, heuristicsII. Normative Theories of Probabilistic Reasoninga. Critical Infoi. Current evidence1. P(E / H): probability of current evidence if hypothesis true2. P(P(E / H): probability of current evidence if hypothesis is falseii. Base rate1. P(H): probability of hypothesis independent of current evidenceb. Bayes’ Theoremi.c. Mammogram Outcome Examplei. Current evidence: Patient A.C. has a positive mammogramii. Base Rate: 80% of all women with breast cancer have a positive mammogram result1. What’s the probability patient A.C. has cancer?iii.iv.v. Using Bayes’ Theorem1.vi.d. Poker Chips Example 1i. Given: suppose there are 2 bags of poker chips1. 70 red and 30 blue2. 70 blue and 30 reda. A person chooses one bag. What is the possibility that it is the predominantly red one?3. Base rate is 0.5 for each bag:a. Ie. P (red bag) = 0.5 and P (blue bag) = 0.5ii. Possibilities:1. Suppose we choose one chip from that bag and the chip is reda. By Bayes’ Theorem, what is the probability of the red bag?b. Results:2. Person picks 8 reds and 4 blues, what is the probability chips were drawn from bag 1?a. Normative: 0.97b. People say: 0.75i. Results: Again, too much attention to base rate (0.5) not enough to weight to current evidencee. Poker Chips Example 2i. Given1. Bag A: 10 blue, 20 red2. Bag B: 20 blue, 10 reda. Probability of choosing from bag A is 0.80ii. You draw 3 chips from the bag in question w/ replacement, and look at the color; they are 2 blues and 1 red. What is the probability that you’ve chose from bag A?iii. Result: most people guess there’s a higher probability of having chosen bag B1. Normatively, the proper answer Bag A = 0.67a. Base rate ignored2.III. Descriptive Theories of Probabilistic Reasoninga. Representativeness(Tversky and Kahneman)i. Judge whether A has some characteristics by relying on the