Probability Judgments: Overview I  Heuristics and Basis:  Availabilty heuristic  Representativeness heuristic.  Anchoring and Adjustment.

Probability Judgments: Overview I  Biases in handling probability information  Probability matching.  Conditional probability.  Base rate neglect.

Probability Judgments: Overview II  Probabilistic Reasoning: Methods  Theory of Probabilistic reasoning.  Variants of Bayes theorem.  Probabilistic Reasoning: Classical problems  Cab problem.  Monty Hall problem.

Probability Judgments: Overview III  Criticisms of the Heuristic and Bias Approach  General criticisms.  Specific criticisms.  Answers to criticisms.

Probability Judgments: Overview III  Paradoxes and Biases in Decision making  Sunk cost.  Framing effects.  Nontransitivity of decisions.  Allais & Ellsberg Paradox.  Prospect theory and mental accounting.

Heuristics and Biases  Availability Heuristic: The frequency of events is judged due to the easiness of how particluar instances can be generated (or come to mind).

Availability heuristic: Personal experience and exampels  Examples:  Memory and availability: Famous people.  Death rates.  Influence of imagination.  Influence of personal experiences and examples.  Central lession to be learned: Beware of arguments based on examples.

Representativeness Heuristic  Functioning: Assessment of the frequency of events according to similarity / typicality.  Example: Evaluation of the probability of random sequences: Random sequences do not exhibit any pattern.

Representativeness Heuristic:  Example: Linda-Problem (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. RankingStatement (5.2)Linda is a teacher in elementary school. (3.3)Linda works in a bookstore and takes Yoga clas­ses. (2.1)Linda is active in the feminist movement.(F) (3.1)Linda is a psychiatric social worker. (5.4) Linda is a member of the League of Women Vo­ters. (6.2)Linda is a bank teller.(B) (6.4)Linda is an insurance salesperson. (4.1) Linda is a bank teller and is active in the feminist movement.(BF)

Representativeness Heuristic:  Conclusion (Basic lession):  Beware of detailed internally coherent and plausible scenarios (those concerning the future as well as those concerning the past).  More detailed scenarios appear as more plausible. However more detailed scenarios are less probable since each added de­tail reduces the probability of the scenario.

Probability Judgments: Probability Matching  Basic phenomenon:  Peoples’ answers reflect probabilities 70%30%

Handling probability information  Probability Matching (PM)  Non-optimality of PM Outcome Participant’s prediction  »Red light«»Green light« Red light Green light 

Handling probability information  Probability Matching (PM): Humans and animals: PM also found in animals  Animals: birds  Animals: ducks  Individual differences:  Intelligence and PM  Gender differences

Handling probability information  Probability Matching (PM):  Explanation of PM: Greed as a possible explanation  Rationality and PM

Probability Judgments: Conditional probabilities (CP)  Conception: The distribution of the values of the random variable X, given that the random variable Y has taken a specific value y.  Notation:

Conditional Probabilities (CP)  Conception: The distribution of the values of the random variable X, given that the random variable Y has taken a specific value y.  Notation:

Conditional Probabilities (CP)  Contingency tables:

Conditional Probabilities (CP) P(Success| Tr eatment ): P(Treatment|Success):

Conditional Probabilities  Conditional Probabilities and stochastic independence: Stochastic independence: Knowledge of B does not provide any information about the occurence of A (same distribution).

Conditional Probabilities (CP)  Asymmetry of CP

Conditional Probabilities  Conditional Probabilities (CP) and Causal Reasoning:  Preference for causal to diagnostic reasoning contradicts the principle:

Conditional Probabilities  Conditional Probabilities (CP) and Causal Reasoning:  Preference for causal to diagnostic reasoning contradicts the principle:

Conditional Probabilities  Problem A: Which of the following probabilities is higher?  The probability that, within the next five years, Con- gress will pass a law to curb mercury pollution, if the number of deaths attributed to mercury poisoning dur- ing the next five years exceeds 500.  The probability that, within the next five years, Con- gress will pass a law to curb mercury pollution, if the number of deaths attributed to mercury poisoning dur- ing the next five years does not exceed 500.  140 of 166 subjects chose the first alternative.

Conditional Probabilities  Problem B: Which of the following probabilities is higher?  The probability that the number of death attributed to mercury poisoning during the next five years will ex- ceed 500, if Congress passes a law within the next five years to curb mercury pollution.  The probability that the number of death attributed to mercury poisoning during the next five years will exceed 500, if Congress does not pass a law within the next five years to curb mercury pollution.  Most subjects chose the second alternative.

Conditional Probabilities  Participants’ preference is inconsistent, since it contradicts the principle: L = Congress passes law D = Death rate > 500  Explanation: The problem with this line of reasoning consists in neglecting the diagnostic impact of information.

Conditional Probabilities  Explanation: People reason causally: Many deaths cause a law:  The presence of a law causes a low rate of deaths (second case).

Conditional Probabilities  Diagnostic reasoning: The presence of a law indicates fewer deaths. Or the other way round (second inequality): A high death rate indicates the absence of a law.  The pattern of results indicates: People reason causally.

Conditional probabilities  Principle lessions:  There exists a principle difference between human reasoning and the results of the probability calculus.  People prefer causal reasoning to diagnostic.  Probability caluclus: Neither the causal direction nor time is relevant. Only the degree stochastic dependency counts.

Conditional probabilities  Principle lessions:  Peoples’ error constists in the fact that different causes are used in the two problems (the same events play different roles in the two problems): Problem A: Death rate as a cause of the congress passing a law. Problem B: Presence of a law as a cause of the (low) death rate.

Conditional Probabilities  Non-monotonic CP:  New facts can completely reorder probabilities: Yet and

Conditional Probabilities  Simpson Paradox: yet,

Base rates  Ignoring base rates  What is base rate information?  Example: Base rate neglect.  Causal base rates.

Base rates  What are base rates?  Probabilities (distribution of) a feature within a specific population (reference class).  Examples: Proportion of women within the world’s population. Proportion of people with symtoms of depression within the Swiss population.

Base rates  Base rate neglect: Empirical result:  People ignore the information due to base rates in the presence of (more) diagnostic information.

Base rates  Example: Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles. Question: The probability that Jack is one of 30 (70) engineers in the sample of 100 is _______%. (Either 30 or 70 out of 100 persons were engineers or lawers)

Base rates  Results:  The base rate information (30/100 or 70/100) had practically no effect on peoples’ judgments.  With the null description base rates are taken into account: Suppose now that you are given no information whatsoever about an individual chosen at random from the sample. The probability that the man is one of 30 (70) engineers in the sample of 100 is _______%.

Base rates  Results:  With a perfect non diagnostic description base rates are ignored: Dick is a 30-year-old man. He is married with no child- ren. A man of high ability and motivation, he promises to be quite successful in his field. He is well liked by his colleagues.  People estimates were about 50% in both groups (30/70 vs. 70/30).

Base rates  Conclusion: In the presence of more specific information (either diagnostic or not) base rates are simply ignored.

Base rates  Causal Base Rates: The base rates are associated with a causal factor that is also relevant for the target event.

Base rates  Causal Base Rates: Example: Two descriptions:  Two years, ago a final exam war given in a course at Yale University. About 75% of the students failed (passed) the exam.  Two years ago, a final exam was given in a course at Yale University. An educational psychologist interested in scholastic achievements interviewed a large number of students who had taken the course. Since he was primarily concerned with reactions to success (failure), he selected mostly students who had passed (failed) the exam. Specifically, about 75% of the students in his sample had passed (failed) the exam.

Base rates  Causal Base Rates: Explanation  The first description indicates a causal factor: the difficulty of the exam (with a success rate of 75% the exam seems to be easy compared to a success rate of 25%).  No such indication is given by the second description.

Base rates  Causal Base Rates: Results The judged probability that a subjects of a specific academic abilities (shortly described) was quite different for the two descritption:  With the first description: Base rates were taken into account.  With the second description base rates were ignored: The academic ability was the main factor for the decision.