Reasoning and Decision Making - Lecture Notes

Introduction

• Reasoning and Decision Making are the main topics.
• The lecture will cover heuristics, biases, and their effects on decision-making.

Key Terms

• Algorithm: A rule that guarantees a correct solution.
• Heuristic: A mental shortcut that generally works but isn't always correct.
• Bias: A predictable, systematic error in thinking.

Intuitive Reasoning

• Copier Experiment (Langer et al., 1978): Demonstrates how people respond to requests based on how they are phrased.
  • Request phrased as "Can I use the copier?" resulted in 10% compliance.
  • "Can I use the copier? I’m in a rush" resulted in 60% compliance.
  • "Can I use the copier? I need to make copies" resulted in 40% compliance. The addition of a reason, even if obvious, increases compliance.

Heuristics and Reasoning

• Availability Heuristic: Estimating the frequency or probability of something based on how easily instances or associations come to mind.
  • Information that is more easily remembered is assumed to be more common.
  • Examples:
    • Which causes more deaths in the United States?
      • Traffic accidents vs. homicide
      • Traffic accidents vs. colorectal cancers
      • Homicide vs. suicide
    • Actual 2017 causes of death (CDC):
      • Motor vehicle accidents: 40,231
      • Colorectal cancer: 53,447
      • Homicide: 19,510
      • Suicide: 47,173
• Tversky and Kahneman (1973):
  • Participants were given a list of names (39 names), either:
    • 19 famous women and 20 non-famous men
    • 19 famous men and 20 non-famous women
  • Participants judged whether there were more men or women on the list, and falsely judged the group with famous names to be more frequent 81% of the time because famous names are easier to recall.
  • Consider the letter K:
    • Is K more likely to appear in the first or third position of a word?
    • A typical selection of text contains twice as many words in which K is in the third position than words which start with K.
    • It is easier to think of words starting with K.
• Schwarz et al. (1991):
  • Students were asked to recall past episodes in which they had been assertive.
    • One group gave 6 examples, and another gave 12 examples.
    • Those who gave 6 examples judged themselves as more assertive because it was easier to come up with 6 examples than 12.

Representativeness Heuristic

• How do we judge if something is a member of a category?

• Representativeness heuristic: The probability that something is a member of a category can be determined by how well it resembles the properties normally associated with the category.

  $Member \ resembles \ Prototype \ resembles \ Category$

• Which sequence is more likely to be produced by flipping a fair coin?

  • HHTHT
  • HHHHH

  $P(HHTHT | fair \ coin) = (1/2)^5 = 1/32$

  $P(HHHHH | fair \ coin) = (1/2)^5 = 1/32$

  • HHTHT is more representative of a fair coin even though both sequences are equally probable.

• Tversky & Kahneman (1983):

  • 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 antinuclear demonstrations.
  • Which of these statements is more likely to be true?
    • A. Linda is a bank teller.
    • B. Linda is a bank teller and is active in the feminist movement.
  • Option B includes A, and the conjunction fallacy makes people choose B even though A is more probable.

Anchoring Effect

• Kahneman & Tversky, 1974:
  • Step 1: Is the percentage of nations in the UN that are in Africa greater or less than 65% [10%]?
  • Step 2: What is your best estimate of the actual percentage of nations in the UN that are in Africa?
  • Anchoring effect: People use initial numbers as a starting point and adjust from there.
    • 10% anchor group, mean estimate: 25%
    • 65% anchor group, mean estimate: 45%
• Even occurs for experts (Northcraft & Neale, 1987):
  • Real estate agents were asked to estimate the value of a house.
  • Given 10 pages of information that varied only by listing price.
  • Agents said they disregarded the listing price in their judgments.
    • Listing price $65,900 à appraisal value $67,811
    • Listing price $83,900 à appraisal value $75,190

Status Quo Bias

• Status quo bias: The tendency to do nothing when faced with a decision.
  • Organ donation:
    • Opt-in procedure: low rate of organ donation
    • Opt-out procedure: high rate of organ donation (consent rate ~99% in France and Belgium)

Base Rate Neglect

• Eddy (1982):

  • The probability of breast cancer is 1% for a woman at 40 who participates in a routine screening.
  • If a woman has breast cancer, the probability is 80% that she will have a positive mammography.
  • If a woman does not have breast cancer, the probability is 9.5% that she will also have a positive mammography.
  • A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
  • Correct answer (7.8%). 95 out of 100 doctors gave the wrong answer.

• Explanation:

  $P( disease | test \ positive ) = \frac{80}{(80 + 950)} ≈ 7.8$

  • Bayes Rule

• High Base Rate Example (50%):

  • 100 people: 50 sick, 50 healthy
  • Accuracy of test: 90% accurate if sick, 90% accurate if not sick
  • 45 true positives, 5 false negatives
  • 45 true negatives, 5 false positives
  • If you test positive, how likely is it that you’re really sick?
    • 45 true positives + 5 false positives = 50 total positives
    • 45 true positives ÷ 50 total positives = 90% chance of being sick if the test is positive

• Low Base Rate Example (10%):

  • 100 people: 10 sick, 90 healthy
  • Accuracy of test: 90% accurate if sick, 90% accurate if not sick
  • 9 true positives, 1 false negative
  • 81 true negatives, 9 false positives
  • If you test positive, how likely is it that you’re really sick?
    • 9 true positives + 9 false positives = 18 total positives
    • 9 true positives ÷ 18 total positives = 50% chance of being sick if the test is positive

• Base rate neglect: The tendency to misjudge the likelihood of a situation by not considering how frequently something occurs in general.

  • Improving reasoning about base rates:
    • People are more sensitive to base rates when they’re presented as frequencies rather than percentages.
      • Percentage: “1.2% of cases…”
      • Frequency: “12 out of 1,000 cases…”

Confirmation Bias

• I’m thinking of a rule for sequences of three numbers. Your job is to guess what the rule is. I’ll start by telling you that the following sequence obeys the rule: 2, 4, 6
  • Your turn: Guess a sequence and I’ll tell you whether it satisfies the rule.
  • The rule is: increasing numbers.
  • Wason (1960): People guess sequences that will confirm their hypothesis (e.g., 6, 8, 10; 10, 12, 14) rather than sequences that would disconfirm their hypothesis (1, 2, 3).
    • Confirmation bias: The tendency to seek out information that confirms an existing hypothesis and avoid information that would challenge it.
• Wason Card Selection Task
  • Cards all have a letter on one side and a number on the other.
  • If a card has a vowel on one side, then it has an even number on the other side.
  • The correct answer is E & 7 (10% get it right).
  • Common answers are E, E & 4.
  • E: see an even number - confirm
  • 4: not even needed, but feels like it confirms
  • 7: would disconfirm - if there is a vowel on the other side
• Permission Schema
  • If you have a beer, you must be 21 or older.
• Reasoning and Prior Knowledge:
  • Beer/Soda example (Griggs & Cox, 1982; Cheng & Holyoak, 1985)
    • Permission schema: If you satisfy a specific condition, you get to carry out an action.
    • Easier to apply this schema to concrete situations.

Framing Effects and Prospect Theory

• Expected Utility Theory: People make decisions that will maximize gains and minimize losses.
• Prospect Theory (Kahneman & Tversky): The value of an amount of money is not equivalent to the monetary value; it is based on the subjective experience of value.
  • Diminishing sensitivity: Each additional dollar added/lost feels less valuable.
  • Loss-aversion: The negative effect of a loss is larger than the positive effect of a gain.
• Curved shape: additional gains (or losses) are not valued as much as early gains (or losses).

Framing Effects

• Imagine the US is preparing for the outbreak of an unknown disease, expected to kill 600 people
  • If program A is adopted, 200 people will be saved.
  • If program B is adopted, there is one third probability that 600 people will be saved and two thirds probability that no people will be saved
  • 72% preference for A, 28% preference for B
• Imagine the US is preparing for the outbreak of an unknown disease, expected to kill 600 people
  • If program C is adopted, 400 people will die
  • If program D is adopted, there is one third probability that nobody will die and two thirds probability that 600 people will die
  • 28% preference for C, 72% preference for D
• Framed in terms of gains
  • If program A is adopted, 200 people will be saved
  • If program B is adopted, there is one third probability that 600 people will be saved and two thirds probability that no people will be saved
  • Risk averse: choose sure bet rather than gamble
• Framed in terms of losses
  • If program C is adopted, 400 people will die
  • If program D is adopted, there is one third probability that nobody will be die and two thirds probability that 600 people will die
  • Risk-taking: take the gamble to avoid loss
• Why?
  • Prospect theory says: difference between a perceived loss or perceived gain
  • In general, when a choice is framed in terms of gains, people are risk-averse; when a choice is framed in terms of losses, people use a risk-taking strategy