PSYC 333 Lecture 4 Our probabilistic intuitions

Lecture Overview

  • Course: UofA PSYC 333 - Judgment and Decision Making

  • Instructor: Massimo Piattelli-Palmarini

  • Topic: Our Probabilistic Intuitions

Quiz Results

  • Class average for Quiz 1: 84%

  • Notable low performance on one question: Only 58% correct responses.

The Three Prisoners Dilemma

  • Scenario: Three prisoners on death row; one prisoner will be spared by the tyrant, but only the jailer knows who.

  • Jailer's Role: Communicates that one will be spared but keeps the identity secret.

  • Prisoner 2’s Strategy: Offers a bribe to find out who will be executed.

Jailer’s Decision

  • Jailer tells Prisoner 2, "Prisoner 3 will be executed!"

  • Prisoner 2 assumes the chance of being spared went from 1/3 to 1/2.

  • Actual Outcome: Prisoner 2's real chance remains 1/3.

Analysis of Probabilities

  • Counterintuitive Results for Prisoner 1:

    • Chance remains 1/3 for the prisoner who didn’t negotiate (Prisoner 1).

    • Prisoner 3's chance of being spared is now increased to 2/3 due to the jailer's logic.

Understanding the Logic

  • If Prisoner 2 is spared, the jailer chooses one of the remaining prisoners to execute, which has a probability of 1/3.

  • If Prisoner 2 is executed, the jailer must choose the other one to execute, which has a probability of 2/3.

Cognitive Dissonance in Decision-Making

  • Subjects often realize intuitive errors after questioning (examples: Maternity Ward Problem, Monty Hall Problem).

  • Rationality is felt internally by subjects rather than being imposed externally.

Evolutionary Biases in Decision-Making

  • Heuristics and biases may have been adaptive historically but can lead to irrational choices today.

  • Critique: It's unwise to overlook the dangers of cognitive illusions while misjudging narrow rationality.

Thought Experiment: Russian Roulette

  • Scenario: 6 prisoners must participate in a game of Russian roulette.

  • Rule Setup: Only one round in a spinning cylinder; survival leads to freedom.

  • Freedom to choose positions in the lineup.

Survivability Analysis

  • Preference Order: Participants often believe being first is best; this belief is based on intuition rather than probability.

  • Actual Probability: All prisoners have an equal survival probability of 5/6.

Alternative Scenarios

  • Variant with Six Revolvers: Each with a bullet placed differently.

  • Consequence: Format changes perceptions but not the underlying probabilities.

Key Insights on Probabilistic Intuition

  • People are typically risk-averse with gains and risk-seeking with losses.

  • Cognitive biases can lead to dramatically different decision-making outcomes based solely on framing effects.

Case Study: Tversky and Kahneman (1981)

  • Decision 1: Choose between a sure gain of $240 vs. a gamble.

  • Decision 2: Choose between a sure loss of $750 vs. a gamble.

  • Findings: Strong preference for gains (A) and against losses (D).

Manipulation of Preferences

  • New combinations presented reversed previous preferences despite being objectively equivalent.

  • Example Choices:

    • Option E: 25% chance to win $240 vs.

    • Option F: 25% chance to win $250

  • Result: People overwhelmingly prefer option F, showing how presentation impacts choices.

Cognitive Processes Involved

  • Mental Editing: Difficulties in integrating losses with gains once separated.

  • Psychological factors influence choices beyond objective rationality.

Normative Principles in Decision-Making

  1. Dominance Principle: Choose A if it excels over B in one area and is equal in others.

  2. Description Invariance: Preferences should not change based on presentation if logically equivalent.

  3. Aggregation of Gambles: Combines two gambles' expected values.

Conclusion on Cognitive Biases

  • These biases are systematic and resistant to intervention, independent of education and culture.

  • Important to recognize the role of heuristics in shaping decisions and intuitions.