Base Rate Neglect and Bayes' Theorem

• The text provides notes on decision-making and reasoning.

Base Rate Neglect and Bayes' Theorem

• Base rate neglect is the failure to consider the basic frequency of something in a population.
• Farmers are more common than opera singers, so base rate neglect would be thinking an opera singer would be more common because they are more highly thought of
• Bayes' Theorem establishes the strength of evidence for a belief and is useful for decision-making.
• It combines base rates with new information by updating beliefs.
• Bayes' Theorem assesses the likelihood of two beliefs
• The formula includes: p(HA|D) = Probability of hypothesis given data ("updated belief") calculates Prior probability of hypothesis ("base rate") times Probability of data given hypothesis ("new information")

Bayes' Theorem: Taxi Cabs

• Bayes' Theorem is applied to the scenario of taxi cabs, considering that 15% of city cabs are blue, and an eyewitness identifies a cab as blue but is only correct 80% of the time.
• The probability of the cab being blue, given the eyewitness testimony, is calculated using the formula: p(blue|eyewitness says blue) / (p(blue|eyewitness says blue) + p(green|eyewitness says blue))
• For instance, with probabilities: p(blue eyewitness says blue) = 0.12, p(eyewitness says blue green) = 0.20, p(blue) = 0.15, and p(green) = 0.85, the probability of the cab being blue is 0.12 / (0.12 + 0.17) = 0.42

Importance of Base Rates and Heuristics

• Base rates are important in the medical profession because errors and false positives can have lasting effects on patients.
• Heuristics are strategies used to simplify decision-making by ignoring information, sacrificing accuracy for speed and minimal effort.
• Algorithms provide precise methods, such as Bayes' Theorem, that always yield the correct answer.
• The representativeness heuristic is judging something based on how representative it is of a particular category.
• The availability heuristic relies on how easily information is accessed in memory.
• The affect heuristic is influenced by emotional reactions; if something feels scary, it's perceived as more likely.
• Explicit description increased perceived probability.
• Knowing the source of information can increase its perceived likelihood, aligning with availability heuristics.

Expert Decision Making and Probabilities

• Experts, when provided with more explicitly stated diseases, tend to increase their perceived probabilities.
• In a study, doctors were given descriptions of women with abdominal pain and asked to assign probabilities.
• Condition A had lower red values (M = .50) compared to Condition B (M = .69), indicating how additional information influences probability assessments.

Theoretical Perspectives on Decision Making

• Herbert Simon suggests fast and frugal heuristics are used because they are quick and require limited neural computing power.
• Daniel Kahneman presents a dual-system approach: System 1 operates quickly and intuitively and is prone to biases, while System 2 is slower, effortful, and governed by rules.
• Stress or pressure favors System 1 decision-making, potentially increasing the likelihood of criminal or illegal actions.
• Rational responses to problems are slower and more affected by secondary tasks, indicating System 2's involvement.

Heuristics in Real-World Decision Making

• In real-world scenarios, gut feelings and heuristics can be effective and yield correct answers, based on recognition of knowledge over missing information.
• Inductive reasoning involves drawing general conclusions from specific instances.
• Deductive reasoning allows drawing certain conclusions, including modus ponens and modus tollens.

Deductive Reasoning: Modus Ponens and Modus Tollens

• Modus ponens proves the consequence to be true by demonstrating the premise is true.
• Example: If it is raining, then Nancy gets wet; it is raining; therefore, Nancy gets wet.
• Modus tollens proves the premise false by demonstrating that the consequence is false.
• Example: If it is raining, then Nancy gets wet; Nancy does not get wet; therefore, it is not raining.
• Belief bias is the tendency to accept invalid conclusions if believable and reject valid conclusions if unbelievable.

Prospect Theory and Decision Making under Risk/Uncertainty

Expected utility is the probability of an outcome multiplied by the utility of the outcome

• Outcome bias is judging decisions based on their outcomes rather than the quality of the decision-making process at the time of the decision.
• Anticipated regret influences decision-making, with the aim of minimizing potential regret.

Loss Aversion, Valuation, and Framing Effects in Prospect Theory

• This is a valuation under prospect theory, trying to avoid Loss aversion
• The subjective value levels off as losses get larger or gains get bigger
• People tend to be risk-averse when it comes to potential gains but risk-seeking when it comes to potential losses. Framing effects, as studied by Kahneman, show that how things are framed can affect decision-making

Framing Effects on Decision-Making

• The notes discuss the effects of framing, where the same information presented differently can alter choices.
• Subjects tend to choose options framed as gains and avoid those framed as losses, even if the outcomes are equivalent.

Endowment Effect and Sunk Costs

• The endowment effect is when people value things more when they own them.
• The selling price is approximately double the buying price when people have an opportunity to sell something
• People hate losses more than they like gains.
• Sunk cost includes the tendency to pursue a course of action even after it has proved suboptimal, due to resources already invested.
• People are less preferred to be at the potential loss location than being at home
• Base rate neglect can be described as overweighting of new information compared to old information.
• Most will flip a coin to avoid a potential loss based on prospect theory.

Notes on decision-making and reasoning, explaining base rate neglect and Bayes' Theorem, which helps combine prior beliefs with new information to update probability assessments. It is useful for decision-making. Bayes' Theorem assesses the likelihood of two beliefs.