Judgments, Decision Making, and Reasoning

Judgments are

Estimates that people make of important real-world quantities: height, weight, intensity, probability, etc.

Judgment heuristics

Easy, natural strategies for making judgments that provide answers that are often reasonable but systematically biased.

Availability

This is one important quantity that people must estimate: the probability of events. People often estimate this on the basis of examples of the event that are readily available in memory, but what we remember is not always more probable.

Human risk assessment accuracy (Lichtenstein et al.) experiment

They asked Ss to judge the rates of many causes of death: tornado, botulism, cancer, stroke, flood, car accidents, etc.

Results show that people overestimate the probability of rare events and underestimate the probability of common ones. This is due to the fact that rare events, when heard about, are more salient in people’s minds.

This demonstrates availability influencing risk assessment: people overestimate accidents and natural disasters.

Judged vs. actual mortality rates (Hertwig et al.) experiment

Infrequent but dramatic events are over judged by people, and frequent but non-dramatic events are under judged severely.

Availability and risky decisions

In 2004, Gigerenzer analyzed patterns of travel after 9/11. In the following months, there was a decrease in air travel, and actually a 2.9% increase in freeway driving of that led to an increase in driving deaths.

Does availability correspond to probability?

No, because of availability, we often think that something more memorable makes it more probable.

In reality there are many factors that determine what we can remember, i.e., semantic elaboration, interference, imagery.

Representativeness

People make judgments of probability on the basis of similarity and ________.

Examples are

1. Conjunction fallacy

2. Neglect of the law of large numbers

3. Base rate neglect

Conjunction fallacy

A probability fallacy, this tells us that the probability of the conjunction of two events cannot be greater than either of the events themselves.

P(A&B) ≤ P(A)

However, people sometimes judge the conjunct probability as more likely when it can only be less likely than the probability of one.

Why do people make the conjunction fallacy?

This occurs because often the conjunct is less probable but more representative or similar to what Ss knows about the situation.

Neglect of the law of large numbers

This law states that larger samples provides stronger evidence than smaller ones. However, this probability neglect occurs because people often ignore sample sizes.

Demonstrating the law of large numbers (urn with red/green balls experiment)

Ss were asked: imagine an urn filled with balls 2/3 one colour and 1/3 another.

Individual A draws 5 balls from the urn, 4 were red and 1 was green.

Individual B drew 20 balls from the urn, 12 were red and 8 were green.

Which individual should feel more confident that the urn contains 2/3 red and 1/3 green. Most people chose individual A when really individual B should be more confident.

Base rate neglect

When estimating the probability of an event given evidence, people often ignore the event’s base rate: the probability of the event in the absence of any evidence.

Engineers and lawyers (Tversky et al.) experiment on base rate neglect

Ss were asked to identify an individual in a group of 100 as an engineer to a lawyer. Population distribution as specified to 30/70 condition: 30 engineers and 70 lawyers, and 70/30 condition: 70 engineers, 30 lawyers.

A description of an individual is provided which indicates engineer, neutral, lawyer, or none. Ss are then asked if that individual is an engineer.

Results show that Ss attended to base rates only when no description was provided, a description led Ss to exhibit base rate neglect.

Green and blue cabs (Tversky et al.) experiment

Ss are told that a cab is involved in a hit-and-run accident. 2 cab companies, green and blue operate in the city.

Ss know: 85% cabs are green, 15% are blue.

A witness identified the cab as blue, the court tested the witness’s ability to identify cabs: 80% were correct, and 20% were incorrect. What is the probability that the cab was blue?

Ss median response was 80% when in reality the correct answer is 41%.

This demonstrates that Ss were insensitive to the 85%/15% base rates.

Medical example of base rate neglect

Suppose 1% of all 40 y/o women have breast cancer. When breast cancer is present, a mammogram will be positive 80% of the time. When absent, it will be positive 20% of the time. The test comes back positive for a particular 40 y/o woman. How likely is it that she has the disease?

95% of physicians estimated the answer to be between 70-80% when in reality it’s 7.8% because of the 1% base rate.

Why does base rate neglect occur?

This is one of the most common mistakes people make while reasoning probabilistically. Likely caused by:

1. Unclear causal relevance of base rates

2. People are not good at reasoning with probabilities vs. frequencies.

Causal relevance of base rates (Tversky and Kahneman) experiment

A version of the “cab” problem in which the causal relevance of base rates was emphasized.

Ss told that a cab is involved in a hit-and-run accident. And informed that although companies are roughly equal in size, 85% of accidents involve green cabs and 15% involve blue cabs. Witness identified cab as blue, 80% correct and 20% incorrect testimonies. What is the probability that the cab as blue?

When this causal relationship is clear to Ss, they did attend to base rates and answered closer to the correct answer of 41%.

Base rates as frequencies (Gigerenzer et al.) experiment

Testing whether base rates are used when expressed as frequencies.

Ss told that Team A won X games. Some of their games were randomly selected and scores were checked at half-time and then at final. Ss in several conditions: X = 7 or 10 or 15 or 19. They were then told that Team A was ahead at half, tied at half, and behind at half, and then they were asked a probability estimate that this game is one of X games Team A won that season.

Results show that the lower the number of games the team won in the season the less likely people say that said game was one of the ones they won.

People do attend to base rates when they are presented as frequencies rather than probabilities.

Why are frequencies preferable to probabilites?

According to Gigerenzer, evolution has prepared people to deal with the frequency of observed events. In contrast, the notion of probabilities are a relatively recent invention.

What makes use of base rate more likely?

• When individuating information is not present

• When base rates are causally related to judgment

• When base rates are expressed as frequencies rather than probabilities

Cognitive illusions are

Like perceptual illusions, consistent and persistent discrepancies between a true state of affairs and its mental representation.

Confirmation bias

An unconscious tendency to process information in a way that supports one’s prior beliefs or values.

Types of confirmation bias

Manifests itself in several forms.

1. Biased information search

2. Biased evidence evaluation

Biased information search

Ideally, evidence that people seek out to test their beliefs should lead to correct beliefs eventually being adopted. Yet, people tend to seek out only evidence that is likely to be consistent with their existing beliefs.

Real world biased information search (Shafir) experiment

Ss were asked to choose which parent should receive custody of a child. One had strong positive and negative features, while the other had neutral ones.

The wording of the question was varied: to which parent would you award custody? To which parent would you deny custody?

How would the wording affect Ss choice?

When Ss were asked about awarding custody, 64% chose parent B, as they focused on the positive attributes of parent B relative to A. When Ss were asked about denying custody, 55% chose parent B as well because they focused on the negative attributes compared to parent A.

This hypothesis tells us that what one focuses on can determine what information is sought and so the ultimate decision.

Biased evidence evaluation

The evaluation of evidence should be independent of whether it agrees or disagrees with our current beliefs. However, people tend to discount evidence that they disagree with, a phenomenon referred to as myside bias.

Biased evidence evaluation: Myside bias (Lord et al.) experiment

Ss were presented with fictional studies about controversial topics, e.g., capital punishment.

Ss had strong prior attitudes: proponents and opponents. Each Ss read two studies, one supporting capital punishment and one not. They were asked to rate the quality of each study and then re-rate their attitude toward capital punishment.

Results show that participants exhibited belief polarization, their opinions were more extreme after reading the studies than before.

Unfortunately, this tells us that people’s evaluation of evidence is influenced by which theory they advocate.

Reasons for confirmation bias and the backfire effect

There have been several explanations for this:

1. Maintenance of self-esteem

2. Avoidance of cognitive dissonance

3. Simplified cognitive processing

When disconfirming evidence sometimes leads to a mistaken belief becoming stronger is called the _______ effect.

How to combat confirmation bias?

Seek other viewpoints, especially from those you disagree with, ask neutral questions, test things you think are not true, tolerate disagreement, be humble, don’t be afraid to be wrong, find experts who have gathered high quality evidence.

Confirmation bias in people (and scientists!)

People are often biased in how they:

• Test hypotheses—they tend to look for positive confirming evidence.

• How they evaluate evidence—they are more critical of evidence they don’t agree with.

Decision making

This involves choosing among a set of alternatives.

Decision making under uncertainty

This occurs when you have an idea of a choice’s likely outcome but you don’t know for certain, thus, you must consider all the possible outcomes associated with each alternative.

Decision making theories and phenomena

• Expected value theory

• Expected utility theory

• Prospect theory

• Decisions and emotions, context effects, complex decisions, neuroeconomics (pp. 420-422).

Normative vs descriptive theories of decision making

• Specify how people should make decisions

• Specify how people do make decisions. They describe how and why people diverge from normative theories.

Expected value theory

This states that one should first compute the expected value of each alternative. Then choose the alternative with the highest expected value.

EVT violations in people

People frequently violate this decision making theory in everyday decisions.

• People often exhibit risk aversion, they prefer an option with a lower expected value if it is less risky.

Wealth vs. Subjective utility

One reason people violate EVT is that their subjective utility usually differs with objective wealth. Utility is what people personally value.

EUT

A theory in which decisions are made on the basis of utility rather than value. This requires computation of expected increase in utility of each choice, and causes to choose the option with the highest expected utility.

Diminishing marginal utility

This is the phenomenon when people usually value each additional unit of wealth a little bit less. Results in the function relating utility to objective wealth having a concave shape.

Why do people violate EUT

EUT forms the basis of much of modern economic theory: it is a much more plausible theory of human decision making. Nevertheless, it’s easy to show that people also frequently violate EUT for these reasons:

1. Loss aversion (some instances)

2. Certainty effects

3. Framing effects

4. Gambling

Loss aversion

A reason for EUT violation. This is where the magnitude of the pain of a loss being greater than the magnitude of the pleasure of a gain. This alone does not challenge EUT though because it can be seen as arising from diminishing marginal utility, but other examples of loss aversion challenge EUT because they imply risk seeking behaviour.

Risk aversion vs. risk seeking

When gains are involved, people are more attracted to certain options, so they are risk averse in those scenarios.

When losses are involved, people are attracted to less certain options.

Certainty effects

This is a phenomenon where alternatives with a certain outcome are evaluated differently than those with uncertain outcomes. Certainty effects can be demonstrated by comparing choices on two problems.

Framing effects

This phenomenon is about how people’s choices change depending on how they are worded.

When people start off with a lower amount of money, choices are framed as gains. As a result, they exhibit risk aversion when faced with gains.

When people start off with higher amounts of money, choices are framed as losses. As a result, they exhibit risk seeking.

Sunk cost effect

This is the tendency we have as humans to continue on with an endeavour based on pats investments and not current benefits; continuing despite evidence that stopping is better. People feel that a resource or benefit on which money has already been spent must be used, even if they’d rather not.

People are less likely to stop something if they paid more for it.

Also referred to as irrational escalation, escalation of commitment, and commitment bias.

Gambling and its explanations

Although people are generally risk averse, many also enjoy gambling. This can be explained by complex utility functions and problems representing small probabilities.

Gambling and utility

Some explanations of gambling are consistent with EUT. Gambling can provide utility other than money, i.e., excitement, camaraderie, impressing others, the challenge, etc. As a result, in some regions, the utility function may be convex rather than concave.

Gambling and probabilities

People have a hard time understanding probabilities, especially when it’s involved with really big numbers. So the availability in memory of successful bets may distort one’s view of the probabilities and override that of losses.

When are examples of EUT violations?

Expected utility theory forms the basis of modern economic theory, but people violate many of its assumptions: loss aversion, certainty effects, framing effects, aspects of gambling.

Prospect theory

This is a more recent decision-making theory with two components,

1. A new utility function

2. A function mapping objective to subjective probabilities.

Utility function of PT

This function is relative—defined in terms of changes in wealth or welfare, i.e., gains and losses, which explains framing effects. Utility is defined with respect to current wealth.

When the function is concave, it designates gains and explains risk aversion. When function is convex it designates losses and explains risk seeking and framing effects. When losses is steeper than gains, it explain loss aversion.

The shape of the utility curve explains other phenomena that challenged EUT: risk avoidance, risk seeking, loss aversion.

PT and probability

EVT and EUT assume that people represent probabilities vertically. However, PT probability is subjective. π is the function that maps objective to subjective probabilities, and this subjective probability function provides explanations for some gambling phenomena and certainty effects.

EVT vs. EUT vs. PT

EUT accounts for effects not explained by EVT: people exhibit diminishing marginal utility which explains risk and loss aversion.

PT accounts for effects not explained by EUT: explains certainty effects, risk seeking in losses, framing effects, etc.

Expected emotions

When considering alternatives, decision makers must anticipate how a possible outcome will affect their utility. When in fact, how people think they will feel about an outcome can be different than how they actually feel.

Expected emotions (Kermer et al.) experiment

Ss rate their current happiness, which is the S’s baseline happiness. They are then given $5 and told that on the basis of a coin flip, they will either win $5 or lose $3. S then predicts their level of happiness if they were to win or lose.

Results show that Ss anticipated more regret than they actually experienced. Before, they focused on losing $3, but after actually losing, they focused on having $2 left!

So we know that people do not always accurately predict how they will feel about the outcome of a decision. They often have more resources for dealing with a negative outcome than they realize.

Context effects

According to EVT, EUT, and PT, the attractiveness of an alternative should be independent of other alternatives. However, in reality, one alternative can affect the evaluation of another. For instance, the relative expected utility of two alternatives can be affected by a third.

Includes phenomenon known as the attraction effect.