9.1 Heuristics

Some of the heuristics biases that make our probability judgments go awry.

The Lesson in Context

Humans make many decisions on a daily basis, often in the absence of complete information or under constraints of limited time and cognitive capacity. We use heuristics as useful shortcuts for quick decision making, which may introduce bias into our conclusions. The purpose of the lesson is not to cast doubt on our use of heuristics, but to recognize the limitations of quick human judgments and their consequences. This parallels 2.1 Senses and Instrumentation and 2.2 Systematic and Statistical Uncertainty, where the limitations of instruments are discussed and quantified, without rejecting the validity and usefulness of instruments altogether.

2.1 Senses and Instrumentation

• Senses and instrumentation are inherently imperfect, but imperfect tools can still be useful in obtaining partial knowledge. Similarly, heuristics are flawed, but they can make useful tools when time, knowledge, and mental resources are limited.

2.2 Systematic and Statistical Uncertainty

• The use of heuristics can often introduce bias into our judgments — tendencies to make one decision more often than another, paralleling the idea of systematic uncertainty in instrumental measurements.

9.2 Biases

• This lesson focuses on heuristics that affect our judgments of frequencies — how often things occur or likelihoods of events. The next lesson discusses biases in decision making that stem from a self-centered view of the world—an overemphasis on "me" and "now" and overusing defaults and assumptions.

10.1 Confirmation Bias

• We single out confirmation bias into its own topic, as it permeates scientific and group decision making, affecting both our sense of the prevalence of events around us as well as the importance of "me" and "now".

Takeaways

Learning GoalsDefinitionsExamplesCommon Misconceptions

After this lesson, students should

1. Know that we use heuristics as a shortcut in everyday decision making.
2. Recognize that while heuristics can be useful and necessary, they can also lead us astray by introducing biases into our decision making.
3. Be able to identify cases of Base Rate Neglect.
4. Be able to avoid the temptation to engage in Base Rate Neglect.
5. Be able to identify cases of the Representativeness Heuristic, and not fall for it.
6. Be able to identify cases of the Conjunction Fallacy, and not fall for it.
7. Be able to identify cases of the Availability Heuristic, and not fall for it.
8. Learn the basics of Bayesian reasoning.

Heuristics

Mental shortcuts people make instead of analyzing all relevant information while making decisions.

Base Rates

The base frequency of a given attribute in a whole population.

• Base Rate Neglect

The act of overlooking the importance of base rates when calculating the probability of an event based on probabilities that seem more relevant to the specific case.

• Bayes' Rule

[math]\displaystyle{ \begin{align} &\ \ \quad\text{(probability that a positive is a true positive)} \\ &= \frac{(\#\text{ true positives})}{(\text{total } \# \text{ positives})} \\ &= \frac{(\#\text{ true positives})}{(\#\text{ true positives})+(\#\text{ false positives})} \\ &= \frac{\text{(base rate)}\times\text{(true positive rate)}}{\text{(base rate)}\times\text{(true positive rate)}+(1-\text{base rate})\times\text{(false positive rate)}} \end{align} }[/math]

Representativeness Heuristic

Cases in which how representative something is of a category or outcome is used as a proxy/heuristic for evaluating how likely the category membership or outcome is (not taking base rates into account).

Conjunction Fallacy

The tendency to neglect that something is less likely to be part of a subset of a set than a set itself. In reality, [math]\displaystyle{ A }[/math] is always more likely to be true than [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] because if [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] is true then [math]\displaystyle{ A }[/math] must be true. This usually happens as a consequence of the representativeness heuristic, when [math]\displaystyle{ B }[/math] appears more representative of the set in question.

Availability Heuristic

Cases in which people use how readily something comes to mind as a proxy for an estimate of its probability. This can be influenced by factors unrelated to probability, such as vividness or frequency of appearance in the media.

Bounded Rationality

The idea that people have limited information and capacity to analyze all factors when making decisions (i.e. "rationality" is "bounded"). Given bounded rationality, it's often reasonable (that is, better than if we decided randomly) to use heuristics to guide our decisions.

Availability Heuristic: Plane Crashes

Ever since reading about plane crashes in the news, Harriet insists on driving even long distances. She is falling into the availability heuristic. She is actually much more likely to die in a traffic accident than a plane accident. Traffic accidents are extremely common but rarely make the news, whereas plane accidents are rare but always make the news, making them more "available" to her memory and thus seem more common than they are.

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Representativeness Heuristic: Pit Bulls

Having been assured that the rescue dog was extremely friendly, Milo was shocked to discover it was a pit bull. He knew that pit bulls are often less friendly than other dogs, and did not know that pit bulls are over-represented among rescue dogs (in part because of this reputation).

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Conjunction Fallacy: Tabbies

Even though tabbies are the commonest brown cat, the fact that all brown tabbies are brown cats but not all brown cats are tabbies means that it must be more likely that the cat is brown than that it's a brown tabby.

If you look at the numbers, you can see that there are actually more vaccinated people vaccinated getting sick than unvaccinated people. So getting vaxxed actually makes you more likely to get sick!

This is a case of base rate neglect. Because more people are vaccinated than unvaccinated, you can get this pattern even when vaccination is strongly protective. For example, if 85% of people are vaccinated, and being vaccinated makes you 30% as likely to catch the disease, then out of every hundred people, .85 * .3 * 100 ＝ 25.5 vaccinated people on average will get sick, while .15 * 1 * 100 ＝ 15 unvaccinated people will get sick. So even though more vaccinated people are getting sick in terms of absolute quantity, getting the vaccine still makes any given person 1/3 as likely to get sick.

Heuristics cause us to make wrong judgements so they're bad and we should stop using them.

Heuristics can sometimes lead us towards fallacies. But, that does not mean that they are useless! Heuristics still tend to be better than making decisions arbitrarily. And we don't always have the time or means to fully analyze every decision.

Useful Resources

Lecture VideoDiscussion SlidesHandouts and ActivitiesReadings and Assignments

Discussion Slides Template

The discussion slides for this lesson.

Bayes' Theorem Visualizer

An interactive tool for visualizing and calculating quantities with Bayes' Theorem.

Bayes' Theorem Visualizer (Datahub Link)

Special link for use at UC Berkeley only. An interactive tool for visualizing and calculating quantities with Bayes' Theorem.

Validity: What Follows From What?

Excerpt from Logic: A Very Short Introduction. By Graham Priest.

Judgment Under Uncertainty: Heuristics and Biases

Biases in judgements reveal some heuristics of thinking under uncertainty. By Kahneman and Tversky.

Recommended Outline

Before Class

[Any steps that need to be taken before class.]

During Class

5 Minutes	As your students the Jessie question.
25 Minutes	Go through the KOALA-23 example and exercise. Note that this has many sub-steps and is worth reviewing how you'll present it.
6 Minutes	Guide the students through the Jessie Again prompt and let them work through the problem.
17 Minutes	Have the students answer the conjunction fallacy problem and present the corresponding examples.
16 Minutes	Have the students answer the availability heuristic problem and present the corresponding examples.
11 Minutes	Have the students discuss bounded rationality in small groups.

Lesson Content

Jessie

You're sitting in your room cramming for an exam when your roommate decides to throw an impromptu party and invites people from all over the university. Realizing that you're not going to get any work done, you decide to make the most of it and start mingling with the crowd. In the process, you strike up a conversation with someone named Jessie who starts droning on and on about rockets. They go on for so long that you start to lose interest and begin thinking about what sort of person Jessie really is.

Here's some helpful numbers:

• One in four students study engineering at your college.
• Half of all engineering majors like rockets.
• A sixth of all non-engineering majors like rockets.

Which is more likely?

1. Jessie is an engineering major.
3. Jessie is a non-engineering major.
4. It's equally likely that Jessie's an engineering or non-engineering major.

Do not tell the students the answer yet! It's actually 50/50 odds that Jessie is an engineering major. This is explained later Jessie Again.

Activity 1

[Brief description of and motivation for the activity]

[Common misconception or thing to look out for.]

[Thing you really need to look out for!]

[Title]

[Useful tip, guideline, or other background.]

Instructions

[n] Minutes	[Activity.]
[n] Minutes	[Activity.]

Discussion Questions

[Question 1]

[Possible misconception that may need to be corrected and clarified.]

[Intended answer to the above question.]

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[Question 2]

[Possible misconception that may need to be corrected and clarified.]

[Intended answer to the above question.]

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