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In this lesson, you will learn the basic concept of the conjunction fallacy and be introduced to the Linda problem. Several examples will be presented to help clarify the concept.

What Is the Conjunction Fallacy?

Imagine you are walking down the street, and a political reporter stops you and asks if he can interview you. You are not in a hurry and agree. He asks, ‘Which is more probable of Emily Swinton, a Democrat and presidential nominee, scenario A or B:’Scenario A: Emily Swinton wins the 2016 presidential electionScenario B: Emily Swinton wins the 2016 presidential election and becomes an advocate for women’s rights in the workplaceWhich scenario would you pick? Many people would pick scenario B because they assume that Emily Swinton, a woman, and a Democrat, will become an advocate for women in the workplace. But the truth is that Scenario A is more likely.

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When people pick scenario B, they are falling for the conjunction fallacy.The conjunction fallacy is faulty reasoning inferring that a conjunction is more probable, or likely, than just one of its conjuncts. (In this context, a conjunct just represents one of the ideas in the sentence, and a conjunction is a sentence with multiple conjuncts connected together.

) Further, it demonstrates the faulty assumption that detailed conditions are more probable than general ones.What exactly does this mean, you may ask? In the example above, Scenario B has two conjuncts:

  1. Emily Swinton wins the 2016 presidential election
  2. Emily Swinton becomes an advocate for women’s rights in the workplace

In fact, a situation with just one conjunct, or condition, is more probable than a situation with two conditions. To further illustrate, if A and B are two different events, then the probability of just A occurring is more likely than A and B occurring.

Examples of the Conjunction Fallacy

Confused? Let’s take a look at a few more examples.Example 1: Cliff went to the local carnival last night with his son. He and his son rode the roller coaster. Is Cliff more likely a man or a man who is a thrill seeker and adrenaline junkie?Many people would pick the latter choice because they assume that, since Cliff rode on a roller coaster, he must be a thrill seeker and adrenaline junkie.

The truth may be that he rode the roller coaster because his son begged him to. Maybe Cliff was afraid and faced his fears only for his son? The actual reason is beside the point. What matters is that it is more likely for Cliff to be a man rather than a man and a thrill seeker and adrenaline junkie because the former includes just one of the conjuncts instead of both. In other words, it’s more likely because it just requires one condition instead of two.

Example 2: Mary went to the store and bought tofu, eggplant, broccoli, and frozen meatless lasagna. Is it more likely that Mary is a woman or a woman who is a vegetarian?Again, many people would pick that it is more probable that she is a woman who is a vegetarian, when it is actually more probable that she is a woman. Based on her name, we can be pretty sure that she is a woman. However, we may assume that she is a vegetarian based on her shopping cart, but she may not be.

She may just like tofu, veggies, and meatless lasagna.

Why Do People Fall for the Conjunction Fallacy?

When considering these questions, people usually don’t consider which scenario or situation is more probable. Instead, they think of options A and B as alternatives to each other. What they don’t realize is that one scenario is simply a subset of the other.

Another reason that was posed by psychologists Amos Tversky and Daniel Kahneman in the 1970s is that people tend to choose the scenario that is most similar to (in other words, representative of) their preconceived ideas about the person or situation being described. They coined this the representativeness heuristic.

Conjunction Fallacy Theorem Inequality

The following inequality uses variables to clearly illustrate the conjunction fallacy.

Conjunction Fallacy Theorem Inequality

Example: Event A= Tornado, Event B= HailThe probability of a tornado (A) AND hail (B) is less probable (or equally) than just a tornado (A) or just hail (B).

The Linda Problem

The Linda problem is based on a study that was conducted by Tversky and Kahneman, and is the most oft-cited example of the conjunction fallacy in effect.

In their study, they told the participants: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 anti-nuclear demonstrations.They then asked: Which is more probable?Scenario A: Linda is a bank tellerScenario B: Linda is a bank teller and is active in the feminist movementMany participants chose scenario B because of the description of Linda met the stereotype for a feminist. But scenario A is actually most probable because it only has one conjunct, or condition.

Lesson Summary

The conjunction fallacy is faulty reasoning in which one believes that a conjunction of scenarios or situations is more probable that just one of its conjuncts.

People sometimes gravitate towards the scenario that is more detailed than the more general one. This happens because people tend to think that the options are alternatives to each other, when in fact one is a subset of the other. It also happens because of ‘representativeness.

‘ As Tversky and Kahneman’s representativeness heuristic tells us, people tend to choose the scenario that is most similar to their preconceived ideas about the person or situation being described.Tversky and Kahneman’s Linda problem asked study participants whether or not Linda was more likely to be a bank teller or a bank teller who is active in the feminist movement. Because the description they had previously given of her fit stereotypes about feminists, study participants chose the second answer instead of the bank teller subset, which is mathematically and statistically more probable.

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