Reasoning with Probability
Introduction
Human beings naturally see patterns everywhere and use these patterns to make judgement and decisions. The present experiment is a popular paradigm used to show how human decision making sometimes defies the laws of probability.
Summary
In this experiment you were given two options on every trial; one option listed a single event (e.g. Mary is a teacher) and one option listed a conjunction of events (e.g. Mary is a teacher who likes to read). In general, participants will indicate that the conjunctive option is more likely but statistically, it never is. The probability of a single event is x% and the probability of that event and another event co-occurring is x% x y%, which is ALWAYS less than x%. Tversky and Kahneman (1983) were the first to coin the phrase ‘conjunctive fallacy’ and suggested that the phenomenon was the result of individuals using the representativeness heuristic, rather than mathematical probability, to choose an alternative. The representativeness heuristic is ‘problem solving short cut’ where material that is considered to be representative of a population (such as teachers liking to read) forms the basis of judgements about that population.
Review Questions
Question: 1. Suppose you gave someone the following question:
Which is more likely?
Option a: Mary is a teacher
Option b: Mary is a teacher and a professional kickboxer
Which option do you think most people would choose and why?
Answer: Most people would choose option a because they don’t consider being a kick boxer to be representative of being a teacher. In cases where the conjunction is NOT representative of the population participants usually choose the more probably single alternative. Psychologists sometimes call this an effect of 'typicality'.
Question: 2. Suppose you gave someone the following question:
Which is more likely?:
Option a: Mary is a political activist and a feminist
Option b: Mary works at Tim Horton's
How do you think participants might respond here and why?
Answer: participants will probably choose option a because of the conjunctive fallacy even though far more people work at Tim Horton's than are political activists and feminists. The conjunctive fallacy can also be observed when the two alternatives compare different populations (e.g. the population of political activists and the population of people who work at Tim Horton's). The option that seems more 'representative' will usually be chosen regardless of which is more common in the WHOLE population.