The
base rate fallacy, also called
base rate neglect, is an error that occurs when the
conditional probabilityConditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P, and is read "the probability of A, given B"....
of some hypothesis H given some evidence E is assessed without taking sufficient account of the "
base rateIn probability and statistics, base rate generally refers to the class probabilities unconditioned on featural evidence, frequently also known as prior probabilities...
" or "
prior probabilityIn Bayesian inference, a prior probability distribution, often called simply the prior, is a probability distribution representing knowledge or belief about an unknown quantity a priori, that is, before any data have been observed...
" of H.
In a city with 100 terrorists and one million non-terrorists there is a surveillance camera with an automatic face recognition software. If the camera sees a known terrorist, it will ring a bell with 99% probability.
The
base rate fallacy, also called
base rate neglect, is an error that occurs when the
conditional probabilityConditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P, and is read "the probability of A, given B"....
of some hypothesis H given some evidence E is assessed without taking sufficient account of the "
base rateIn probability and statistics, base rate generally refers to the class probabilities unconditioned on featural evidence, frequently also known as prior probabilities...
" or "
prior probabilityIn Bayesian inference, a prior probability distribution, often called simply the prior, is a probability distribution representing knowledge or belief about an unknown quantity a priori, that is, before any data have been observed...
" of H.
Example
In a city with 100 terrorists and one million non-terrorists there is a surveillance camera with an automatic face recognition software. If the camera sees a known terrorist, it will ring a bell with 99% probability. If the camera sees a non-terrorist, it will trigger the alarm 1% of the time. So, the failure rate of the camera is always 1%.
Suppose somebody triggers the alarm. What is the chance he/she is really a terrorist?
Someone making the base rate fallacy would incorrectly claim that the false alarm rate must be 1 in 100 because the failure rate of the device is 1 in 100, and so he/she is 99% sure to be a terrorist if the device rings. The fallacy arises from the assumption that the device failure rate and the false alarm rate are equal.
This assumption is incorrect because the camera is far more likely to encounter non-terrorists than terrorists. The higher frequency of non-terrorists increases the false alarm rate.
Imagine that all 1,000,100 people pass in front of the camera. About 99 of the 100 terrorists will trigger a ring — and so will about 10,000 of the million of nonterrorists. Therefore 10099 people will be rung at, and only 99 of them are terrorists. So, the probability that a person who triggers the alarm is actually a terrorist is 99 in 10,099 (about 1/102).
The base rate fallacy is only fallacious when non-terrorists outnumber terrorists, or conversely. In a city with about 50% terrorists and about 50% nonterrorists, the real probability of misidentification won't be far from the failure rate of the device.
Findings in psychology
In some experiments, students were asked to estimate the grade point averages (GPAs) of hypothetical students. When given relevant statistics about GPA distribution, students tended to ignore them if given descriptive information about the particular student, even if the new descriptive information was obviously of little or no relevance to school performance. This finding has been used to argue that interviews are an unnecessary part of the
college admissionsUniversity admission or college admissions is the process through which students enter tertiary education at universities and colleges. Systems vary widely from country to country, and sometimes from institution to institution....
process because interviewers are unable to pick successful candidates better than basic statistics.
PsychologistA psychologist is someone who studies the human mind and behavior. Research psychologists study human perception, cognition, attention, emotion, motivation, personality, behavior and interpersonal relationships...
s
Daniel KahnemanDaniel Kahneman is an Israeli psychologist and Nobel laureate, notable for his work on the psychology of judgment and decision-making, behavioral economics and hedonic psychology....
and
Amos TverskyAmos Nathan Tversky, was a cognitive and mathematical psychologist, and a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his early work concerned the foundations of...
attempted to explain this finding in terms of the
representativeness heuristicThe Representativeness Heuristic is a rule of thumb wherein people judge the probability or frequency of a hypothesis by considering how much the hypothesis resembles available data as opposed to using a Bayesian calculation. While often very useful in everyday life, it can also result in neglect...
. Richard Nisbett has argued that some
attributional biasIn psychology, an attributional bias is a cognitive bias that affects the way we determine who or what was responsible for an event or action ....
es like the
fundamental attribution errorIn social psychology, the fundamental attribution error describes the tendency to over-value dispositional or personality-based explanations for the observed behaviors of others while under-valuing situational explanations for those behaviors...
are instances of the base rate fallacy: people underutilize "consensus information" (the "base rate") about how others behaved in similar situations and instead prefer simpler
dispositional attributionDispositional attribution is the explanation of individual behavior as a result caused by internal characteristics that reside within the individual, as opposed to outside influences that stem from the environment or culture in which that individual is found...
s.
See also
- Bayesian probability
Bayesian probability is one of the most popular interpretations of the concept of probability. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with uncertain statements. To evaluate the probability of a hypothesis, the Bayesian probabilist...
- Inductive argument
- Misleading vividness
The logical fallacy of misleading vividness involves describing an occurrence in vivid detail, even if it is an exceptional occurrence, to convince someone that it is a problem...
- Data dredging
Data dredging is the inappropriate use of data mining to uncover misleading relationships in data...
External links