Base Rate Fallacy: Ayngmatic Bayesian Inference Problem
Base Rate Fallacy
Base rate fallacy is when probabilistic inference is made based only on data relating specifically to the situation but ignores additional background or general data relating to the instance of the situation that sometimes leads to wrong conclusions. Base rate fallacy is a “paradigmatic Bayesian inference problem” (Bar-Hillel, 1979).
If we consider a situation where a hit and run occurred at night in a city where there are 2 cab companies and a cab was suspected to have been involved. One of the cab companies have the blue colour while the other company have the green colour for their cabs. The blue cabs consists of 85% of the total cabs in the city while the remaining 15% of the cabs in the city belongs to the green cab …show more content…
This fallacy normally arise when assumptions about independence of events are made leading to a misunderstanding of conditional probability and the neglecting of prior odds of guilt before the introduction of the evidence being used to infer guilt. In order words, this fallacy consists of showing that to explain that the defendant is innocent is highly improbable and then deducing that the defendant is guilty is therefore the correct one (Buchanan, 2007).
In the controversial case of Sally Clarke, where the jury only had an option to decide whether she murdered her children or they died of a very rare and unexplained natural causes, and the prosecutor argues that the chances of them dying of natural causes was 1 in 73 million therefore she was guilty of murdering them. However, assumptions of independence of the two events were made in arriving at the probability of 1 in 73 million, therefore confusing conditional probability. Also, slim chance for an event not to occur is not relevant in deciding when the event has occurred and cannot be considered independently without comparing it to the chance of the event occurring that is the relationship between the chances of Sally killing her children cannot be looked at independently whilst ignoring the chances she didn’t do …show more content…
In this instance, the likelihood of finding a match increases in relation to the size of the database. Suppose the city in which a suspect lives has 500,000 adult inhabitants. Given the 1 in 10,000 likelihood of a random DNA match, (this is not the probability that the person did it because their DNA was found at the scene of the crime), it works out that about 50 people in the city would have DNA that also matches the sample. So the suspect is only 1 of 50 people who could have been at the crime scene. Based on the DNA evidence only, the person is almost certainly innocent, not certainly guilty as against if the fallacy was evoked to suggest the suspect is 1 in 10,000 chance of being innocent so he is
Base rate fallacy is when probabilistic inference is made based only on data relating specifically to the situation but ignores additional background or general data relating to the instance of the situation that sometimes leads to wrong conclusions. Base rate fallacy is a “paradigmatic Bayesian inference problem” (Bar-Hillel, 1979).
If we consider a situation where a hit and run occurred at night in a city where there are 2 cab companies and a cab was suspected to have been involved. One of the cab companies have the blue colour while the other company have the green colour for their cabs. The blue cabs consists of 85% of the total cabs in the city while the remaining 15% of the cabs in the city belongs to the green cab …show more content…
This fallacy normally arise when assumptions about independence of events are made leading to a misunderstanding of conditional probability and the neglecting of prior odds of guilt before the introduction of the evidence being used to infer guilt. In order words, this fallacy consists of showing that to explain that the defendant is innocent is highly improbable and then deducing that the defendant is guilty is therefore the correct one (Buchanan, 2007).
In the controversial case of Sally Clarke, where the jury only had an option to decide whether she murdered her children or they died of a very rare and unexplained natural causes, and the prosecutor argues that the chances of them dying of natural causes was 1 in 73 million therefore she was guilty of murdering them. However, assumptions of independence of the two events were made in arriving at the probability of 1 in 73 million, therefore confusing conditional probability. Also, slim chance for an event not to occur is not relevant in deciding when the event has occurred and cannot be considered independently without comparing it to the chance of the event occurring that is the relationship between the chances of Sally killing her children cannot be looked at independently whilst ignoring the chances she didn’t do …show more content…
In this instance, the likelihood of finding a match increases in relation to the size of the database. Suppose the city in which a suspect lives has 500,000 adult inhabitants. Given the 1 in 10,000 likelihood of a random DNA match, (this is not the probability that the person did it because their DNA was found at the scene of the crime), it works out that about 50 people in the city would have DNA that also matches the sample. So the suspect is only 1 of 50 people who could have been at the crime scene. Based on the DNA evidence only, the person is almost certainly innocent, not certainly guilty as against if the fallacy was evoked to suggest the suspect is 1 in 10,000 chance of being innocent so he is