The Critical Factor in Identifying False Information
We work with a lot of data each day - according to Forbes, 2.5 quintillion bytes of data are created each day.
But, having lots of data doesn’t guarantee we’re right about everything. When we have loads of data, there occur different statistical fallacies – one of them is the prosecutor’s fallacy.
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| Photo by Markus Winkler on Unsplash |
The prosecutor’s fallacy is when someone thinks that just because the evidence is unlikely to happen by chance, it means the person accused is guilty.
A Definition
The prosecutor’s fallacy occurs when the likelihood of a false positive is underestimated, leading to erroneous conclusions.
This is best explained using an example.
An Example
Imagine this situation: you are the attorney of an innocent person who is charged with murder.
The evidence of the prosecutor is that the DNA of your client was found on the murder weapon.
You ask for the probability.
The prosecutor confidently states that the probability of the DNA test failing is one in a million. Hence, the probability that the client is guilty is 99.9999 %.
Fortunately, you are an attorney with knowledge of statistics and come with a different argument.
- Let’s assume that 4 million people are living in the urban area of the crime scene.
- We know the DNA test failing is one in a million. Hence, 4 people in the urban area are both, a positive match and innocent.
In total, there are five matches, but only one of them is guilty. So the probability of my client being guilty is only 20 %. Would you convict someone guilty only on this probability?
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| Image by the author, example of the prosecutor’s fallacy |
Conclusion
The prosecutor’s fallacy shows how quickly we could fall for the wrong assumption when using statistics.
As Daniel Kahnemann underlines, humans are bad intuitive statistics and can be told wildly different stories with the same numbers.
Be careful when presenting statistics and think of the conditional probability.
Thank you for reading!
I used what I’ve picked up about the Prosecutor’s Fallacy in the last years. For example, I’ve used this YouTube video as a source.
If you are interested in how to deal with fake news, stay tuned for my upcoming article, where I’ll reveal some strategies on how to identify and refute misinformation.