I Does this defense lawyer's probability argument sound like BS?

AI Thread Summary
The discussion critiques a defense lawyer's use of probability in a legal context, particularly regarding the application of Bayes' theorem. Participants express concern over the initial assumption of guilt being set at 1 in 200,000, arguing it fails to account for the defendant's status as a known sex offender. There is a consensus that many people lack a solid understanding of probability, which complicates the evaluation of such arguments. The likelihood ratio is clarified as a measure of evidence strength rather than a direct probability, emphasizing the need for careful interpretation. Overall, the conversation highlights the complexities and potential misinterpretations in applying statistical reasoning to legal cases.
swampwiz
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Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well.

https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence
 
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swampwiz said:
Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well.

https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence
What's wrong with it? This seems like an ok application of Bayes theorem.
The main problems with this kind of calculation are the difficulty of establishing the prior probability that someone is guilty, and the interpretation of the result. (What percentage was reasonable doubt again, your honour?)
 
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The general point seems sound to me, but I'd have a couple of objections;
1. General: most people don't have a good enough understanding of probability to properly evaluate the arguments.
2. Specific: I'm not happy with the initial assumption of guilt of 1/200000. That seems to assume he was randomly selected from the local population to be put on trial, or at least to have his DNA tested, but that isn't the case. He was a known sex offender, and therefore likely to be of interest as a suspect, and his DNA was already on the database and found to be a match. He was not a random choice.
 
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I would have to think about the defence's likelihood ratio argument. I have never seen a likelihood ratio interpreted as a probability. I think that may be an error. Or it may be using the term "likelihood" in a different context than I am used to.
 
mjc123 said:
Specific: I'm not happy with the initial assumption of guilt of 1/200000. That seems to assume he was randomly selected from the local population to be put on trial, or at least to have his DNA tested, but that isn't the case. He was a known sex offender, and therefore likely to be of interest as a suspect, and his DNA was already on the database and found to be a match. He was not a random choice.
I think that is a good point. Probably the beat approach would have been to start with the “random male” number but add “convicted sex offender” as an additional explicit piece of evidence.
 
FactChecker said:
I would have to think about the defence's likelihood ratio argument. I have never seen a likelihood ratio interpreted as a probability. I think that may be an error. Or it may be using the term "likelihood" in a different context than I am used to.
The likelihood ratio isn’t a probability because it can be greater than 1. It is the strength of the evidence. If you multiply the prior odds by the likelihood ratio then you get the posterior odds.
 
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