Talk:Prosecutor's fallacy

message: Mathematicians and scientists are desperate to be complete, correct, and precise. That's a good thing. But this is a very bad thing for the introductory sentences of an article. The result is that we get introduction bloat. This problem has grown in Wikipedia over the years.  I see this in page after page.
Introductions must be short and simple summaries. I think a rule of thumb would be a max limit of 3 sentences with 10 words for each sentence. I know this idea is intimidating. It has been for me. But now when I try to read other people's articles, I just get confused.
I'm working on a computer science thesis for Bayes Rule. I really want to modify the intro paragraph for this article to make it simple. I would much rather that someone else started swinging the scythe. It is a thankless task that can easily make enemies. But I appeal to all you my colleagues. Think of the poor high school kid seeing this for the first time...or the poor lawyer who can't do math...or the dumb politician who only has 30 seconds...or the poor thesis writer who wants to know the difference between the general idea and the exceptions, boundary conditions, contrarian opinions, idoesyncracies, latest developments, anticipations, implications, bullet lists, subordinate concepts, and everything else that doesn't go in an introduction. I'm thinking that maybe the brevity of a dictionary definition is about right for an introduction.
A really really simple math-free example with provocatively relevant teeth should be right after the introduction. After that, the triple integrals can really fly.
My apologies in advance if I've offended. But please, let us work together. Let's try to remember rhetorical architecture. Wiki will be better for it.
--ClickStudent (talk) 16:49, 23 May 2008 (UTC)
thread_title: About Introductions in Every Wikipedia Article

message: I removed the following paragraph from this article:
Another instance of the prosecutor's fallacy is sometimes encountered when discussing the origins of life: the probability of life arising at random out of the physical laws is estimated to be tiny, and this is presented as evidence for a creator, without regard for the possibility that the probability of such a creator could be even tinier.
''
There is absolutely no way to establish the probability of there being a creator. One person might say the probability is zero. Another might say that it's 1. A few may put it somewhere in between. But the question isn't really one of probability at all. :-Rholton 02:40, 3 Dec 2004 (UTC)
replies: text: That's not a valid reason to remove the paragraph.  The described argument takes the probability of there being a creator as the inverse of the probability of life arising at random out of physical laws.  Within that framework, the argument is an example of the prosecutor's fallacy.  Whether that inverse relationship really holds or whether its actually possible to calculate the probability of life arising at random out of physical laws is beside the point. 68.6.73.60 11:50, 13 March 2006 (UTC)
thread_title: spurious argument

message: This seems to be incorrect, unless I'm missing something:
:When the photographic evidence is combined with the match, the two together point strongly towards guilt, since (assuming the chance of being in the photograph and having the match are independent) the chance that the accused is innocent falls to about 0.01%.
It seems that the probability of innocence only falls to 89.1%, since 0.9 x 0.99 = 0.891. Even with the untenable independence assumption (for example, someone may be framing them by setting up several pieces of evidence), it would take quite a bit more evidence to show anything beyond reasonable doubt. Deco 07:16, 17 Feb 2005 (UTC)
replies: text: You are indeed missing something and falling into the defendant's fallacy.  The argument goes that the prior probability that the man is innocent is 9,999,999/10,000,000.  While the likelihood of having the match and being in the video may be 1 if guilty, the likelihood of the match if innocent is 1/1,000,000, and the likelihood of being in the video if innocent is 1/100,000,  so (assuming independence since this is mathematics, not real life) the likelihood of both happening if innocent is 1/100,000,000,000.  That gives a posterior probability of being innocent of  9,999,999/100,009,999,999 which is 0.000099989991... or about 0.01%. --Henrygb 03:11, 12 Mar 2005 (UTC)
replies: text: Thanks, I get it now - I forgot we were dealing here with conditional probabilities, not just prior probabilities. This result fits with common sense, too — we often consider 2 pieces of strong evidence conclusive. Deco 03:30, 12 Mar 2005 (UTC)
thread_title: Strange statement

message: This is rather minor, doesn't take anything away from the article, but in the interests of accuracy...
At the top, the article mentions a 1-in-a-million chance in a community with 10 million people, saying that on average 10 people will match. Then later it says that this means that if someone matches it only means a 1/10 chance of guilt. However this is not the case - if we know someone matches it changes the expected number of people that will match. There is one person (the defendant) who we know matches, and there are 9,999,999 people who each also have a 1-in-a-million chance of matching, fro which we can expect about 10 people to match. This gives the defendant a 1/11 chance of guilt. Of course this figure changes again if numerous tests were performed and only the defendant matched - it's 1 in (1 + one millionth of the untested population).
Though I don't want to add this straight into the article, I want to get some confirmation I'm not completely wrong in my calculations here... most notably that I'm not falling on the wrong side of the trap "Expected number given this particular person matches" vs "Expected number given at least one person matches" - I think I have it right though. Phlip 06:49, 6 October 2005 (UTC)
thread_title:  Right answer to the wrong question 

message: A friend of mine sent me  this example. It may deserve a paragraph here or in the Bayes theorem article. Bill Jefferys 21:36, 16 December 2005 (UTC)
thread_title:  A surprising example 

message: "When the photographic evidence is combined with the match, the two together point strongly towards guilt, since (assuming the chance of being in the photograph and having the match are independent) the chance that the accused is innocent falls to about 0.01%. This low probability of innocence is not proof of guilt." - the derivation of 0.01% is unclear. This could be wrong.
:I said the same thing. See above. Perhaps this should be clarified in the article. Deco 18:52, 22 December 2005 (UTC)
thread_title:  Possibly erroneous statement 

message: In legal terms, the prosecutor is operating in terms of a presumption of guilt, something which is contrary to the normal presumption of innocence where a person is assumed to be innocent unless found guilty. A more reasonable value for the prior odds of guilt might be a value estimated from the overall frequency of the given crime in the general population.
In the UK at least, procecutors are oblidged to presume guilt, reguardless of evidence to the contrary.
Defendants are oblidged to presume innocence, reguardless of evidence to the contrary (unless their client pleads guilty).
jurors are oblidged to initially presume innocence, and change their mind according to the cases presented, but only return a guilty verdict if they are sure 'beyond reasonable doubt' of the defendant's guilt.
And, finally, expert witnessess are oblidged to initially presume nothing -- neither innocence nor guilt -- and approach the situation unbiasedly.
So, prosecutors assuming guilt is not contrary to the normal presumption of innocence ;)
I took it out. Figured the edit needed explainin --DakAD 15:42, 7 June 2006 (UTC)
replies: text: Can you provide evidence to support your statement that UK Prosecutors are required to presume guilt please? ---*- u:Chazz/contact/t: 02:26, 26 February 2007 (UTC)
replies: text: This is profoundly wrong, DakAD might like to read the Crown Prosecution Service's "Statement of Ethical Principles" to be found at - http://www.cps.gov.uk/legal/s_to_u/statment_of_ethical_principles_for_the_public_prosecutor/#a04 in particular Section 4 which states both that prosecutors "have a duty to the court in question to act with independence in the interest of justice" and "remain impartial and objective". 82.6.156.126 (talk) 23:09, 23 February 2010 (UTC)
thread_title:  Another possibly erroneous statement 

message: Where does the fact that Sally Clark died of alcohol abuse come from? Not from the article linked... 193.166.223.5 (talk) 11:04, 26 August 2008 (UTC)
thread_title:  ... and later died from alcohol abuse

message: This whole section is completely fallacious, since a lot of its contents is falsely based on the gambler's fallacy. The section goes on a very long and incomprehensible description of why should the defendant be almost definitely guilty and I had to read it three times to understand it, although my knowledge of the probability theory goes quite far, since I studied mathematics and I play poker for a living. So, as far as I have understood, the test is 99.9999% correct, but there is only one person out of 10 million who is actually guilty. So, in fact, the expected value of guilty people is 1*99.9999%, or almost one person and the expected value of false positives is 99,999,999*0.0001%, or about 10 and, according to the Bayes' theorem, defendant's reasoning is actually correct, he just used a shortcut to get there.
The section goes on to add some video, where (IANAL, I just use common sense) using it to show guilt is mathematically nonsensical. Also, it assumes a probability of 0.1% of the two events having happened (where, also, assuming their mutual independence changes the odds by a very large degree), which is utterly false, as it revolves around the same idea that a coin having come tails 10 times in a row is now only 2-10 to come tails on the next throw. I suggest this section to be removed or at least completely rewritten, as it is full of false information that contradicts the rest of this article. 93.136.119.103 (talk) 17:32, 11 September 2009 (UTC)
replies: text: I don't see that.  The article says "the likelihood of both happening if innocent is 1/100,000,000,000" so the combination of tests does not lead to your 99.9999% accuracy but 99.999999999%, and so the combination of tests leads to a very much smaller expected false positve number. --Rumping (talk) 08:07, 27 January 2010 (UTC)
thread_title:  Defendant's fallacy 

message: The thought experiment involving balls in a bowl is fallacious (ironic since it supposed to be exposing a fallacy).  Drawing a white ball actually does give you good reason to believe the ball is wood, since it is (Bayesian) evidence that there are not a large majority of red (plastic) balls in the bowl. Anyone who wants to revert this edit, please provide source/reference for this thought experiment, which is currently un-attributed. 
Joncolvin (talk) 05:40, 2 February 2010 (UTC)
thread_title:  Mathematical analysis thought experiment is fallacious 

message: This section seems to be a re-worked Defendant's fallacy. I should point out I'm not familiar with this fallacy. However, this appears to me to be a very different argument. The Defendant's fallacy (seen above in this talk page) seems to address the problem of dismissing two separate items of evidence as weak, when they can be combined and as such are quite strong. The article now seems to suggest that by conducting a test of 10 million people with a probability of a positive of 1 in a million given innocense, it is false to assume that a positive result is only indicative of a 10% chance of guilt. Leaving aside the question of whether the 10 million people are sure to contain the guilty party (a question raised above), it seems to me that this evidence alone does only give approximately a 1 in 10 (or 11) chance of guilt. The earlier article coupled a similar test with a further test to obtain an increased probability. This chapter seems an example of the fallacy cause by multiple testing, mentioned above. While a probability of 1 in 10 (or 11) may actually be significant with other evidence, as the citation seems to suggest, it hardly seems a fallacy to produce this sort of probability without further supporting evidence.
Probability is an area I have some knowledge in, but I'm in no way specialized in this area. I don't assume that I haven't missed something, and so I'd rather someone corrected me here than I mistakenly corrected the article.
Timbo76 (talk) 05:49, 11 January 2011 (UTC)
replies: text: I have added a sentence to indicate how to interpret the probability that a group of suspects might not include the guilty person.  —DIV (1.144.109.102 (talk) 04:30, 5 October 2019 (UTC)

text: I agree: How do they get the 90% chance of guilt? The prosecutor argued what proportion to reach the 90%? The rate of the gene in the population of the town? Because it would require furher elaboration, somethong like: as only 10% of the population could have the gene, 90% of the population is innocent, 10% could be guilty. That doesn´t add to 90%. Sbriones (talk) 15:12, 23 March 2023 (UTC)
thread_title:  Defense attorney's fallacy 

message: The article says the one of two possibilities must be true:
Both died from SIDS
or Both were murdered.
What about the probability of one dying from SIDS and one murdered, or deaths from other causes?  —Preceding unsigned comment added by 149.171.196.222 (talk) 02:40, 11 March 2011 (UTC)
replies: text: These issues are tackled in: Hill, R. (2004). Multiple sudden infant deaths – coincidence or beyond coincidence? Paediatric and Perinatal Epidemiology, 18, 320-326. 114.72.190.236 (talk) 06:41, 2 June 2011 (UTC)
replies: text: No, this is a problem with the article. It shouldn't say there are only two possibilities, since obviously there is a third possibility: one child dies of SIDS and the other is murdered. Perhaps it should be reworded, such as "If we consider the following two possibilities..." 206.116.243.76 (talk) 02:41, 3 September 2012 (UTC)
replies: text: It's also (and ironically) a problem with the RSS press release, which read: "Two deaths by SIDS or two murders are each quite unlikely, but one has apparently happened in this case." However, there is a plausible argument (which doesn't appear to be given explicitly by Hill) why the one-of-each hypothesis can be neglected. If a single death is much more likely to be SIDS than murder (Hill gives this ratio as 17:1, and we would see many more murder suspects if it were not so), then SIDS-SIDS is more likely than SIDS-murder (by the same ratio) even if double SIDS deaths are uncorrelated (and a positive correlation would enhance the ratio; a negative correlation would be needed to reverse it -- or other relevant information about a given case, of course). I've neglected to consider the factor of 2 associated with SIDS-murder vs. murder-SIDS, but 2 is much less than 17.  — Preceding unsigned comment added by 163.1.19.73 (talk) 14:41, 4 October 2012 (UTC)

text: The preceding paragraph is based on the assumption that the probability of murder (or SIDS) is independent of prior SIDS (or murder), which would also have to be tested. But it seems likely that the ordering is indeed as given, i.e. that (in the absence of other evidence) double-SIDS is more likely than one-of-each. (Of course, if other evidence indicates that murder is more likely than SIDS in one of the two deaths, then it may well be that the entire ordering is reversed: SIDS becomes less likely than murder in the other death too, and hence double-SIDS becomes the least likely explanation.)  — Preceding unsigned comment added by 163.1.19.73 (talk) 14:52, 4 October 2012 (UTC)
thread_title:  The Sally Clark case 

message: The wording of a lede should not be as difficult to follow for the ordinary reader as this; it's far too technical. I very much doubt anyone without real knowledge of statistics will be enlightened by it, many will be put off reading further. The detailed knowledge that Melcombe obviously has should be used to simplify the lede, even if that makes it less complete. The full technical explainations should be moved to the main body of the article, which is the proper place to go into them. Overagainst (talk) 21:19, 11 June 2012 (UTC)
replies: text: The lede is unintelligible and I have an expertise is this area.CSDarrow (talk) 21:31, 16 April 2013 (UTC)
thread_title: Lede

message: I have a few college degrees and I'm still not sure I understand what the prosecutor's fallacy is, even after reading this article. It seems like a common problem with logic-related articles on Wikipedia. 
Can the Editors working on this piece pretend that the average reader a) knows nothing about the philosophical field of logic, b) knows little about the processes of law and statistics and c) can not decipher these cryptic equations? The average person who comes across this article (probably because another article links to it) does not have a background in logic or philosophy. Do not write for those who already knows what a prosecutor's fallacy is, write for those who don't even know what a "fallacy" is. That's the best contribution you could make. Liz Read! Talk! 14:41, 10 November 2013 (UTC)
thread_title:  Clarity in writing 

message: Hello fellow Wikipedians,
I have just added archive links to  on Prosecutor's fallacy. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive http://web.archive.org/web/20030528061717/http://www.colchsfc.ac.uk:80/maths/dna/discuss.htm to http://www.colchsfc.ac.uk/maths/dna/discuss.htm
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thread_title:  External links modified 

message: There appears to be a typo in the intro of this section. It lists a change from 10% to 10%, but that's the same number both times. I am not familiar enough with the subject to know what the correct wording should be. Here is the sentence I am talking about:
"If, for example, the police came up with a list of 10 suspects, all of whom had access to the crime scene, then it would be very illogical indeed to suggest that a test that offers a one-in-a-million chance of a match would change the defendant's prior probability from 1 in 10 or 10 percent to 1 in 10 or 10 percent."
173.161.135.17 (talk) 16:47, 31 October 2018 (UTC)
thread_title:  Possible typo in the "Defense attorney's fallacy" section 

message: Great job, you guys managed to make a simple fallacy almost completely incomprehensible to anyone who isn't an expert in logic or law. BinkeBint (talk) 11:37, 1 April 2023 (UTC)
thread_title:  Clarity issues 

message: Consider this article (prosecutor's fallacy or PF) and that about base rate fallacy (BRF). I do not think there is much question that PF is synonymous, or a subset of, the BRF. Hence it would make sense to merge the two; the only question is how.
As of now, the BRF article is much clearer than the PF one (in particular, the lead of PF is atrocious). I would suggest to redirect PF to BRF and to incorporate the following modifications in BRF:
#add one sentence to the lead such as 
#move the blood type example (currently in the lead of PF) into a fourth example at BRF
#create a new section "examples in law" and move there (1) the OJ Simpson defense argument (trimmed down a bit), (2) the Sally Clark case (trimmed down a lot), (3) the multiple-testing DNA-database-search.
The rest of the PF is more or less a less clear duplicate of parts of the BRF article.
Any objections? TigraanClick here for my talk page ("private" contact) 16:25, 21 April 2023 (UTC)
replies: text: @Tigraan Given that no one has clarified the wording on this article for more than a year, according to the maintenance tag... sure seems like you might as well go ahead and do this. -- asilvering (talk) 20:58, 20 June 2023 (UTC)
replies: text: Done. Two months without comments, I sure hope nobody objects now... TigraanClick here for my talk page ("private" contact) 08:52, 22 June 2023 (UTC)
thread_title:  Selective merge to [[base rate fallacy]]