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# History Main / ProsecutorsFallacy

18th Nov '17 4:03:55 AM RedScharlach
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An argument of this form often ignores that unusual cases are, well, unusual. We tend to notice unusual events more than common events, and the very fact that the issue is being argued over guarantees that it is likely an unusual event. For instance, if a practised hunter accidently shoots his friend, one could argue that the odds of him making such a serious error is very small. But then, the alternative explanation is that the hunter ''purposefully'' shot his friend, which is also somewhat unlikely. In the end, the event itself can ''only'' be explained by one of several improbable explanations, and so the fact that they ''are'' improbable ceases to be relevant.

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An argument of this form often ignores that unusual cases are, well, unusual. We tend to notice unusual events more than common events, and the very fact that the issue is being argued over guarantees that it is likely an unusual event. For instance, if a practised hunter accidently accidentally shoots his friend, one could argue that the odds of him making such a serious error is very small. But then, the alternative explanation is that the hunter ''purposefully'' shot his friend, which is also somewhat unlikely. In the end, the event itself can ''only'' be explained by one of several improbable explanations, and so the fact that they ''are'' improbable ceases to be relevant.
17th Nov '17 8:05:58 AM garthvader
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** Another issue with this is that it assumes that the odds in question are meaningful. If one sees three specific cars on the way to work, one can calculate that the odds of seeing those three specific cars in that order, out of all the cars on the road at the time, are staggeringly low. But since the same would be true of ''any'' combination of three cars, there is no meaning to this figure.
17th Nov '17 7:57:01 AM garthvader
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* This was one of two errors in statistical reasoning that contributed to the result of the [[http://en.wikipedia.org/wiki/Sally_Clark Sally Clark]] trial in the UK. Sally Clark was arrested, charged, and wrongfully convicted of killing her two sons, who had died of sudden infant death syndrome, on the basis that two cot deaths in one family was extremely unlikely (an example of the prosecutor's fallacy -- double homicide isn't likely either). This error was compounded by an expert witness, who asserted that the probability of a double cot death was 1 in 73 million (a figure which assumed, without evidence, that both deaths were independent of each other -- ignoring possibilities such as a family with a genetic predisposition towards cot deaths).
8th Jul '17 9:15:10 AM nombretomado
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* A hypothetical example from [[TheOtherWiki t'other wiki]]: if a DNA sample with a 1 in 100,000 chance of producing a match is run through a database of 1 million people, it will probably produce around 10 meaningless matches - on its own, it can't be taken as proof (the related defender's fallacy is to argue that this evidence should be dismissed for that reason).

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* A hypothetical example from [[TheOtherWiki t'other wiki]]: Wiki/TheOtherWiki: if a DNA sample with a 1 in 100,000 chance of producing a match is run through a database of 1 million people, it will probably produce around 10 meaningless matches - on its own, it can't be taken as proof (the related defender's fallacy is to argue that this evidence should be dismissed for that reason).
17th Jun '17 9:11:12 PM nombretomado
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{{Wikipedia}} has an article on the subject [[http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy here]].

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{{Wikipedia}} Wiki/{{Wikipedia}} has an article on the subject [[http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy here]].
10th May '17 9:20:29 PM Luigifan
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* This was also a problem in [[https://en.wikipedia.org/wiki/People_v._Collins People v. Collins.]] A mixed-race couple (a black man with a mustache and beard and a white woman with blonde hair) were seen robbing an old woman and fleeing in a yellow car. The Collinses were a mixed race couple with the hair and car described. The prosecution famously claimed that the odds that such a couple existed in the area were 1 in 12 million, based on made-up statistics. [[note]]He asked his secretaries what they thought the odds were for a woman to be blonde, for a black man to have facial hair, and so on. He then gave these statistics to a mathematician, who treated each variable as if it was independent, even if it wasn't (men with beards are likely to have mustaches as well, but he treated them as independent variables.[[/note]] Even if the statistic was correct, and the likelihood of such a couple existing was 1 in 12 million, all it proves is that it is statistically unlikely for them to exist. Another couple, just as statistically unlikely, could have robbed the old woman. It doesn't mean that the chances that ''the Collinses weren't robbers'' was 1 in 12 million, though that was what the jury seemed to believe.

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* This was also a problem in [[https://en.wikipedia.org/wiki/People_v._Collins People v. Collins.]] A mixed-race couple (a black man with a mustache and beard and a white woman with blonde hair) were seen robbing an old woman and fleeing in a yellow car. The Collinses were a mixed race couple with the hair and car described. The prosecution famously claimed that the odds that such a couple existed in the area were 1 in 12 million, based on made-up statistics. [[note]]He asked his secretaries what they thought the odds were for a woman to be blonde, for a black man to have facial hair, and so on. He then gave these statistics to a mathematician, who treated each variable as if it was independent, even if it wasn't (men with beards are likely to have mustaches as well, but he treated them as independent variables.variables).[[/note]] Even if the statistic was correct, and the likelihood of such a couple existing was 1 in 12 million, all it proves is that it is statistically unlikely for them to exist. Another couple, just as statistically unlikely, could have robbed the old woman. It doesn't mean that the chances that ''the Collinses weren't robbers'' was 1 in 12 million, though that was what the jury seemed to believe.

* In ''The Poisoned Chocolates Case'' by Anthony Berkeley, Mr Bradley makes a list of twelve statements about the murderer, and declares that the odds against a random person meeting all the conditions are 4,790,000,516,458 to 1 against. But what he should be calculating is "What are the chances that, given that a particular person fulfills all the conditions, that person is the criminal?" -- which isn't the same thing at all. As Bradley goes on to points out that he himself meets all twelve conditions and is therefore, logically, the murderer, it's clear that he's only using the fallacy to {{troll}} his audience.
* In medicine, a test will have various numbers which indicate to the practitioner how much stock to put into the test's result. The four most commonly reported are: sensitivity (what percentage of people who have the tested condition test positive), specificity (what percentage without the condition test negatively), positive predictive value (what are the odds that a random positive answer means that someone is positive for the condition), and negative predictive value (odds a negative test means you don't have the condition. This fallacy is most similar to a situation where a test has a high sensitivity and high specificity, but a low positive predictive value.

to:

* In ''The Poisoned Chocolates Case'' by Anthony Berkeley, Mr Bradley makes a list of twelve statements about the murderer, and declares that the odds against a random person meeting all the conditions are 4,790,000,516,458 to 1 against. But what he should be calculating is "What are the chances that, given that a particular person fulfills all the conditions, that person is the criminal?" -- which isn't the same thing at all. As Bradley goes on to points point out that he himself meets all twelve conditions and is therefore, logically, the murderer, it's clear that he's only using the fallacy to {{troll}} his audience.
* In medicine, a test will have various numbers which indicate to the practitioner how much stock to put into the test's result. The four most commonly reported are: sensitivity (what percentage of people who have the tested condition test positive), specificity (what percentage without the condition test negatively), positive predictive value (what are the odds that a random positive answer means that someone is positive for the condition), and negative predictive value (odds a negative test means you don't have the condition.condition). This fallacy is most similar to a situation where a test has a high sensitivity and high specificity, but a low positive predictive value.
6th May '17 2:01:02 AM SMARTALIENQT
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* This was also a problem in [[https://en.wikipedia.org/wiki/People_v._Collins People v. Collins.]] A mixed-race couple (a black man with a mustache and beard and a white woman with blonde hair) were seen robbing an old woman and fleeing in a yellow car. The Collinses were a mixed race couple with the hair and car described. The prosecution famously claimed that the odds that such a couple existed in the area were 1 in 12 million, based on made-up statistics. [[note]]He asked his secretaries what they thought the odds were for a woman to be blonde, for a black man to have facial hair, and so on. He then gave these statistics to a mathematician, who treated each variable as if it was independent, even if it wasn't (men with beards are likely to have mustaches as well, but he treated them as independent variables.[[/note]] Even if the statistic was correct, and the likelihood of such a couple existing was 1 in 12 million, all it proves is that it is statistically unlikely for them to exist. Another couple, just as statistically unlikely, could have robbed the old woman. It doesn't mean that the chances that ''the Collinses weren't robbers'' was 1 in 12 million, though that was what the jury seemed to believe.
27th Nov '16 2:59:38 PM chc232323
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* In ''The Poisoned Chocolates Case'' by Anthony Berkeley, Mr Bradley makes a list of twelve statements about the murderer, and declares that the odds against a random person meeting all the conditions are 4,790,000,516,458 to 1 against. But what he should be calculating is "What are the chances that, given that a particular person fulfills all the conditions, that person is the criminal?" -- which isn't the same thing at all. As Bradley goes on to points out that he himself meets all twelve conditions and is therefore, logically, the murderer, it's clear that he's only using the fallacy to {{troll}} his audience.

to:

* In ''The Poisoned Chocolates Case'' by Anthony Berkeley, Mr Bradley makes a list of twelve statements about the murderer, and declares that the odds against a random person meeting all the conditions are 4,790,000,516,458 to 1 against. But what he should be calculating is "What are the chances that, given that a particular person fulfills all the conditions, that person is the criminal?" -- which isn't the same thing at all. As Bradley goes on to points out that he himself meets all twelve conditions and is therefore, logically, the murderer, it's clear that he's only using the fallacy to {{troll}} his audience.audience.
* In medicine, a test will have various numbers which indicate to the practitioner how much stock to put into the test's result. The four most commonly reported are: sensitivity (what percentage of people who have the tested condition test positive), specificity (what percentage without the condition test negatively), positive predictive value (what are the odds that a random positive answer means that someone is positive for the condition), and negative predictive value (odds a negative test means you don't have the condition. This fallacy is most similar to a situation where a test has a high sensitivity and high specificity, but a low positive predictive value.
** A concrete example: suppose an amazingly accurate test comes out that picks up on 99% of people with a disease and comes up negative in 99.9% of people without the disease. Now you test ten million people for a disease which occurs in 5 people per 100,000. There are 500 true cases of the disease. Your test identifies 495 of them. Your test also mislabels 1 in 1,000 as having the disease when they don't, which is approximately 10,000 people out of that 10 million! The positive predictive value is about 495/10,000, so a given positive test result only has an approximately 5% chance of actually identifying a person who has the condition.
24th Sep '16 11:00:29 AM Josef5678
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* This is also a favorite for conspiracy theorists when some (apparently) unlikely coincidence becomes part of the event in question. To use a WorldWar2 example, one radar site picked up the Japanese aircraft headed toward Pearl Harbor and reported the contact but were dismissed because entirely coincidentally a flight of aircraft from mainland was due to arrive at roughly the same time. This has been used by conspiracy freaks to argue the Japanese were allowed to attack because the odds of that sort of coincidence seem so remote.

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* This is also a favorite for conspiracy theorists when some (apparently) unlikely coincidence becomes part of the event in question. To use a WorldWar2 UsefulNotes/WorldWarII example, one radar site picked up the Japanese aircraft headed toward Pearl Harbor and reported the contact but were dismissed because entirely coincidentally a flight of aircraft from mainland was due to arrive at roughly the same time. This has been used by conspiracy freaks to argue the Japanese were allowed to attack because the odds of that sort of coincidence seem so remote.
29th Jul '16 12:17:24 PM john_e
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* The implicit assumption behind the ''Series/JudgeJudy''-ism "If it doesn't make sense, it isn't true."

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* The implicit assumption behind the ''Series/JudgeJudy''-ism "If it doesn't make sense, it isn't true.""
* In ''The Poisoned Chocolates Case'' by Anthony Berkeley, Mr Bradley makes a list of twelve statements about the murderer, and declares that the odds against a random person meeting all the conditions are 4,790,000,516,458 to 1 against. But what he should be calculating is "What are the chances that, given that a particular person fulfills all the conditions, that person is the criminal?" -- which isn't the same thing at all. As Bradley goes on to points out that he himself meets all twelve conditions and is therefore, logically, the murderer, it's clear that he's only using the fallacy to {{troll}} his audience.
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