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One other example of the flaw (I think) that came out in pop culture was a few years ago during the Serial podcast about Adnan Syed. Near the end when the host

One other example of the flaw (I think) that came out in pop culture was a few years ago during the Serial podcast about Adnan Syed. Near the end when the hosts were wrestling about whether they should think he was guilty, the interviewer's friend (the producer? Dana?) came on and shared why she thought he was guilty, and it was this convoluted argument about if Syed was innocent, he'd have to be the unluckiest guy in the world, so therefore he was probably guilty. Her point was that it was just too strong a coincidence that it was his ex-girlfriend that got killed, on that particular day during some period of time when he didn't have an alibi, etc etc. That seemed to me like it could be a bad Bayesian argument - like it would have been a good argument had Serial selected a random citizen to interview, but they selected someone they already knew was connected to the story. Murders happen and by definition the circumstances are always highly unlikely because murders are so rare, and innocent people closely connected to the circumstances of the crime are very, very unlucky by definition. You can't point to that unluckiness as evidence that they're probably guilty.

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roywiggins 7y ago
Add to that, highly unlikely events occur all the time, but most of the time they're not anywhere near a murder. Once you start digging around for unlikely things, you'll find them. Heck, even if you dig into a random person associated with a murder, you'll find some unlikely things, but if you dig into a person who has already been accused of the crime (rightly or wrongly), of course there will be loads of suspicious circumstances. That's why they were accused in the first place.
- richk449 7y ago
  > highly unlikely events occur all the time They do?
  - reallydude 7y ago
    This is fundamental to Chaos theory (how small initial states can lead to rich systems that contain both expected and unexpected outcomes), which isn't a theory as much as an area of mathematical modeling of the most complex systems. Me waving off a butterfly is just as likely to influence a hurricane as the unmolested butterfly flapping. Any given reader's brain existing to comprehend this comment is highly unlikely, yet it occurs and continues within layers of chaotic systems, that exist turbulently, in perceived reality.
  - cataphract 7y ago
    Yeah, sure, it's a matter of how you define the event. Let's say some day you find an acquaintance on the street. Not extraordinary. But that specific acquaintance that you hadn't seen in 10 years. On that specific day, on that specific street, at that specific time. If you had wondered the day before how likely it would be that that specific set of circumstances would come togethet, you would have rightly concluded it was exceedingly unlikely. This is another way of looking at the first example in the article. The question was not how likely it was that that specific woman had their two children die of natural causes, but how likely it was that someone in the country or the world would have such a thing happen in a large interval of time.
    - roywiggins 7y ago
      "The chances of this exact event are 1 in a trillion, therefore with a high degree of confidence, it isn't happening and I am in fact hallucinating. You're not real, Bob from highschool!" And imagine how often you almost run into acquaintances on the street, and don't notice. It must happen more often than when you do notice. If you made a concerted effort to look for near-coincidences, you would suddenly find yourself noticing lots more unlikely things that were happening all along. Once you start digging into someone's life you'll learn all sorts of things that might seem really unlikely... but you'd find unlikely things in someone's life picked at random, you just never dug into them, because they're not accused of murder.
  - bzbarsky 7y ago
    Yes. Your chance of being hit by lightning in a given year is quite low. The average number of people struck by lightning in the US annually in the last decade is 270, according to https://www.weather.gov/safety/lightning-odds https://www.weather.gov/safety/lightning-odds (and while that's an estimate, the 27 average deaths/year over that period is not). So a specific person being killed by lightning within a given year is pretty unlikely (less than one in 10 million chance), and on average it happens once every two weeks in the US. Lots of people, see. Same thing with other situations where there are lots of observations...

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roywiggins 7y ago

Add to that, highly unlikely events occur all the time, but most of the time they're not anywhere near a murder. Once you start digging around for unlikely things, you'll find them. Heck, even if you dig into a random person associated with a murder, you'll find some unlikely things, but if you dig into a person who has already been accused of the crime (rightly or wrongly), of course there will be loads of suspicious circumstances. That's why they were accused in the first place.

richk449 7y ago
> highly unlikely events occur all the time They do?
- reallydude 7y ago
  This is fundamental to Chaos theory (how small initial states can lead to rich systems that contain both expected and unexpected outcomes), which isn't a theory as much as an area of mathematical modeling of the most complex systems. Me waving off a butterfly is just as likely to influence a hurricane as the unmolested butterfly flapping. Any given reader's brain existing to comprehend this comment is highly unlikely, yet it occurs and continues within layers of chaotic systems, that exist turbulently, in perceived reality.
- cataphract 7y ago
  Yeah, sure, it's a matter of how you define the event. Let's say some day you find an acquaintance on the street. Not extraordinary. But that specific acquaintance that you hadn't seen in 10 years. On that specific day, on that specific street, at that specific time. If you had wondered the day before how likely it would be that that specific set of circumstances would come togethet, you would have rightly concluded it was exceedingly unlikely. This is another way of looking at the first example in the article. The question was not how likely it was that that specific woman had their two children die of natural causes, but how likely it was that someone in the country or the world would have such a thing happen in a large interval of time.
  - roywiggins 7y ago
    "The chances of this exact event are 1 in a trillion, therefore with a high degree of confidence, it isn't happening and I am in fact hallucinating. You're not real, Bob from highschool!" And imagine how often you almost run into acquaintances on the street, and don't notice. It must happen more often than when you do notice. If you made a concerted effort to look for near-coincidences, you would suddenly find yourself noticing lots more unlikely things that were happening all along. Once you start digging into someone's life you'll learn all sorts of things that might seem really unlikely... but you'd find unlikely things in someone's life picked at random, you just never dug into them, because they're not accused of murder.
- bzbarsky 7y ago
  Yes. Your chance of being hit by lightning in a given year is quite low. The average number of people struck by lightning in the US annually in the last decade is 270, according to https://www.weather.gov/safety/lightning-odds https://www.weather.gov/safety/lightning-odds (and while that's an estimate, the 27 average deaths/year over that period is not). So a specific person being killed by lightning within a given year is pretty unlikely (less than one in 10 million chance), and on average it happens once every two weeks in the US. Lots of people, see. Same thing with other situations where there are lots of observations...