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> In fact vos Savant messed this up herself. I don’t think it’s _that_ bad. She writes that “the host, who knows what's behind the doors, opens another door w

by kgwgk 3y ago

> In fact vos Savant messed this up herself. I don’t think it’s _that_ bad. She writes that “the host, who knows what's behind the doors, opens another door which has a goat.” Why would the problem statement say that the host knows what's behind the doors (devoting 10% of the description to making this clarification) if not to indicate that he knowingly opens another door which has a goat?

DoctorOetker 3y ago
The host knowing what's behind the doors doesn't specify the host's behavioural protocol. There are multiple host protocols that are compatible with the stated run of events. They result in different probabilities. For example protocol 1: if the player chose the door with a car behind it, open one of the doors with a goat, else don't open any doors and immediately reveal the player got a goat and "lost". In this scenario it's better to stay with your pick, i.e. the opposite advice of the "solution" since under this protocol the host opening a second door indicates you guessed the right door. Your selected fragment "the host, who knows what's behind the doors, opens another door which has a goat.” does not exclude this scenario. Example protocol 2: after the player has chosen a door, the host throws a coin for the remaining 2 doors, but only opens that door if it has a goat. You can make countless variations that are perfectly compatible with the givens in the problem statement yet have different probabilities associated with them. The problem really is ill-posed. If more than a 1000 PhD's wrote back in complaint, then perhaps a more probable explanation is that while reading the problem statement they assumed distinct host protocols, and if that happens, its worth checking if the givens are actually part of the problem statement, and not extraneously appended in the "resolution". Otherwise the puzzle just becomes "guess the probability of what I supposedly convey".
- kgwgk 3y ago
  > The host knowing what's behind the doors doesn't specify the host's behavioural protocol. I agree. I just said that it was not _that_ bad. > If more than a 1000 PhD's wrote back in complaint, then perhaps a more probable explanation is that while reading the problem statement they assumed distinct host protocols, I wonder how many of them pointed out that the problem was ill-posed - instead of assuming distinct protocols or just failing to solve properly the problem. At least one those PhDs went from "Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful." to "I wrote her another letter, telling her that after removing my foot from my mouth I'm now eating humble pie. I vowed as penance to answer all the people who wrote to castigate me. It's been an intense professional embarrassment."
  - DoctorOetker 3y ago
    >> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. > I agree. I just said that it was not _that_ bad. It's great we can agree the problem is ill-posed. But that is a binary thing, either it is ill-posed or it is not. It can't be a little bit ill-posed. I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. It's not easy to design a proper puzzle, so it's tempting to simply hide a non-given "given" in the "solution". The best way to not get caught is to have separate identities ill-pose-without-the-given and "solve"-with-the-given. Flame wars guaranteed... EDIT: now that I think of it, I even fail to verify that the poser "Craig F. Whitaker" didn't collude, or even that he existed. Looking at the archive.org copy of vos Savant's own website: https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... I see something very suspicious about the first 2 letters quoted (including the one you requoted): They are ostensibly written by different people, yet use very similar wording, and essentially contain the same information sentence by sentence. First I will repost both integrally: Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D. George Mason University You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida Both use "blew it", where there are many other alternatives like "mess it up" (which I used). Robert: If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. Scott: After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. Both also somehow connect this with public literacy and public shaming. Robert: As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Scott: There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! These people at least seem to exist, but something strange is going on. It's also regrettable I can't find the original Parade articles on the internet archive...

by kgwgk 3y ago

DoctorOetker 3y ago

The host knowing what's behind the doors doesn't specify the host's behavioural protocol. There are multiple host protocols that are compatible with the stated run of events. They result in different probabilities. For example protocol 1: if the player chose the door with a car behind it, open one of the doors with a goat, else don't open any doors and immediately reveal the player got a goat and "lost". In this scenario it's better to stay with your pick, i.e. the opposite advice of the "solution" since under this protocol the host opening a second door indicates you guessed the right door. Your selected fragment "the host, who knows what's behind the doors, opens another door which has a goat.” does not exclude this scenario. Example protocol 2: after the player has chosen a door, the host throws a coin for the remaining 2 doors, but only opens that door if it has a goat. You can make countless variations that are perfectly compatible with the givens in the problem statement yet have different probabilities associated with them. The problem really is ill-posed. If more than a 1000 PhD's wrote back in complaint, then perhaps a more probable explanation is that while reading the problem statement they assumed distinct host protocols, and if that happens, its worth checking if the givens are actually part of the problem statement, and not extraneously appended in the "resolution". Otherwise the puzzle just becomes "guess the probability of what I supposedly convey".

kgwgk 3y ago
> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. I agree. I just said that it was not _that_ bad. > If more than a 1000 PhD's wrote back in complaint, then perhaps a more probable explanation is that while reading the problem statement they assumed distinct host protocols, I wonder how many of them pointed out that the problem was ill-posed - instead of assuming distinct protocols or just failing to solve properly the problem. At least one those PhDs went from "Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful." to "I wrote her another letter, telling her that after removing my foot from my mouth I'm now eating humble pie. I vowed as penance to answer all the people who wrote to castigate me. It's been an intense professional embarrassment."
- DoctorOetker 3y ago
  >> The host knowing what's behind the doors doesn't specify the host's behavioural protocol. > I agree. I just said that it was not _that_ bad. It's great we can agree the problem is ill-posed. But that is a binary thing, either it is ill-posed or it is not. It can't be a little bit ill-posed. I don't believe it's a coincidence that the ill-posed problem gets the high profile attention. It's not easy to design a proper puzzle, so it's tempting to simply hide a non-given "given" in the "solution". The best way to not get caught is to have separate identities ill-pose-without-the-given and "solve"-with-the-given. Flame wars guaranteed... EDIT: now that I think of it, I even fail to verify that the poser "Craig F. Whitaker" didn't collude, or even that he existed. Looking at the archive.org copy of vos Savant's own website: https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... I see something very suspicious about the first 2 letters quoted (including the one you requoted): They are ostensibly written by different people, yet use very similar wording, and essentially contain the same information sentence by sentence. First I will repost both integrally: Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D. George Mason University You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! Scott Smith, Ph.D. University of Florida Both use "blew it", where there are many other alternatives like "mess it up" (which I used). Robert: If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. Scott: After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. Both also somehow connect this with public literacy and public shaming. Robert: As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful. Scott: There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame! These people at least seem to exist, but something strange is going on. It's also regrettable I can't find the original Parade articles on the internet archive...