Morning Ed: Hodgepodge {2017.10.12.Th}

[Hp1] Use labels. It helps.

[Hp2] Teens are growing up so slowly! But that’s not such a bad thing.

[Hp3] Holy crap, these are awesome.

[Hp4] Instead of learning a language, maybe you should learn a dialect.

[Hp5] The Economist looks at claustrophobia.

[Hp6] “Black lives matter”… accidentally.

[Hp7] Robert VerBruggen says that everybody was wrong on the Monty Hall (RIP) problem.

[Hp8] I see a lot of comparisons to the sex robots and pornography, and a lot of impulses to come to different conclusions as to whether or not they might reduce sex crimes. It seems to me the same mechanisms should mostly work for both or neither.

[Hp9] There are priors and there are priors, but there are always priors.


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Will Truman is a former professional gearhead who is presently a stay-at-home father in the Mountain East. He has moved around frequently, having lived in six places since 2003, ranging from rural outposts to major metropolitan areas. He also writes fiction, when he finds the time. ...more →

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77 thoughts on “Morning Ed: Hodgepodge {2017.10.12.Th}

  1. Hp7: I have been saying just this for well over a decade now. The problem, in its standard Vos Savant formulation, is unsolvable. That someone whose sole claim to our attention is that she is super duper smart can’t see the unstated assumptions is why I role my eyes at the mention of her. But when I point out the unstated assumption in the Monty Hall problem, there usually are people prepared to jump in and claim that it need not be stated, as it is implied by, um…, stuff–mostly that otherwise you don’t arrive at the correct answer.

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    • I must be dense because I don’t see it. Assuming I don’t want goats and want a car, why wouldn’t it be to my advantage to try the other door, regardless of whether the host is trying to sway my choice and in which direction he/she is trying to sway it? I suppose there’s the opportunity cost of the 10 seconds or so it takes to say, “yes, I’ll try door #2.” But other than that, do I really lose by trying another door, even if it’s the one suggested by the host?

      Again, though, maybe I’m missing something about the nature of the problem.

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      • The conventional “correct” answer includes the unstated assumption that Monty will always open a door and offer to let the contestant switch (at least if the car isn’t behind the door he opened). Suppose instead that he both knows where the car is, and wants to fuck with you. You pick door number 1. Monty knows that the car is indeed behind door number 1, so he opens door number 2 and asks if you want to switch to door number 3. You, being the good logician that you are, naturally jump at the chance. You end up with a goat. But suppose you pick door number 1 and Monty knows the car is behind door number 3. Here he doesn’t make the offer. You end up with a goat. Congratulations.

        Add in the assumption that Monty always opens a door other than the one the contestant picked, and the logic of the conventional answer is flawless.

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          • All this shows is that people don’t understand the problem. That is not a good look if the individual person demonstrating his incomprehension is the one presenting it, and crowing about other people not getting it right.

            It doesn’t matter whether or not Monty knows there the car is. If you pick door number one, and Monty opens door number two to reveal the car, then he obviously isn’t going to offer to let your change your pick. But in the fact set presented in the problem, he opens a door to reveal a goat. Whether or not Monty knew that before opening the door doesn’t affect the problem.

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            • I’ll probably just have to surrender and decide I don’t understand the problem or even the question that’s being asked. Smart people here who I respect say I’m missing something, so I must be.

              ETA: I’m not trying to be maudlin or snarky. I’m just stating something that I think is a fact. At any rate, I’m too lazy to try to figure it all out right now.

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    • it need not be stated, as it is implied by, um…, stuff–mostly that otherwise you don’t arrive at the correct answer.

      This sort of thing is conventional with puzzles with real-world elements, though — you make the assumptions necessary to make it reasonably solvable. The question is whether the assumption of consistency in the Monty Hall problem is a reasonable one or not. It depends to some extent on the context and on exactly how it’s presented.

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      • This makes the puzzle into one of those badly worded SAT questions, where the trick to getting the “correct” answer is to correctly guess the prejudices of the test writer. This is indeed testing something, but surely it is better to have a well worded question that tests what you want it to test.

        In the instant case, it is trivially easy to avoid the problem:

        “Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” You know from having watched the show that he always makes this offer. Is it to your advantage to switch your choice of doors?”

        I added the penultimate sentence. Ambiguity removed. Note that the problem as previous stated includes a statement much like this, but unlike this, it is unnecessary. It does not matter whether the host knows what is behind the doors. If he opens door number 3 and there the car is, the contestant has no decision to make. That circumstance would make for much of a logic problem, but it has no bearing on the fact set presented.

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        • It’s easy to handle any one particular case, but it’s hard to answer every possible objection without a three-page intro into the problem — what if I already have three cars and would rather have a goat? What if I only have a week to live and will die before I get either prize? What if the game show is a sham and I won’t get anything no matter what I pick?

          So we make what we think are reasonable assumptions. I agree that as the puzzle is often presented, this particular one would be good to state so that we know we’re dealing with a probability puzzle and not a psychology puzzle, but I don’t think it’s as clear-cut as you’re suggesting.

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          • I will grant you that there are certain conventions. The relative desirability of a car and a goat is understood. Someone objecting that maybe the contestant would prefer a goat is just being an asshole. But is there a convention that “The problem as stated does not provide sufficient information” is not a permissible answer? This is not at all obvious to me. Even if we stipulate to this, we aren’t out of the woods. When the problem in fact does not provide sufficient information it becomes the problem solver’s responsibility to fill in the assumptions, based on real-world experience, to arrive at a problem that is in fact solvable. But in the real world of Let’s Make a Deal, Monty did not in fact always follow this behavior pattern. It is the person claiming the problem is properly worded who has to reject real-world conventions. It certainly is possible to go down this path indefinitely, but it all amounts to “Answer the question I meant to ask, not the one I actually asked.”

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            • My main point was that it comes down to questions of reasonability and expectations, so naturally different people will have different takes. Absent a well-defined judge or jury, it’s not a question of what’s “permissible” but of what people can agree on. One person’s reasonable objection is another person’s “being an asshole”. And this is complicated even more by the existence of “trick” puzzles whose answer depends on discarding a typical assumption.

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        • The issue you bring up is whether it’s rational for a person to view Monty’s offer to take door # 2 as evidence of which door the car is behind, and the fact that the original framing didn’t exclude that possibility renders the conclusion of a determinate answer about switching incorrect. That view, it seems to me, assumes that his behavior when offering the choice to switch, without further information to the contrary, actually is informative.

          I’m curious as to why you think that. Is there a decision-making model which provides evidence that Monty would be trying to direct you towards or away from picking the door with a car absent the presumption that the game is rigged?

          Or is that ultimately your objection to the standard framing: that it doesn’t explicitly exclude the possibility that the game is rigged?

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          • I’ll point out, again, that it literally doesn’t make sense as a probability problem if the prizes can move, or if Monty decides to reveal the car. (Given the problem is, succinctly, “Should you stay or switch with the other door to have a better chance of winning the car”).

            If Monty can switch prizes, your gut instincts on probability are correct. It’s 50/50, because the car can be behind either closed door. If Monty can reveal the car, it’s a pointless problem because your odds of winning are zero.

            If Monty cannot reveal the car, and the prizes cannot switch, that’s when you see probability and gut instinct diverge and thus have a teachable moment. Or, at least, an actually interesting probability problem.

            So if the original formulation of the problem is unclear, a little actual exploration of the problem is sufficient to work out that the question of “Can he switch the prizes” and “Can he reveal the car” is “No” unless your puzzle is under the “really easy, don’t even have to do the math” category.

            In short, the fact that it’s a an actual probability problem or an actual puzzle nails down those assumptions, unless you’re also assuming “This problem/puzzle is trivial”.

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            • Right. I’m trying to figure out if Richard’s criticism of Vos Savant’s framing of the problem is semantic-y or logic-y. Seems to me that if Monty Hall were to run the game for someone who’d never heard of it before and said “Now, do you want switch your choice to door 2?”, that person may try to glean information from his making such an offer. What I’m wondering is how presupposing *that* possibility in our decision-making entails that the original description of the puzzle is indeterminate. Doing so requires presupposing that Monty’s having asked the question constitutes determinate evidence of where the car is.

              Seems to me at that point we’re like Vizzini trying to figure out which glass contains iocaine powder.

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            • Yes.

              The sole clarification missing from the question, which the entire article seems to hinge on, is ‘Is the switching a predetermined part of the game?’.

              If yes, that makes the entire thing subject to calculatable probability, and switching is always a good idea.

              If not, the probabilty includes the chance he might deliberately be trying to trick you. You are no longer just playing the odds, you are possibly _competing_ with someone.

              Which, as you point out, is literally impossible to calculate the probability for, at least within the question as stated.

              Heck, we don’t even know what his incentives are…it seems logical he doesn’t want to give away the car…but is it? I mean, they’re not his personal cars! Maybe he get paid based off viewership, and more viewers tune in on average when he’s giving away cars, so he’s rigging the game for excitement, so he tries to help most people win cars…and then again, maybe he knows if everyone wins, that looks bad, so he’s trying to get ~80% of people to win, and all the other contestants have a better sob story and make for better TV if they win, so he’s trying to trick you. Hell, maybe he’s racist and sexist and only helps white men win, so now we have to consider what ‘we’ are in this hypothetical.

              We have no possible way of knowing any of this based on the question.

              Even if we know what he’s trying to do, if we know he’s trying to keep the car for example, the question is still impossible. If Monty is trying to trick people into switching, he also is trying to trick people into thinking he’s trying to trick people into switching.

              If he always only offered the switch if the person picked the car to start with, pretty soon everyone would know and no one would ever switch, rendering the game pure 1/3 odds. So he has to offer a switch sometimes when it’s the right thing to do, so that people will switch it when it’s the wrong thing to do.

              Which mean we’re basically trying to calculate a ‘I know he knows I know he knows’ situation.

              ‘I know he thinks that I won’t switch, so I will switch instead. Except he must know that all that, and so, I shall trick him by not switching as originally planned. *pauses*…is what he knows I have to be thinking, so instead I shall switch.’

              This has nothing to do with probability. (And is just complete nonsense to try to attempt.(1))

              So, yes, it makes sense to say ‘I shall interpet this problem in a way that is actual solvable, instead of in a way that it is impossible to solve because it’s involves the possibly unknown motives of someone trying to preemtively trying to figure out what we’re going to do.’

              1) If you ever find yourself in a situation like this, remember that people in a competition have an implicit bias towards ‘doing stuff'(2), and often assume their opponant will also. So, if there’s an ‘inaction’ option, and you have no other clues, assume they are not going to take it, and assume they think you won’t either.

              (I am, of course, merely telling everyone this so that I know what you’re going to do. Mwhahaha.)

              2) Which is, indeed, why most people on Monty Hall, most who didn’t know the math, did choose to switch anyway.

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              • Which, as you point out, is literally impossible to calculate the probability for, at least within the question as stated.

                Yes and no — you could do an RCT, put X number of people in the position of host in this situation and analyze the frequency with which they do or don’t offer the switch in different situations, then factor that into your calculation. If we say that an average person does action A 60% of the time, then that’s in some sense a probability for whether the unnamed host in the problem would do so as well.

                Obviously not the intention of the puzzle, but there are more options than just saying it’s under-determined. There are professional Rock, Paper, Scissors players who’ve done similar analysis and win significantly higher percentage of games than random chance would allow for.

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                • Yes and no — you could do an RCT, put X number of people in the position of host in this situation and analyze the frequency with which they do or don’t offer the switch in different situations, then factor that into your calculation. If we say that an average person does action A 60% of the time, then that’s in some sense a probability for whether the unnamed host in the problem would do so as well.

                  I was talking about after you did that.

                  Let’s say you do that, and you know, on average, when he offers to let someone switch, 72% of the time it’s a bad idea. So people should not switch, and you are planning to outsmart him by not switching if offered.

                  And then…you show up, play the games, and before you get to choose to switch or not, he spends about an hour interacting with you on and off camera, and watches how you play the various games. He also has some inkling of your personal history. (I have never watched Monty Hall, but other game shows like to throw in personal information, and it’s clear there’s some sort of pre-game meet.)

                  Whoops.

                  Now, after talking to you, he suspects you’re the sort of person who would have gone and figured out the odds, which he also knows. So he will indeed offer you the chance to switch to the actual car, and you will fail, and he will reveal that.

                  Now he once again has caused more confusion in whether it’s a good thing or not, because the clearly intelligent person who did supposedly the right thing failed.

                  Except…wait…he thinks you know you should not switch…but do you think he thinks that, and, just as importantly, does he think you think he thinks you know?

                  The fundemental problem here is, if the behavior of the host is not completely blind, if they are not functionally the equivilent of the blackjack dealer following specific rules, than they are, in fact, _playing the game_ also, which means any calculation of probibility has to include the host’s actions also….and, which means not only do we have to include what they are likely to do, but they have included what we are likely to do in response to what they do, and infinite recursion.

                  Obviously not the intention of the puzzle, but there are more options than just saying it’s under-determined. There are professional Rock, Paper, Scissors players who’ve done similar analysis and win significantly higher percentage of games than random chance would allow for.

                  That’s not exactly how professional RPS players do it. They do it by looking for patterns and tells and basic statistical knowledge. They don’t generally go and look at their own opponents stats because their own opponents a) are responding to others, and b) know that people look at their stats, so could easily use that to screw with them.

                  But more importantly, if two professional RPS players meet, on the first throw, there is, obviously, no strategy one of them can use to usually win. (How would that even work?)

                  In the Monty Hall situation, it’s more like the host is the professional RPS player, and the contestants are the amateurs, so he can win by throwing paper most of the time…and thus the real question is: Can the host recognize you are smart enough that you are about to throw scissors? The host does this professionally, after all.

                  There’s no way to know that. There’s no way to know what will set off his ‘Wait, this guy is a sneaky one who looked up what he should do on the internet, I better deliberately play this differently.’ alarm, nor is there any way to tell if he has higher levels of sneakiness models and might think you’ve already realized he is going to do that.

                  It’s worth pointing out that, if the host really wanted no ‘smart person’ beating the odds, the second he thought someone might be sneaky, he could just flip a coin before each show to decide if he was going to offer a switch, regardless of the situation later.

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                  • So, I’m not strongly committed to this and have mostly just been spit-balling, but I do want to respond to a couple of things.

                    First, the point of doing random trials is precisely because the problem isn’t amenable to direct analysis. Instead of trying to work through the infinite regress, you just put 1000 people in the situation and see if there are any patterns that occur beyond what a random distribution would suggest.

                    Second, re RPS, I bet if you asked a professional player what s/he would throw in a single round against a random person, you would get an opinion besides just “not enough information”. That opinion would depend on how much is known about the pool from which the person is selected (general populace would have different distribution than someone who’s thought about the game at all), but except maybe among the professionals, the distribution is probably not 33% across the choices.

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                    • First, the point of doing random trials is precisely because the problem isn’t amenable to direct analysis. Instead of trying to work through the infinite regress, you just put 1000 people in the situation and see if there are any patterns that occur beyond what a random distribution would suggest.

                      …you cannot do random trials of a single host playing a game against multiple competitors. Why would he agree to that?

                      More to the point, you don’t have any sort of _blind_ trials.

                      And even if you did, the game itself is not blind. The host isn’t in some booth somewhere, getting told ‘The player you have never met has picked A, and the car is in C. Do you want to reveal B and offer a switch or not?’

                      Second, re RPS, I bet if you asked a professional player what s/he would throw in a single round against a random person, you would get an opinion besides just “not enough information”. That opinion would depend on how much is known about the pool from which the person is selected (general populace would have different distribution than someone who’s thought about the game at all), but except maybe among the professionals, the distribution is probably not 33% across the choices.

                      Yes, but the problem here is in the Monty Hall example, the question is exactly the other way around.

                      It’s the host that is the professional player, and everyone else is an amateur. He does it once a day, every day (Or more, I have not seen the show.), and they don’t. They, admittedly, can see plenty of examples of how the host behaved, but they cannot see any of the off-camera interactions.

                      You are, in essence, suggesting that amateur poker players should be able to beat a professional poker player, because the professional was on the World Series of Poker and the amateur can, statistically, figure out what moves he makes and when.

                      That’s not how poker works.

                      The professional player is as much playing what he reads from his opponents as the cards…and the host literally can only have one of two cards dealt to him (They picked correct to start, or not.) so will almost entirely be playing against what he thinks his opponent will do.

                      The host holds one card, either good or bad for the player, and the entire question for him is: What sort of person is this? Is this the sort of person who is going to automatically switch, is this the sort of person who ‘knows’ they should switch because of Vos Savant, is this the sort of person who thinks I am trying to trick them and won’t switch, is this the sort of person who has gone and look at my statistics and has calculated if they should switch or not…or can I not figure any of that out and I should or should not offer based entirely on what card I’m holding?’

                      Or, to put it another way:

                      The host could offer switching sometimes and yet keep the odds of someone winning exactly the same as if he offered no switching. (Which is only 33%.) All he would have to do is offer a switch on every correct choice, and exactly half the incorrect choices.

                      That, mathematically, locks whether or not you should switch at 50%. So you have a 33% chance of losing outright, and then a 50% chance of guessing correctly if you should switch.

                      And that’s if the host is a computer. But the host is not, and a host who can learn to read people think, who can watch how they play the other games and know what profession they are and other stuff, should be able to make the players do even worse than the original 33%.

                      Even if he’s only right only some of the time, that still screws up the odds, and if he cannot read someone, he can still follow the rule I said above.

                      Now, this does not mean there are not tactics that will win, if you are playing. But, like poker, these tactics mostly won’t have anything to do with the cards, but have to do with attempting to fool the other guy, or figure out if he’s trying to fool you. You could try mentioning Vos Savant, see if he assumes that you know the ‘solution’ to this, so he’ll only offer you a switch if you are on the car to start with, and then, obviously, do not switch.

                      But…the problem is, duh, that way you have a 2/3rd chance of outright losing on your first choice, and won’t get offered another.

                      So what you really want to do is to make him assume you won’t switch if offered because now he’ll offer that. (Assuming he wants to sometimes offer to let people to switch to the winning car, but only when they won’t.) At that point, the problem has turned back into the original problem…and thus you should always switch.

                      So…act very mulish and refuse any of his suggestions? Try to emphasize how you never change your mind? Tell him earlier that you know the secret, the winning prize is always behind the one of the things in the middle, never at the ends, and then pick the middle door?

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                • There are professional Rock, Paper, Scissors players who’ve done similar analysis and win significantly higher percentage of games than random chance would allow for.

                  If we were in meat world and not rock-paper-scissors world, rock would always win. It’s already established that a rock can destroy scissors. And being covered with paper doesn’t really do anything to the rock except cover it. The rock could easily break through the paper.

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                  • I have a dim memory of this coming up in an old sitcom. The protagonist was in a group of people with a slightly different culture (a tribe maybe? Was this F Troop?), and they proposed RPS to decide something, but in their rules, rock beat everything (for basically the reasons you give). So they did about five rounds which all ended up in a tie of rock vs rock before they realized it was pointless.

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          • Is there a decision-making model which provides evidence that Monty would be trying to direct you towards or away from picking the door with a car absent the presumption that the game is rigged?

            The Let’s Make a Deal game is basically an honest Shell game, which is a bet between the player and the operator — so the operator actively wants the player to pick the wrong shell (unless he’s trying to build up false confidence). So if the player picks the right shell, the operator would naturally want to convince him to change his mind. On the other hand, he knows that the player knows he would do this, so he might be doing a reverse psychology move, and so forth. This can all still be the case even if no trickery is happening with the location of the ball.

            Monty presumably had no direct stake in how many prizes were awarded, except to keep the game interesting, but that’s the role he played. So if you use this assumption instead of the Monty-as-blind-automaton assumption, the question becomes not a probability question but a psychology/anticipation question — you might analyze it the way people analyze Rock, Paper, Scissors.

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            • To the last point: that’s what I’m wondering about. Let’s assume that the original framing of the problem didn’t exclude Monty’s psychology from the game. Does it follow that a solution to the game is indeterminate? Only if the psychological game has a determinate answer, seems to me. And without further argument I don’t have reason to think that it is determinate and that it drops out as not relevant.

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            • Monty presumably had no direct stake in how many prizes were awarded, except to keep the game interesting…

              But the producers are probably very interested. It’s not like they’re buying the car — the manufacturer puts it up, and if the contestant wins, there’s 30 seconds worth of nice pictures and the announcer reading their advertising copy. Plus the closing shot of the contestant, any supporters, the spokesmodels, and Monty, all standing around beaming over the wonderful prize.

              I would not be surprised if, when the rules were being worked out, the statisticians said, “Look, pigeons figure out to switch. So will people, so you’ll be getting your advertising slot two times out of three, on average.” Must have been disappointing that people don’t figure it out.

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          • My objection is close to your last paragraph. It is that the problem in the vos Savant framing is underspecified. We have only one example of the host’s behavior. This one example is consistent with multiple motivations, with resulting behavior patterns. It is asking us to extrapolate a line from one point.

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            • Ahh, good. So here’s my question. Stipulating that Vos Savant’s original description didn’t exclude Monty’s motives from the Monty Hall Problem, how does his having motives entail that the problem can’t be solved as described? Seems to me that would be the case only if identifying where the car is could be determined from a) his asking if you want to change your choice to door 2, and b) attributing to him a motive to get you to choose the goat. But that starts us on a regress, does it not? One that results in indeterminacy?

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                • You’ve lost me. His motivation could be any number of things. He doesn’t like you, so he is going to fuck with you. He likes you, so he is going to give you a second chance at that car that he knows is not behind the door you chose. Or he doesn’t care about you one way or the other, but he he has an opinion on what sort of reaction you will have either way, and is going for the better television. Or perhaps it is indeed the unstated assumption, and he does this every time. We don’t have enough information to make an inference.

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                  • We don’t have enough information to make an inference.

                    Exactly. Your argument is that the absence of reliable information re: motive renders Vos Savant’s answer to the puzzle incorrect, ie., that it’s *not* always the case that we should change our door choice. I’m wondering how DS’s failure to exclude the possibility of a motivated Monty means her answer is wrong.

                    The issue isn’t whether a motivated Monty can or will effect a contestants choice, but whether knowing that Monty might have a motive changes what constitutes a rational decision by that persons. As you say, we don’t have enough information to know what his motive might be. For all we know it could be anything. That being the case, it’s rational to exclude Monty’s motive as contributing to a rational decision regarding switching door choice.

                    Maybe the question is whether a contestant is rational to allow a motivated Monty to persuade them to not change their pick after he opens one of the doors. Given that we don’t know enough about his behavior given the limited evidence (ie., his motive can’t be determined), it seems to me that contestant would not be.

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    • The Monty Hall problem is a teaching problem designed to show students that “gut instincts” on statistics are often wrong.

      The assumptions (Monty always opens a door, that door never shows a car, the prizes are not moved after the first door is opened) have always been stated in the problem.

      This might not be how the TV show worked, but for showing students that their guts are wrong on statistics, it’s an excellent problem.

      I’ve never actually seen the Monty Hall problem brought up as, well, anything but a probability example with stated rules. Well, and a thing people argue about on the internet when they want to be angry but politicians are being boring.

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      • The assumptions (Monty always opens a door, that door never shows a car, the prizes are not moved after the first door is opened) have always been stated in the problem.

        This claim is objectively false, as shown by the linked article. The puzzle achieved widespread prominence via Marilyn vos Savant, who botched it (and, so far as I know, has never acknowledged this). It be that professors using this as a classroom problem are more careful, but within the broader culture the necessary assumptions frequently are omitted.

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        • I’ve never seen the problem brought up without the specifics.

          That the prizes don’t move and that Monty always opens one of the unchosen doors, demonstrating the goat.

          Except in internet arguments, wherein the specifics get nailed down pretty quickly, in order to argue the probability behind it.

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    • A couple things to keep in mind:

      1. In the column, the puzzle was given by a reader who wrote in, not stated by vos Savant.

      2. The controversy was premised on the assumption that this was a probability problem. Math professors were writing in to say that she got it wrong based on the assumption that the host would always open a goat’s door and offer the switch.

      3. If you don’t make that assumption, there’s no probability problem. You’re just speculating about psychology.

      Yes, she could have used up extra column space to clarify the assumptions, as she did in a follow-up column:

      So let’s look at it again, remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose. (There’s no way he can always open a losing door by chance!) Anything else is a different question.

      But that’s not what all the kerfuffle was about, and it’s not why people are still talking about it almost 30 years later. Talking about this is like finding a way to save all six people in the trolley problem — it totally misses the point.

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      • The link is fascinating reading. Her certainty never waivers. Towards the end you get two interesting comments. The first is from a newly-converted dude accusing vos Savant of getting help “from a real mathematician”.

        The other will be of interest to @marchmaine:

        One of my students wanted to know whether they were milk goats or stinky old bucks. Presumably that would redefine what a favorable outcome was!
        Daphne Walton, Bayview Christian School
        Norfolk, Virginia

        Virginia!

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      • It’s a fun problem to demonstrate. I’ve had people who simply refused to believe the math (after laying it out). I then put together a simple simulation* (maybe a hundred lines of code, perhaps) and showed the results matched the math — they still didn’t believe, despite being able to read the code for themselves and conclude they couldn’t “spot the mistake” (it had to be there, apparently).

        *Real simple. Three doors, randomly assign one “true” two “false” — true being the car. Then randomly select a door (contestant choice), have Monty open one of the two remaining doors (either the only “false” door or randomly select one of two “false” doors). Repeat one million times, logging how many times the initial door was “true”.

        Repeat the problem, this time switching to the remaining closed door (the one not initially selected, but not opened by Monty) and log how many times the “switched” door was true.

        Output results. Very clear results in line with the math. Anyone who can read even simple code can follow the code.

        I think I had the best result talking about the “extended Monty Hall problem” in which there are a million doors, you pick one, Monty opens up 999,998 of the remaining doors, and asks if you want to switch.

        That tends to highlight that the “Switch/not-switch” choice is really “The door you first picked, or ALL the unpicked doors”.

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  2. Hp1: Probably unfair, but I find this hilarious:

    One thing that Doug Medin and Andrew Ortony noticed about nouns was that when people use a noun, they often assume that the objects labeled by that noun have some essence that makes them a member of that category. Calling an object a cat will increase your belief that all objects called “cats” share some essence (such as cat DNA) that makes them a member of the category. While this may be true for some categories, there are many for which it is not. For example, tree refer to plants that are larger than people and have woody stems. Many of the objects that we call trees are more related to other items we would call flowers or bushes than to other objects we would call trees

    Zounds! They have invented nominalism! Thomas Aquinas will be devastated!

    But seriously, cats and trees are standard examples. My guess is is that Medin and Ortony knew perfectly well that they were restating standard examples and didn’t intend anyone to think otherwise, but Markman, the author of the linked piece, had his head explode at this amazing concept.

    Moving onto the study described in the article:

    …they had participants read about a person who acted in a strange way (stealing a painting because someone jokingly told them to). They explained this behavior either by saying this person had a “tendency” to act that way, they had a “condition” that made them act that way, or that they had “Depathapy,” which was a made-up name used for the experiment.

    Color me; unsurprised. A tendency is just a personality quirk or moral failing, like being a Yankees fan. A condition with a name is a medical diagnosis. Why shouldn’t we expect this to be more impressive?

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      • Sometimes a severe stomach ache that lasts for several hours is simple bean poisoning, usually from red beans. Yes, those and many other common beans are poisonous. If you throw dried beans into a crock pot without ever heating them above 180F you can suffer extremely painful bean poisoning from as little as three beans. It will only hurt for about three hours, but does send people to the ER. All canned beans are safe, however. It’s just fresh or dried beans that can cause it.

        This knowledge has lots of uses at church picnics, cookouts, and family gatherings because so few people know about it and you can claim ignorance if they do find out about it. “Bean poisoning? That’s a real thing?” But you have to play it by ear. “Would it be fun to have my mother-in-law on the couch moaning that she’s dying? Or would I be suffering more than she is?”

        All the packages say boil for 10 minutes. That denatures the poison. But people ignore that and just throw dried beans into a crock pot, sometimes to make chili. I suspect that this might explain most of my childhood stomach cramps.

        Ignorance of bean poisoning is so widespread that I think, in a Senfieldian way, that we should all poison everyone we know, and then go “Ha! You have bean poisoning because I didn’t boil the beans!”

        You would all be hailed as heroes who risked all to inform the public of a dire threat to their safety by making everybody wish they were dead for a few hours. People won’t forget that. They’ll walk up to you on the street and say “That time I felt like you’d repeatedly kicked me in the stomach until I puked because you poisoned me? I am sooo grateful because now I know how to cook beans!”

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  3. Hp2: You got my hopes up. I thought this would be an article about the average height decreasing. Boo hoo. In all seriousness, we really need to define what you mean by ready for adult life. Even in ages where teenagers had to start living an adult life earlier because there was a good chance both their parents died or going out and earning a living as a day laborer was what you did rather than go to college, a lot of teens seemed to have made a hash of it and messed up. Medieval authorities were just as anxious about teenage apprentices as modern authorities about eighteen year old college students.

    Having to do adult things doesn’t necessarily make you mature. World War II was mainly fought with soldiers in the early to mid-twenties. In Vietnam, the average age of an American soldier was nineteen. It showed.

    Hp3: Those look cool.

    Hp8: Goes to a link about solving gerrymandering.

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  4. Hp6: The curse of Google translate in all it’s glory. I love that we get a language lesson to properly explain the fail.

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  5. Hp3 – those guys are cool! I would totally get some for my wife, but the Japan-only thing…

    Hp4 – My wife has a degree in German, speaking beautiful Hoch Deutch, along with a smattering of the Schweibia dialect. One of my oldest friends was born in Austria to an American mother and a Germanic father. Neither of them can understand my father, who learned German as a child from his Mutti and her family, all native speakers. This is because they are part of the German diaspora, having spent generations in Romania. My father speaks Lederdeutsche, a very obscure dialect.

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  6. [Hp8] Pending the actual link (as opposed to the gerrymandering link), I’ll say this: I’m not sure if we can predict how sexbots will be similar or different from pornography. Certainly, after they arrive, and after an initial decade (or whatever) for them to be integrated into our social/sexual landscape, people will write articles on how [whatever happens] was inevitable. However, I’d hesitate to guess what [whatever happens] will be.

    I expect, once they’re perfected, they’ll be very fun to fuck. So there is that.

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    • I predict that humans will argue about the ethics and effects forever because thats what humans do. Different sides will wax and wane in strength but there will always be an argument. We still have a substantial population that believes in no sex or even kissing before marriage and definitely none of the kinkier stuff. They are weak right now but they exist. The same will be true with sexbots. Some will see them as fun and good, ethical outlet for people who can’t find a human sex partner. Others will see menace in them. Some might argue that men will use them so they can have a traditional subservient people. Others will threat about sexbots designed to look like humans considered off limits age wise. Conservatives will be up and arms because you can’t marry a sex bot.

      My personal belief is that sex bots do have a potential to be hazardous to society, especially if science gets good a mimicking emotional connection. It could easily bring about a lot of the more negative aspects of human behavior or might cause people to forgo dealing with troublesome other humans in preference for the more certainty of sex bots.

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          • [cw: obviously]

            Speaking of which, I was in Philly a few weeks back with two of my poly partners. Anyhow, we ended up in a way-better-than-average local kink store, where a large, attractive gay black man volunteered to demo some of the electro-play toys on us. We eagerly agreed.

            It was cool. The best part was these metal claw gloves he wore, combined with a static electricity source thingy — little arcs of happy sensation up and down our bodies as he clawed us.

            So anyway, my point: being electrocuted might be a feature not a bug!

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            • I’ve seen some re-appropriation of bark collars (which, i will say, I’m much happier to see used in kink than on poor dogs).

              My lifetime of safety training cringes. I mean it’s probably completely safe, but still….running current through the human body, especially near the chest, gives me the heebie jeebies.

              I trust TENS units and other medical hardware (I’m pretty sure the guys that build those know what they’re doing) used as directed, but…

              Mister Voltage and Mister Amp are not the kindest of friends.

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