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The Time Everyone “Corrected” the World’s Smartest Woman (2015)

priceonomics.com

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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#271

Post by slavik81 »

fourthark wrote: post #217
LanceH wrote: post #187

Earlier quoted context omitted.

It's right depending on your assumptions. If the host has rules of only picking the right most door the contestant doesn't pick, and it happens to be a goat then the answer is 50%. Basically if the host is just as willing to show a car as show a goat and it is a goat which is shown, the answer is 50%. There is a confirmation bias that people expect people who are aware of the Monty Hall Problem expect others to be wr…

Intention doesn’t matter. The problem states that the host opens another door and reveals a goat . It doesn’t matter that the host meant to do that. Now that the information is revealed, the probabilities have changed. Obviously if the host revealed the car, that would also affect the probabilities!

It does matter if he meant to or not, because if he chooses randomly from the remaining doors, the probability of him revealing a goat depends on whether you have already chosen the car. Whereas if you know he could only ever reveal a goat, then the fact that he revealed a goat tells you nothing about your current selection.

If you are interested in more details, Wikipedia lists this as the "Ignorant Monty" variant.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#272

Post by listenallyall »

defterGoose wrote: post #243
listenallyall wrote: post #235

Earlier quoted context omitted.

People come up with the incorrect result because with 2 doors remaining, it would initially appear that they both have equal chance of containing the car. Because it is unclear HOW we arrived at the final two doors. If we arrived there randomly, the probability is in fact 50-50. If there was some manipulation - i.e. if the host knows where the car is AND deliberately opens doors that do NOT contain the car - then the…

I find it a little more intuitive in a visual way with the 100 doors. If the 98 doors that the host subsequently eliminates leaves one in the middle of the pack (e.g. #52), most rational people would look at that door and say "hmm its probably in there rather than in the one i picked, #1"

Except how many people, when presented with option of picking one of a hundred doors, picks Door #1?

Further, the problem with the 100-door (or 1000, or million, etc) rationalization is that it did not appear in the initial Parade Magazine article which generated all the negative responses. Sure, today you know the secret and can explain the problem well, but it isn't fair to judge the people whose only exposure to the issue was the first, original Parade Magazine article.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#273

Post by listenallyall »

wahern wrote: post #251
listenallyall wrote: post #202

Earlier quoted context omitted.

It's a tv show - a valid purpose is that he needs to stretch by 30 seconds before going to commercial. Another purpose is that the audience thinks seeing a goat is funny. Another purpose is to prove the show uses two different goats and doesn't do a switcheroo behind the scenes. What the Parade article does NOT say is that the first door opened is ALWAYS not the contestant's choice and ALWAYS reveals a goat.

That he always opens a door that is not the contestant's choice is a necessary implication of saying that he opens "another" door. That he opens a door containing a goat is similarly implicated. It's not even an implication, really; it's just definitional in vernacular English. And in any event, any of the academics writing in would have been perfectly familiar with the semantic structure of such logic puzzles. Also,…

> That he always opens a door that is not the contestant's choice is a necessary implication of saying that he opens "another" door

It really isn't. It's possible Monte Hall always opens the doors in reverse numerical order, so if you picked Door #3, that would get opened first. Or that if Door #3 contained the car, that would be revealed before any goats. The way the scenario was initially described by Ms. Vos Savant is not clear about that.

And no, not everybody knew Let's Make a Deal in great detail. It's always been a daytime tv show, meaning, it airs while most people are at work.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#274

Post by fastball »

leephillips wrote: post #179
failwhaleshark wrote: post #128

Earlier quoted context omitted.

Lol. I worked at a biomedical informatics shop with IITians and other folks who were MD + PhD CS. No one referred to anyone as doctor and no one there took a MENSA test. I think it's safe to say the only "doctors" are clinical MDs, podunk colleges to seem elitist, and Spies Like Us during the surgery scene.

Only losers take Mensa tests and talk about their IQs. But plenty of PhDs use the Dr title in the right context. It's just the height of jerkdom to insist on people addressing you with it.

What's the right context? Why are PhDs (and MDs) the only people that deserve a special prefix in our society? I know loads of people that have worked harder and smarter than people with PhDs, but they don't get a prefix.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#275

Post by someguydave »

jdashg wrote: post #206
someguydave wrote: post #162

Earlier quoted context omitted.

I think the confusing part for many people is the unstated fact that the host takes all prizes into account when revealing a door, and that the host is forbidden from revealing the car. If the host chooses randomly then his pick adds no information (other than the extra revealed prize)

I don't think people are confused by this in their initial solutions, but rather this after-the-fact problem modification happens to match the incorrect intuition people have. The instinct is strong that "I am right" so "I must have just solved the wrong problem", thus "the problem was confusing". Rather, I think you will find that most people don't expect the host will ever pick a door with a car until after you tel…

yeah, it’s reasonable to attribute those defects to the solver and not their situation and circumstances

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#276

Post by elliekelly »

version_five wrote: post #136

One appealing thing to me about math is how egalitarian it is. It doesn't matter where ideas come from, they are probably right or wrong. It is (maybe unhealthily) rewarding to see critics acting like its another discipline where the senior or otherwise higher status person's opinion has more weight, only to make themselves look ridiculous. Contrast this with so many workplace things where senior people say dumb or i…

> One appealing thing to me about math is how egalitarian it is.

I simply cannot believe anyone could read this article and come to this conclusion. Do you think the same flood of unduly harsh criticism would have resulted from the same column written by Maury von Savant instead of Mary?

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#277

Post by denton-scratch »

tomerv wrote: post #237
TchoBeer wrote: post #64

Earlier quoted context omitted.

I don't understand how this could be. If you start over when the host picks the car, then isn't that the same as the host picking the goat every time, i.e. the same as the host knowing.

At first I agreed with you, but then I thought about the variation with 100 doors (this is what originally helped me grasp the correct answer): you choose a door out of 100 (with very slim chance of choosing the correct one), the host opens 98 of the remaining 99 doors and there are goats behind all of them. Now it's obvious that the car is in the remaining door. If the host is opening random doors, then: * If you ch…

"Now it's obvious that the car is in the remaining door."

No. It could be behind the one you chose, surely.

I understand the explanations, or at least some of them; but I still don't get it. I thought I was intelligent and numerate, and this is making me sad.

I don't see why, after Monty reveals a goat and invites you to switch, you can't re-assess the probabilities from scratch. There are two closed doors, car behind one, goat behind the other, and you have no evidence which is which; therefore 50:50.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#278

Post by spenczar5 »

tomerv wrote: post #228
spenczar5 wrote: post #111

Earlier quoted context omitted.

This is a small enough situation that we can do complete enumeration of the states. Let's say you pick door 1. Let's go through all the possibilities: the states of the 3 doors, which one monty reveals, and what do we do, and what is the result? 1 | 2 | 3 || Monty Reveals | You switch | Result --------------------------------------------------- G | G | C || 2 | Yes | Win G | G | C || 2 | No | Lose G | G | C || 3 | N/…

You are not enumerating the options correctly. You have 3 rows for the GGC and GCG options but 4 for the CGG option, which is assigning the CGG option higher probability. In reality, they have equal weight.

Agh, you are right. There should be two “start over” rows in each of GGC and GCG. I can’t write “N/A;” we must say “yes/no” in those.

Doesn’t change the result though.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#279

Post by dekhn »

glitchc wrote: post #236
Talanes wrote: post #234

Earlier quoted context omitted.

Because in 2/3 scenarios you had to make the host choose the door without a car?

The host can never choose the door with the car, because then the game is over. Ergo the host has to choose the door with goat, every time.

this constraint was unclear to me in the original problem statement, which is why I thought she was wrong, too. It wasn't until somebody wrote in a letter saying they wrote a computer program that I understand what the rules were, and then it was obvious.

I wish the problem was stated more clearly to say, the host has to choose the door with goat.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#280

Post by dekhn »

mkl wrote: post #185
listenallyall wrote: post #166

Earlier quoted context omitted.

You're quoting Priceonomic's 2021 description of the problem. This is NOT the 1990 Parade Magazine description of the problem that generated all the responses.

The 1990 Parade Magazine description is almost identical (and actually more explicit, since "say #3" is a removable parenthetical): "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat" -- https://web.archive.org/web/20130121183432/http://marilynvos... The host's knowledge is explicitly mentioned, and the only purpose this could have is that so he can use it to avoid giving the g…

I read this and thought that sometimes, the host would open the door with the car.
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