demagogue on 9/7/2021 at 14:16
Today I finally saw the evidence of who Tiffany Doe is, the actual witness to Trump's rape of two minors that signed an affidavit to that effect... Actually it was who I thought it was all along, but now I definitively know it was her exactly.
I always found it strange, with so much scrutiny that these Q-nuts gave to her... Nobody goes into this kind of bat shit scrutiny over every little thing that Epstein ever touched, no matter how minutely, quite like they do. And of course Tiffany was a big gun so got some of the most extreme scrutiny of them all.
And it just makes me wonder, looking at crank charts like that, how could they miss that little detail about her? Obviously they know who she is and take her seriously as Epstein's go-to girl that got everything done for him because they followed up on every other damn lead she gave them.
It's just ... what good is a batshit conspiracy monger connecting every line imaginable to Trump that's so completely blind to the one line that actually matters and that should be impossible to miss if you were really leaving no stone unturned?
demagogue on 9/7/2021 at 16:28
It's like: you had one job, man... XD
Cipheron on 9/7/2021 at 16:43
Quote Posted by demagogue
It's just ... what good is a batshit conspiracy monger connecting every line imaginable to Trump that's so completely blind to the one line that actually matters and that should be impossible to miss if you were really leaving no stone unturned?
Their real goal, at least the goal of whoever is actually behind Q, is obfuscation, not enlightenment.
The point is to make so many fake lines that any time anyone says anything real it gets drowned out in the mess.
Cipheron on 9/7/2021 at 18:39
Sadly it doesn't even take that much to confuse people.
For example many people (both sides) interpreted Trump having (according to poll analysis) a 1-in-3 chance to win 2016 as meaning Hillary was predicted to win by a landslide. I have to assume people get confused between "chance of winning" vs "percentage to win by". When in fact, clearly a 1 in 3 chance to win meant it was already called as being anyone's game: rolling a 5 or 6 on a D6 is hardly an unlikely outcome.
When Hillary didn't win by a landslide they assumed that the polling must have been way off. But in fact, the polls were only out by about 1% from the actual results. A 1-in-3 chance of winning actually means it's WAY too close for them to make any sort of definite call.
Anything with numbers and percentages or probabilities, people are shit at that. See the kerfuffle over the Monty Hall problem a few years back with many people refusing to accept it even after it being explained over and over.
Pyrian on 9/7/2021 at 19:38
Quote Posted by Cipheron
See the kerfuffle over the Monty Hall problem a few years back with many people refusing to accept it even after it being explained over and over.
The Monty Hall problem, as it's usually stated, doesn't really define itself very well, and runs counter to our intuition, not of probability, but of people.
Let's say Monty Hall wants you to lose. After all, why shouldn't he? He financially benefits if you do. So if you pick the wrong choice, he just gives it to you, done. But if you pick the
right choice, well,
then he goes through his little song and dance and explains to you how it's better odds if you switch. But he knows. He knows all along.
Cipheron on 10/7/2021 at 05:07
Quote Posted by Pyrian
The Monty Hall problem, as it's usually stated, doesn't really define itself very well, and runs counter to our intuition, not of probability, but of people.
Let's say Monty Hall wants you to lose. After all, why shouldn't he? He financially benefits if you do. So if you pick the wrong choice, he just gives it to you, done. But if you pick the
right choice, well,
then he goes through his little song and dance and explains to you how it's better odds if you switch. But he knows. He knows all along.
I don't agree with that. Those usual objections are based on information that's not stated in the problem. Puzzles set out the rules of the puzzle. And even when all those objections are ruled out, the people who don't get it still don't in fact get it.
Quote:
Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong.[4] Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy.
Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant's predicted result.The problem with the objections you raise is that those are all ad hoc rationalizations about why so many people are so wrong about stuff like this. If that was the case then basically no mathematicians would have fallen for the incorrect thinking, because mathematicians are used to boiling down a problem to equations and then solving for the abstract equation, so they wouldn't have gotten side-tracked by those hypothetical objection you raise: when solving mathematical word problems, mathematicians just don't think like that.
The reason I brought this up in context of the election results is that it stems from the same issues: people have a problem separating concepts like actual odds from knowledge of the odds. In the Monty Hall case, it starts with the fiction "the car is behind any door with 1/3 chance" and they get confused when Monty opens a door, because they say the odds can't "magically" transfer between doors.
So what's the real thinking that people get wrong? Even when we rule out Monty acting counter to the stated puzzle, they still don't accept it. The actual errant logic is probably summed up as "Monty revealing one of the booby prizes doesn't change the odds of the prize being behind either of the other doors, and since the car was behind any of the other doors with an equal chance, it's now 50/50". The rest of the stuff they say isn't that important, it comes down to that one observation: the idea that exposing one of the booby prizes shouldn't affect the other doors at all. One video of someone who did in fact test out the Monty Hall thing, but wasn't a mathematician, did seem confused about how the odds "move" and gave it a sort of quasi-mystical air to it, and seem baffled by how it could be so: how do the odds "move" between doors, as if "by magic" by just "opening a random door". That's the main objection people have.
However, a change of perspective actually solves the dilemma. Was 33/33/33 ever true? Not once the car was placed. 100/0/0 are the "real" odds the entire game. 33/33/33 or 50/50/0 or 66/33/0 just represent different states of knowledge. 66/33/0 is in fact just a better approximation of the already-true situation of 100/0/0. So odds aren't somehow moving between the doors, what's changing is the amount of information different observers have, allowing them to better approximate the true odds (which Monty knew all along, thus could reveal information about).
So while those objections you raised could be possible objections, those don't work in this context because you got hundreds of mathematicians still objecting to this on purely mathematical grounds, not the "Monty might not act like the problem states" grounds. So no, I don't accept the idea that if we just stated the problem in more formal terms and rule out exceptions then more people would have gotten this right. That just seems like a post-hoc rationalization to explain away why humans basically fail at being rational in the first place.
Pyrian on 10/7/2021 at 07:24
I think you are
severely underestimating the human (and, yes, human mathematician) willingness to rationalize logic into agreeing with their intuition. Once a person
feels the answer is a certain way, they will contort themselves to find a way to justify that answer. (And professionals? They're
better at it.)
Quote:
Those usual objections are based on information that's not stated in the problem. Puzzles set out the rules of the puzzle.
But it
is based on statements that
are in the puzzle. If they had formulated the puzzle without them, they wouldn't have had all this confusion. There isn't a Monty Hall problem without Monty Hall. It's the injection of agency that makes it unintuitive. The underlying problem is just that if you pick one of three, what are the odds that you picked the right one? That's
it. What are the odds that the correct choice is the one you picked, or one of the others. But then Monty comes along. And, furthermore, the puzzle
doesn't tell you that Monty
had to perform that action - merely that he did. But the solution
relies on the notion that Monty will
always show a door and ask if you want to change - which is
not stated in the puzzle. It's not a good puzzle, it's not even really a mathematical puzzle at all. It's just wrapping a simple concept in confusing baggage.
...I'm always reminded of the Banner Saga "dialogs" where if you select the right answer, the game gives you another dialog and encourages you to change your mind. (If you initially select a wrong answer, you just do that.)
Quote:
However, a change of perspective actually solves the dilemma.
That's exactly why you can tell the confusion is not in the problem, but in the framing.
Finally, when we say people are bad at probabilities, I don't think the Monty Hall problem is even an example of that, anyway. In Monty Hall, people are confused about what the probability
is, not what the probability
means, and it's the latter that is what we normally talk about when we describe people as bad at probability. People aren't confused about whether Hillary's chances were 2/3's or 1/2, they're confused that someone with a 2/3 chance of winning could lose at all.
Cipheron on 10/7/2021 at 08:26
Quote Posted by Pyrian
I think you are
severely underestimating the human (and, yes, human mathematician) willingness to rationalize logic into agreeing with their intuition. Once a person
feels the answer is a certain way, they will contort themselves to find a way to justify that answer. (And professionals? They're
better at it.)
I don't think we're in disagreement there
Quote:
And, furthermore, the puzzle
doesn't tell you that Monty
had to perform that action - merely that he did. But the solution
relies on the notion that Monty will
always show a door and ask if you want to change - which is
not stated in the puzzle.
I don't agree with this explanation. Most people who object to the solution already had that possibility ruled out, and yet they still object to the solution. That rationalization is mainly used to explain why others got the problem wrong, it's not actually part of the reasoning of anyone I've seen who actually objected to the solution: the objection you're raising is only ever used by people who
do understand the problem and know the correct answer, not by people who object to the actual correct answer. That's just not the reasoning they use.
As a side note, the Monty Hall problem is mathematically the same as the Three Prisoner's problem. And people make the same 50/50 error in logic for that. But in that one there's no possibility that The Warden doesn't reveal a name, which would be the equivalent of Monty not offering you a switch. But people make the same logic error.
(
https://en.wikipedia.org/wiki/Three_Prisoners_problem)
The actual objections do generally boil down to what I said: That if you pick Door A, and then Monty reveals Door C was a booby prize, then since Door A and Door B were originally equally likely, then Door A and Door B are now 50/50 likely.
Quote:
Finally, when we say people are bad at probabilities, I don't think the Monty Hall problem is even an example of that, anyway. In Monty Hall, people are confused about what the probability
is, not what the probability
means, and it's the latter that is what we normally talk about when we describe people as bad at probability.
Monty Hall shows people are pretty bad at conditional probability. And I'd argue that since I've seen many times it's been stripped down to the bare essentials yet people keep insisting on the same mistake.
The issue is that the order of the doors opening and which doors Monty can and can't open are all conditional probabilities, but people are treating them as if they're random independent events. How they actually rationalize it really does boil down to two ideas: (1) opening a random door doesn't change where the car is, and (2) each of the two remaining doors wasn't any more probable than the other one to start with. So they think they're being extra-clever by going against the given explanation: you can't trick them with your sleight of hand, nothing actually changed. As for the assertion that they're merely confused about what the probability "is" and not what it "means". I think that doesn't really boil down whatever you're trying to say. Because of preconceptions, their comprehension of the full scenario is lacking insight, which says plenty about not getting the meaning already. And if a lot of people can't get it for a toy problem like this you can bet they're not getting it for complex real-world phenomena.
Quote:
People aren't confused about whether Hillary's chances were 2/3's or 1/2, they're confused that someone with a 2/3 chance of winning could lose at all.
Well another way to state that is that they confused a 66% chance with a 100% chance: they've confused something that's just more likely with a certainty. So re-stating it like that hasn't actually improved things.
Pyrian on 10/7/2021 at 09:03
Quote Posted by Cipheron
I don't think we're in disagreement there
Really? 'Cause disagreeing with that formed the core of your last argument: "...basically no mathematicians would have fallen for the incorrect thinking..."
Quote:
Most people who object to the solution already had that possibility ruled out, and yet they still object to the solution.
Because the objection doesn't initiate rationally in the first place. They've already chosen their side before they get that far.
Quote:
That rationalization is mainly used to explain why others got the problem wrong, it's not actually part of the reasoning of anyone I've seen who actually objected to the solution: the objection you're raising is only ever used by people who
do understand the problem and know the correct answer, not by people who object to the actual correct answer. That's just not the reasoning they use.
Okay, two things: (1) That's not a part of my argument in the first place, I'm talking about what makes it unintuitive and drives rationalization, and (2) It absolutely
is key to the arguments they're presenting, anyway; their analysis
always hinges on Monty's behavior not being what it is,
even though they expressly reject that in their formulation. Their formulations don't work if Monty acts as he's supposed to - but
do work if he
didn't.Quote:
But in that one there's no possibility that The Warden doesn't reveal a name, which would be the equivalent of Monty not offering you a switch.
That's clearly a better formulation and I expect fewer people would get it wrong, but it's still subject to assumptions about the Warden's state of mind, and I don't see why the Warden couldn't have chosen to not reveal a name.
Quote:
The issue is that the order of the doors opening and which doors Monty can and can't open are all conditional probabilities...
It's worth noting that that is absolutely not stated in the Monty Hall problem in the first place. Let's posit Marley. Marley doesn't intentionally pick a goat. Marley doesn't know which door has which prize. Marley's just a guest, and picks one of the other two doors completely at random. And Marley
just happened to pick a goat. Now, is it better to switch? No, now it's the exact same probability. Monty's knowledge and state of mind in picking are
absolutely crucial to getting the right answer and are not stated in the problem at all.
EDIT: Depressing fact: Between the 3 possible prize locations, the 3 possible original choices, and the coin flip, there's a grand total of just 18 equally-likely possibilities for any of these scenarios. Real easy to work out by hand in just a few minutes.
