Make the analogy more relevant to the case, and then let’s see what we think. For the purposes of this hypothetical, we will use the faulty 0% (<10 cases) that went unchallenged for well over a dozen pages.
There are 99 4’s and one 17, as you say. In this example, a drawn 17 would send three guys to prison for a long time. No matter what number is drawn, all numbers self-destruct as to be unverifiable by anyone.
Now, after the draw, it is reported to be a 17. No way to verify the claim. Is skepticism not warranted? Let’s add in unverified reports of hostility between the one drawing and the three guys facing long prison terms. (The racial insults in the driveway.) Combine that with the 1% chance the draw was actually a 17, and I think initial skepticism is quite legitimate. Note that I also think further investigation would be in order, but I wouldn’t fault some random guys sitting in the audience for being skeptical based purely on the 1% chance of a 17 coming up. Also note that nobody, at any time, asserted that the DoJ numbers by themselves were conclusive of anything.
The point is that the claim is not verifiable. All these hypotheticals involve being able to obtain perfect knowledge about the claim. That simply does not exist in this case. We will never know exactly what happened in that house short of the guys confessing or the accuser recanting.
And damn, this thread was starting to look like ywtf’s blog.
True, I expressed myself poorly there. I should have written: Of course I don’t believe you because in a hypothetical situation about determining odds, belief has nothing to do with it and it’s all about determining the odds. Sorry androids.
How about this to try and explain my point.
There is a hat containing the numbers 1 through 10 on pieces of paper. What are the odds of drawing a nine from the hat?
2)Bob has a hat containing the numbers 1 through 10 on pieces of paper. He draws a piece of paper. Charlie must determine what the odds of the number being a nine are. How does he do so?
3)Bob has a hat containing the numbers 1 through 10 on pieces of paper. He draws a piece of paper and says it is a nine. Charlie is asked to determine what the odds of the number nine being drawn are. How does he do so?
4)Shifty Eyed Bob has a hat containing the numbers 1 through 10 on pieces of paper. He draws a piece of paper and claims it is a nine. Skeptical Charlie must determine what the odds are that Shifty Eyed Bob is actually holding a nine. Without being able to see the piece of paper, how can he possibly do so?
All these word problems are asking you to find the same answer regardless of the level of human intrigue layered on top. If I change the Bob’s and Charlie’s to 'you’s and ‘I’'s it doesn’t remove the problems from the realm of the hypothetical.
So as to the Beckham question, I believe that it is simply this word problem:
A man in London is mugged. He identifies his attacker as Beckham, the famous footballer. Given that in the city of London there are, in addition to the actual Beckham, 999 people who so closely resemble Beckham that the victim is unable to differentiate between them, what are the odds that he was mugged by the actual Beckham?
*sees that you with the face, after declaring herself out of the argument, has checked back in with a triple post. :rolleyes: *
Do you note that your hypothetical includes a lot of information not in the original problem? Had my mathematical model stipulated that there were only three possible cars to choose from, one of which was maroon, you’d have had a case. But in order to give your argument so much as a breath of credibility, you’ve had to bugger about with the numbers again. You’re trying to imply that I think the 98% figure holds true in all circumstances - including when the figure has been shown by evidence to be only 67%. That’s what we in the trade call a “strawman”. Look it up, as you’re so keen on technical terms. Tw@. Look up “Appeal to Ridicule” while you’re at it.
PALATR, especially over her apparent perception of “the whole world” and a belief that her Appeal To Popularity would be valid even if her perception were true. Let me catch you ever referring to your weight (or anyone else’s) in pounds or kilos, then, and I’ll rip you a new one. You know why, of course.
Well, quite. I didn’t say Charlie was more likely than Beckham to be the culprit. You’ve really got to stop beating straw men, if you think I’m the one with credibility issues. What I did say was that the pool of Beckham lookalikes, numbering some nine hundred and ninety-nine, was somewhat more likely than Beckham himself to contain the culprit. My ability to recognise Beckham’s famous face factors into the equation - but unless it can be shown that out of a balanced pool of Beckham lookalikes and Beckham himself, I can pick the football god out more than 99.9% of the time (or, given a pool of 999 lookalikes plus the man himself, I can correctly identify him much more than half the time), my identification should be viewed as dubious.
As to the RNG argument, it seems that not even surgical intervention is going to introduce into your brain the difference between arguing about the likelihood of a particular string of numbers coming up[list=a]before we know what the machine has picked, and after we know what the machine has picked.[/list]
I’m still having problems understanding you here, though. The point about the analogy is that the odds have fuckall to do with whether you should believe me. Any randomly generated string of numbers will have the same odds of being generated as any other randomly generated string, but if you compute the odds it looks amazingly improbable that that particular string would have been chosen. But its not improbable. The machine has to select some numbers, and it just happened to select those.
1/10
Takes the number of pulls and divides it into the number of possible outcomes.
Your questions seem kind of repetitive. The answer is the same as 2).
It’s still 1/10!
Oh for crying out loud, VM. My hypotheticals are not altered at all by “I’s” and “you’s”. It about a claim, period. To be skeptical that Bob pulled out a 9 because the odds are 1/10, 1/100, or even 1,100,000 makes no sense. To be skeptical that Shifty Eyed Bob pulled out a 9 has more to do with his credibility, not odds!
In my hypothetical, no one was making any predictions about what numbers would be generated by the RNG. The numbers had already been generated, I told you what they were, you did the math and was flabbergasted that out of all the possible combinations that could have been chosen, my particular string was generated. Your math told that the odds of this string being generated was 1/1,000,000 Never mind the fact that any string of numbers would have the same exact odds, you don’t believe me.
Do you get how illogical it is to justify skepticism of my claim like this?
Assuming that all Beckham look-a-likes (including Beckham) have an equal chance of being guilty, the probability that it was Beckham is 1/1000.
Guess what the odds are if it was another Beckham look-a-like? 1/1000.
Your hypothetical doesn’t give enough information to answer the question. The take-away message from my hypothetical is that regardless of what the total car population looks like, it has fuckall to do with what the cars that you need to be concerned about. In a real life situation, if all is known is that the guilty car was maroon, you wouldn’t have enough information to prosecute or go to trial. In a real life situation, the police would be able to narrow down the likely suspects, and it is that pool of cars that the witness’s proficiency should be tested against.
What 98% figure?
“Somewhat?” How do you reach this conclusion?
[quote]
As to the RNG argument, it seems that not even surgical intervention is going to introduce into your brain the difference between arguing about the likelihood of a particular string of numbers coming up[list=a]before we know what the machine has picked, and [li]after we know what the machine has picked.[/list][/li][/QUOTE]
But we haven’t been talking about predictions. We’ve been talking about being skeptical of events that have already been said to have happened, remember? So if anyone is concocting strawmen, it’s you.
So what you’re saying is that if there is substantive evidence that renders the witness more credible, the witness is more credible. No duh. Did you notice, btw, that this witness who can tell red from maroon and vice versa 95% of the time falls to a mere 85% [mode=colloquial]reliability[/mode] even when there are only two red cars to one maroon?
Typo for “95%”, the witness’s hit-rate in correctly reporting a red car as red or maroon car as maroon.
By crediting myself with some ability to tell Beckham from a “lookalike”, given that so-called lookalikes seldom exactly resemble their subject; if all Beckham lookalikes were his exact twin there would of course be only a 0.1% chance that Beckham was indeed the culprit (assuming for now that we have no other evidence that he did or didn’t do it). But without putting my Beckham-spotting ability to the test, we can’t assign my testimony an exact numerical credibility.
Try to understand the distinction between events that have been said to have happened, and those that are known to have happened.
Last Saturday’s National Lottery numbers have already been drawn. If I tell you that they were 3, 5, 14, 26, 38 and 44, am I 100% sure to be right simply because the draw has already happened? Or is there a possibility that I am in fact ignorant of the numbers, and am making up a set of numbers OTTOMH? Or is there a possibility that I do know the numbers, but am deliberately yanking your chain by presenting you with a false set? What are the odds? On the other hand, were I to show you a page from a national newspaper reporting what the actual numbers were, neither you nor I would be arguing the odds over that set coming up. See the distinction?
Incidentally, the False Dilemma fallacy applies to your apparent assertion that if I am constructing strawmen, you cannot possibly be.
The witness’s credibility (reliability) is not affected by the prevalence of cars in the population. His proficiency at telling maroons from reds (95%) is not altered by how many maroons there are. See, this is why I told you are misusing the term reliability. You think that just because there are few maroons in the total population, the witness is not credible. That makes no sense.
That 85% stat is the probability that the witness will correctly identify cars as maroon in the total population. This is not the same thing as their proficiency in telling maroons from reds, which will always be 95%. Those are two different statistics telling you two different things. The witnesses reliability is established by the latter, not the former!
This is how I process your hypothetical.
You claim that someone who looks just like Beckham mugged you.
The police rounds up everyone in town that looks like Beckham, including Beckham. It is 1000 people. No one has an alibi, so everyone is a suspect.
Only one person out of this group of 1000 could have mugged you.
What are the odds that it was Beckham? 1/1000
What are the odds that it was Charlie the Bus Driver? 1/1000
What are the odds that it was Beckham’s twin brother? 1/1000
And so and so forth.
In this hypothetical, there is no reason why Beckham would be any less likely to be the culprit than any other bloke that looked just like him. Characterizing the probability that he is guilty as “somewhat” less likely as any other person makes no sense.
And if we factor in the subjectiveness factor, Beckham probably has a slightly higher probability of being guilty. Because you claimed you saw someone who looks “just like Beckham”, that would in turn would mean that guys that look like Beckham but not just like Beckham have a slightly higher chance of being ruled out in a line up than the one guy who looks just like Beckham because he is Beckham.
We are working with claims. In all of the hypotheticals we’re talking about, one person doubts someone else for reasons that are illogical (to me).
What are the odds for what? That you are lying? I don’t know how to calculate that. What are the odds that those numbers were drawn? Well, I could figure it out, but it wouldn’t tell me much. Any string of numbers would have the same odds. The “unlikeliness” of those numbers would not tell me whether or not you were to be believed. Your credibility would, though.
This has absolutely nothing to do with what we’ve been talking about. None of my hypotheticals about RNGs were based on how you could verify that I was telling the truth. It all rests on the question “Why shouldn’t you believe me?”
Oh yes. I hope I never said differently. If you can investigate all claims, likely and unlikely, and eliminate all doubt, then go for it. Throughout, I’ve been addressing hypotheticals only.
Au contraire, it makes a whole heap of sense – which is why in order to lend your argument credence, you had to toss aside my population and substitute one of your own (two reds and one maroon). And lo and behold, with a less skewed population the witness looks better!
What I want is the probability that a car that the witness has identified as maroon is indeed maroon – and your own figures show that with red outnumbering maroon by only two to one, this figure falls to 85%.
No, I said that it is “somewhat” less likely that Beckham is the perp than that the pool of the other 999 guys who look like him includes the perp!
Yes, Beckham is rather more likely than any other one guy to be the culprit, but if you stick him behind Door A and everyone else behind Door B, chances are the mugger is behind Door B.
Well, quite. But if on the one hand you’ve got the set of numbers I just spouted, given that it’s a possibility that I’m either lying or ignorant, but without knowledge that I’m more disposed to lie than most, do you consider it more likely that last Saturday’s Lottery numbers were:[list=a]3, 5, 14, 26, 38 and 44?[li]some other set?[/list][/li]How about if I said, again without any further information about myself, that I have seen at least one sheep this week? A more likely proposition or a less likely one? Without knowing whether I memorise Lottery numbers for fun, does the inherent unlikeliness of any one possibly-random string of numbers being those generated by picking six numbered balls from 49 last Saturday, versus the relative commonness of sheep in the UK, shade your decision at all?
Suppose you had to pick one proposition as true, on pain of death for guessing wrong or refusing to play. Which one would you place your hopes on? Why?
Eh? I thought your quote of Zoe’s thought experiment entailed pointing at a particular set of random numbers and laughing at the proposition that anyone should have thought them unlikely! Why shouldn’t I believe you? Which do you find easier to believe – that I know p to five places of decimals, or that I know e to 100 places? What shades your decision?
Just to play triple-posties, ywft, here is a list of interesting facts. Exactly half of them are true. Try to guess which ones:
[ol]I do not meet legal eyesight requirements for driving without the aid of glasses or contact lenses
[li]My father was a petty officer in the Royal Navy[/li][li]My next-door neighbour is a seven-foot albino[/li][li]I have three cats[/li][li]I like model aircraft but am too ham-fisted to build a plane from balsa and tissue[/li][li]I once turned out for the England cricket team when they were short-handed, and was the highest scorer that day[/li][li]I can extract the square root of 10 in my head[/li][li]I can extract the square root of 2 using pencil, paper and the Binomial Theorem[/li][li]I once won a cup in a singing competition when I was a boy soprano[/li][li]When I was younger, I could run a mile in five minutes[/ol][/li]
Which ones do you believe the likeliest, and why? (It’s no shame not to pick five out of five…)
The fact that you think the total population of cars in the whole city, state, country, or world brings any hint of relevancy to this case is hella funny. The only reason why I had to invent a hypothetical is to show how ridiculous your thought process is.
In the absence of the necessary evidence (such as the composition of cars in the suspect population), its better to say “This question can not be answered” than it is to say “Well, I’ll just use the total population’s makeup instead.”
No, it rises from 28%, remember? Again, you are mixing two different stats. The 95% stat is sensitivity (and specificity), which is fixed regardless of the prevalance.
But your reasoning makes no sense. You need to show mathematically how you conclude this “somewhat” estimate. Or at least explain it better.
Only one person could have mugged you. Not 999. So it makes no sense to reach your conclusion based on this “logic”.
This “logic” also contradicts your “somewhat” estimate because there’s a big difference between 1/1000 (Beckhams odds) and 999/1000 (odds of Beckham lookalikes).
[quote]
Well, quite. But if on the one hand you’ve got the set of numbers I just spouted, given that it’s a possibility that I’m either lying or ignorant, but without knowledge that I’m more disposed to lie than most, do you consider it more likely that last Saturday’s Lottery numbers were:[list=a]3, 5, 14, 26, 38 and 44?[li]some other set?[/list][/li][/quote]
There’s two possibilities: you are lying or you are telling the truth.
If I’m going to be skeptical, it won’t have anything to do with probability, odds, or statistical likelihood. It will be because you’ve demonstrated a history of lying in similar situations or because the information contradicts my understanding of nature.
I don’t understand what is so complex about this. I really don’t. Sweet Jesus, I don’t.
Not knowing anything about you, why would I be skeptical? A lot of people see sheep every day let alone once a week. Shit, I used to be one of those people when I was in vet school. So nothing about this claim is fishy on its face.
No it doesn’t. If you were to tell me yesterday’s lotto numbers and I don’t have any reason to think you would lie to me, and the numbers don’t sound suspiciously non-random to me, then why would I be skeptical?
This question is too ludicrous to answer. Seriously. I don’t know what to make of it.
Yeah, the point of the analogy is that its a laughable offense to be skeptical because a randomly generated string of numbers looks “improbable” based on the odds of it being selected. The question is “Why shouldn’t you believe such a claim?”
What is so unbelievable about a claim that a RNG has spat out one particular string of numbers as opposed to any other randomly selected number string? Please explain this!! I’m dying to know.
I have no idea, Malancandra. Just being honest. Anything that I say would be a guess. The thing about humans is that any one of us could pull up a list of facts that would look “unlikely” but would be true nevertheless. Here’s my list of “unlikely” facts.
My first name sounds identical to a popular 70’s and 80’s rock band.
My father, a black man, was nicknamed called “Mr. Kotter” when he was younger because of his twin-like resemblance to the man. Ironically, he was also a teacher at the time.
My twin sister works in the Florida Everglades and was almost attacked by an alligator after jumping out of a helicopter.
I’ve intentionally killed almost a dozen cats and dogs in my lifetime.
My mother grew up in the same town that Michael Jackson did.
My cat was stuck on the roof of my apartment building one day and I rescued him by coaxing him to jump in a laundry basket that I raised above my head. And he did, bless his heart.
No, you have to invent hypotheticals because the hypothetical I posed didn’t produce the answers that you liked.
Why? Why would you not simply say “The likeliest distribution of colours among the cars in the vicinity at the time of the accident can be presumed to reflect the distribution of such cars in this town”?
Astute! Brilliantly argued! :smack:
[mode=slow]The figure falls to 85% from 95% when the population changes from balanced to skewed 2:1. Or it rises from 28% when the population changes from skewed 49:1 to 2:1[/mode]
Shove your scare-quotes, I didn’t say that 999 men mugged me, I said “chances are the mugger is behind Door B”. You know, that the guilty man is there along with 998 who are innocent?
Exactly, because I’ve assumed there is a greater chance that I will identify Beckham correctly than not – but that is offset by the presence of 999 lookalikes.
You say this as though you were conveying some great insight.
Finally! A breakthrough! And does your understanding of nature allow for the possibility that comparatively few people actually memorise the week’s Lottery numbers on the off chance they will come up in an Internet discussion, but anyone can make up a set of six different numbers between 1 and 49 if he feels like it?
Oh how I sympathise.
Your ability not to actually answer the question that was asked is verging on the astonishing. And at odds with your familiarity with court procedure. More or less likely?
Because your understanding of nature informs you that few people actually memorise those numbers? Supplemental: Given that we’ve already agreed that absolutely any sequence of numbers out of the RNG is as likely as any other, WTF do you mean by “suspiciously non-random”? :dubious:
Well, you know, trying to get you to pick one or the other and explain your reasoning…
You disappoint me more than somewhat, you with the face. Surely it must have struck you as most unlikely that a random dude you meet on the Internet should have stood in for a national sports team on a moment’s notice - and turned in an exceptional performance? Don’t you think it more likely that a mathematically-inclined Doper could extract square roots with pencil and paper than in his head? Doesn’t it occur to you that five-minute miles are generally the preserve of the unusually athletic? How many seven-foot albinos do you think there are in the UK? Doesn’t it occur to you that short-sightedness is very common?
You didn’t answer my question about memorising p to 5 places versus e to 100 places, either. Do you really consider both to be equally likely?
It’s pretty painfully clear at this point that what’s going on here is what we might call a “Monty Hall Problem Problem”, in reference to people’s inability to accept the solution to the Monty Hall Problem.
“Common sense” understandings of probability and statistics just don’t cut it. It’s a trap smart people often fall into, I think, because they’re used to being able to reason things out with little additional training. They learn to rely too much on their own contained mental universe for the solutions to things (hence friend Bricker’s complete divorce from reality on this subject).
This isn’t one of the things your brain just knows about. It’s a science, with rules and terms that Malacandra, for example, not only can’t use correctly, but actually sneers at the idea of using correctly, while at the same time trying to use the science to support his view. It’s preposterous.
face, he can’t get it because he can’t hear anything but his own voice echoing inside his skull. He has Common Sense and it tells him quite clearly that, say, switching his answer couldn’t possibly effect the odds of winning, so therefor he’s right and science is wrong.
Dolt. I knew the solution to the Monty Hall problem years ago. Like most of us, I got it wrong at first sight. I worked it out while on the cricket field, of all places.
Point out my error. Don’t just pitch up and say “I’m on ywtf’s side. She’s right and Malacandra’s wrong”. Add to the discussion, and not with the fatuosity above, or butt out.
I just thought I’d let you know that at least one person in the audience (me) has learned quite a bit from your posts in this thread about statistics, odds and probabilities, and their proper application to events. It really is very, very simple and you’ve made that quite clear.
And just for fun for the record. . .
Someone I’d met online did tell me once that they had a goat. She really did, too – she sent me a picture of herself (we’d met, so I knew it was her) with her new pet and it was absolutely adorabe. The odds may have been slim that any random internet person would actually have a goat, but those odds didn’t affect the credibility of her claim one iota. Because they aren’t relevant to determining it.
So thanks for your contributions here. Hope you have a great day.
I may be a dolt, but you’re apparently illiterate. What does whether you know the Monty Hall solution have anything to do with what I said?
I have pointed out your error. face has pointed it out in great detail, with some help from others, and I have now attempted to point it out in more general terms. You’re not even familiar with the terminology of the science you’re trying to insist is wrong. It’s not face’s opinion, what she’s telling you, it’s facts about how stats and probability actually works.
But you’re paying so little attention to everything but your own bullshit that up until a couple pages ago, you were still mysteriously claiming there was some ideological reason for her position, as if she’s not completely correct about how statistics can actually be used. It’s like you’re a flat-earther arguing with an astronaut, or a Creationist arguing with evolution. You sound that exact level of stupid and ignorant at this point. So no, I can’t possibly do anything else to “point out your error” because your error is the assumption you have that you know what the fuck you’re talking about.
Because that’s a stupid assumption. If the prevalance of maroons is 2%, that means the size of the “suspect population” would have to be, at minimum, 50 cars in order for us to have a sample that comes close to matching the total population. Nevermind the fact that we have no logical reason to assume that this sample would look like the total population in the first place. Fifty cars is unrealistic.
pointing and laughing at the willful ignorance
sigh If I ask you “what’s the lotto numbers from yesterday?” And you say “Okay, I’ll look it up on the internet.” and then you report back to me and I say “I don’t believe you!” Wouldn’t you want to know why I’m skeptical? This has nothing to do with the “odds” you would have memorized something!!!
No. I can’t believe you are being this dense!
If you were tell me that the RNG spit out 16 numbers and those numbers were 1, 2, 3, 4 ,5 … 16, I would not believe you. Even though the math shows that these numbers are just probable as any other string of 16, the fact that they do not appear to be randomly selected triggers skepticism. Not mathematical probability!
I repeat: of course skepticism is warranted. Let me turn it around on you: if instead, someone claims they drew a 4, and drawing a 4 would send three guys to prison for a long time, are you suggesting that skepticism is not warranted? that, since there’s only a 1% chance you’re wrong, you’re happy to send three people to prison on unverifiable evidence?
Because I’m not. And here’s why not: this business about the numbers being destroyed afterwards is bullshit. That’s not how our justice system works: before these three guys can be sent to prison for a long time, their guilt has to be proven beyond a reasonable doubt during a jury trial.
We’re not talking about making a final judgement here. We’re talking about whether to continue an investigation, and there’s a suggestion on the table that since (theoretically and incorrectly) fewer than 10 white-on-black rapes happen every year, those making such claims are “lying whores.” I’m assuming that those making this suggestion believe that accusations by lying whores don’t merit investigation.
Again: if a claim
has more than 0% chance of being valid, and
less than 100% chance of being valid, and
our judgement about the claim’s validity has substantial impact on justice and public safety, and
We’ve got the resources to investigate the claim more fully,
then there’s no reason at all to refuse to investigate the claim more fully, and it’s irresponsible to leap to judgements either about the accuser or the accused until we have more information.
