Look - all you care about is P(person sitting next to me got Q. 47 right). You don’t know anything about the person sitting next to you, so your only unbiased estimate of this probability is your best guess of the overall % of people who get it right. Unless you believe a question is constructed so dastardly as to trick 10,000+ test-takers on the whole to perform worse than randomly guessing, it is better to copy.
I’ll simplify it - pretend there is just one question that 10,000 test-takers attempt to answer…I think we can agree there’s no loss of generality here. The person next to me is essentially a random draw from a population where X people got it right and 10,000 - X got it wrong.
Now, what is the maximum likelihood estimator of p, the probability that a randomly selected person got the answer correct? It’s X/10,000, big surprise!!! (I’m sure you can do a search for “Bernoulli likelihood estimator” if you don’t believe me) Unfortunately I don’t actually know X, but as long as I think that X is greater than 3333 , it would behoove me to take the randomly selected person (i.e. the person next to me) rather than randomly guess.
Math is so black and white, yet people loooooove to argue with it.
You’ve provided a number of probabilistic arguments in an effort to justify a statement that began with the word “always” (actually, “ALWAYS”). Unless the probability is unity – and you know that it is not: you’d have demonstrated that is was if it were – then the statement beginning with “always” cannot possibly be true. Which, I believe, is what I wrote.
Math is so black and white, yet people loooooove to argue with it. And when someone who understands math argues with it, it’s generally because the math was presented incorrectly. As here.
First off, my first reply was “Guessing yields a 33% chance. I would wager that there are no questions where less than 33% of candidates get the right answer, so it is always better to copy than guess.”
If you believe that there are no questions where > 2/3 of all test-takers get it wrong (the initial antecedent), then yes, always (unconditional probability).
Also, I primarily took issue with your claim that “If you’re copying from someone who is so bad that their reasoned answers will be correct less than 1/3 of the time, you’d do better to guess randomly”; I hoped my example would demonstrate that this isn’t the proper way to think about this. I guess this may make sense if you know something special about the person next to you; I think the only fair inferences can be drawn on a population, not on an an individual basis.
It is the proper way to think about refuting a universal statement, which is all I was attempting to do; one counterexample is sufficient. I know that you know this.
I know that one counterexample would be sufficient, but I don’t believe that what you proposed works.
Let’s consider the following scenario, where you are stumped on question #5:
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There are 10 test-takers, and 10 questions on the 3-answer multiple choice test.
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You know that the person next to you, Candidate #9, got 20% of the 10 questions right.
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You also know that 100% of people (other than yourself) answered #5 correctly.
Does the fact that Candidate #9 got less than 1/3 right (and I know this) matter? It appears that even if I know that someone got < 1/3 right, this is not sufficient to convince me that copying their answer is worse than guessing (especially if I have other knowledge that says they must have gotten the answer right). So, this fails as a counterexample…
Besides, which of the two is more likely?
A) The person next to me got < 1/3 of all questions right
B) Out of all the people here, > 1/3 got #15 right
Look, I think you’re a smart guy, but I don’t believe that your initial assertion/conclusion necessarily works in the way you’re claiming it does.
Suppose that I don’t have any idea how many people got any of the answers correct, and I happen to be sitting next to #9 who, in fact, got only 20% of them correct. If I copy from my neighbor, I get 20%. If I guess randomly, I will likely get 33% correct. Guessing’s better.
Suppose that I do know how many people correctly answered the questions (individually, or in aggregate), and I still happen to be sitting next to #9 who, in fact, got only 20% of them correct. If I copy from my neighbor, I get 20%. If I guess randomly, I will likely get 33% correct. Guessing’s better.
guys…WAY WAY off topic on the statistics and whether it is better to copy off someone or just randomly guess…anyway u all mssed the whole point of copying, and that is the mindset of the one who wanted to do it. in his/her mind, stats and probability counts for nothing.
picture this scenario, I did not study for an exam at all, read the question, looked at the mcq answers, nothing made sense, exam paper might as well be in greek, looked over to my neighbour who already is filling in the ovals fast and furious, noticed that everyone is doing that same except me, random guess or copy??..the person who is filling in fast n furious cant be doing it fast and furious if he knows jackshit, if he is, he will be like me…decision made, copy off that guy…
IMO what michelle wanted to ask u guys is…as charterholders and professionals, is there really no turning back if one has made a mistake that borders on integrity/ethics?
likewise my post where there have been many scandals like LIBOR rigging, selling of toxic assets, these also concern integrity/ethics issues, and yet the perpetrators got off the hook.
my 2¢
Gosh…look, let me spell it out.
Assume you know which question everyone got right. You know that 8 of the 9 other people got all 10 questions right, and Candidate #9 got questions 5 and 6, and missed all 8 others.
Here, you know that Candidate #9 gets less than 33% correct. Would you still rather guess than take the answer that you know, based on the fact that everyone got the question right, to be correct, based on your primitive rule?
If you don’t get it by now, I’m guessing it’s not gonna happen…
This is blatantly wrong. If you know two things:
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Candidate #9 got 20% correct
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Everyone got question #5 correct
Are you still going to randomly guess on question #5? Okay, obviously you’re smarter than me, so go ahead 
The OP could have been at a small test centre and could have known the person next to them.
Jeez , you math guys should get a room…all we want to know is HOW this guy cheated. Not because we want to emulate but because this “scenario analysis” thing is intriguing lol.
You keep saying that I know that candidate #9 got 20% correct. I’m saying that I don’t know that (a priori), which is the situation a cheater would face in real time.
I’m pretty sure that this isn’t a discussion about who’s smarter than whom.
The interesting thing about mathematical analyses is that the fact that answers tend to be in black and white, but the parameters and boundary conditions of the problem often only aproximate (and often approximate poorly) a real situation to which it is applied. As a result, you get an exact answer to an approximate scenario, and your black and white answer suddenly looks rather gray when transported to the real world.
This happens quite a bit in finance, and wreaks havoc with risk control. The certainty generated by an exact answer to the wrong question leads people to overleverage themselves.
In this case, we generally don’t know how many people are going to get problem X right, or what proportion of answers the population is going to get right (the MPS varies every year to accommodate this), whether the person you are copying from is a genius or an idiot, or even that the answers are distributed evenly amongst A, B, and C.
About the only thing we can know with reasonable certainty is that most of the people put in a fair amount of effort to study for the exam and that the majority of the problems are designed to be answerable by those who have studied for it (unlike something like the Putnam exam, where the problems are designed to be exceedingly difficult to solve, even by people who study hard). As a result, it’s probably a better strategy to copy if you are sure you can get away with it over guessing.
The structure of this problem is remarkably similar to the Ellsberg urn problem, where drawing from an urn with a known distribution and drawing from an urn with an unknown distribution yield different expected utilities.
My earlier analysis suggested that although your likelihood of getting the right answer is more likely higher if you copy, the chance of getting caught - given the mechanics of looking over to find small ovals - is substantial, whereas guessing an oval will give you “around 1/3” chance and is risk-free. So the real analysis is whether the increment in risk is enough to justify the increment in return, and one would most likely have to be extremely reckless or possibly even risk-loving to conclude it is a good strategy.
now that the big messy maths wank is over; Michelle, tell us how you cheated?
Can anyone do an analysis of the probability that Michelle doesn’t exist and “her” account and post were created by a troll just looking to stir the rest of us?
For all of you who are asserting “what this thread is really about,” here is the original post. It says:
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MK was caught by similarity analysis - which means that MK’s incorrectly filled were substantially similar to a neighboring test-taker’s.
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The CFAI banned MK from the exams in perpetuity.
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MK says that he/she is guilty, and urges people not to do this.
From this, assuming the post is honest, we can fairly safely conclude that MK looked over and copied answers from a neighbor’s exam. We don’t know what level of exam MK used, but probably it was a multiple-choice exam, and most likely Level 1.
The OP then goes on to ask
A) If anyone has ever heard of a sentence being reduced or diminished,
B) If anyone thinks it might make sense to write a letter asking for the sentence to be reduced to 5 years, given that MK is contrite.
The thread then goes on to say that writing a letter is more likely to generate what MK wants than not writing a letter, and that there is little downside other than the opportunity cost of time spent writing the letter.
No one so far responded saying that they have ever heard of CFAI reducing a sentence after imposition (but note that CFAI has little reason to advertise that widely).
Unless you are answering those questions, you are technically “off topic.”
However, there are a whole bunch of ancillary questions that this could bring up. Does it ever make sense to cheat? What are the various ways of cheating? Is CFAI’s sentence justified or draconian? How do you come to an answer about these sorts of things.
I get that they don’t answer the OP’s question, but since the OP has an answer to their question, and they are follow-on thoughts, I don’t get where people get off insisting that “the thread has to address MY PREFERRED TOPIC or I’m going to say it’s irrelevant.” Either things address the OP’s original question or have some follow-on interest promoted by that.
I don’t think people cheat because they did not study at all and just go into the exam room hoping for a pass.
I think people cheat because they have studied a lot and invested a lot of time and effort but still got stuck on questions, fear of failing, they were tempted to cheat by copying people’s answers.
BUT i think people usually get stuck on similar questions, so if the candidate put reasonable amount of effort and still don’t get that question (or questions), it is likely that other average candidate also doesn’t know the answer for certain… so reducing the success rate of cheating.
That’s what i think.
2 questions come into my mind:
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If the cheating were discovered by the similarity analysis, what happened to the other guy? How do they decide who copied from whom?
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In many cases in my experience (in the practice questions) one of the wrong answers is formulated that if you do a typical stupid mistake (like forgetting it’s semiannual yield, or forget ro reset your calculator from BEG mode, etc) you mark that wrong answer. Does it not result in “many” similarly wrong answers among the wrong answers? I’m not talking about statistical probabilities but real world. But if statistical: the probability of choosing the same wrong answer is already 50 percent not 33 which is a lot!
Gosh, what if I’m in the same way “stupid” that the guy next to me?
Here’s my question. How did she know the person she’s copying from has the same version of the exam?