Tell us Michelle - tell us what you did!
I want answers! I want to know!
Like Mike Singletary - I also want winners!!! 
Well, well, well you just can’t tell Well, well, well my Michelle
Kartelite is correct. the word always is fine to use. since you know nothing of your neighbor but you do know that over 40% of all test takers get roughly 65% on the total exam, there is extremely high confidence that a normal probability distrubution will ensure that copying your neighbor will yield a better than 33% chance of being correct. if 99.9999999% of the time does not qualify as always, we should just remove the words always and never from the dictionary. in fact, it should be 100% so long as the distribution remains normal.
i have a hard time believing that there’s somebody so stupid that they are zigging precisely when they’re supposed to zag. I guess it’s possible, but highly unlikely.
Or if I may put it this way–if I go into the test center and find that the test is written in Egyptian hieroglyphics, I’m copying from the dude next to me. There’s no way that he could possibly know LESS than me.
No, he’s not.
If the probability were 99.9999999%, that would mean that only 1 person in 1,000,000,000 would get a score lower than 33%. Given that there aren’t remotely close to a billion people who have ever taken the CFA exams, and that there are probably a lot more than one who have scored below 33%, that number is silly.
The fact remains: it’s possible that you could sit next to someone who is so bad that they score below 33%; should you copy from them, you’re worse off than just guessing. Thus, you are not _ always _ better off by copying. That’s all I said.
Many investors seem to do this all the time. Even ones who most people would consider smart based on other critera.
Statistically, you are ALWAYS better off copying. Your probability copying is higher than your probability random guessing, therefore a rational person ALWAYS copies.
You might have picked a loser, but you should always copy (ignoring ethics completely and just looking at probability).
Although it’s only January 7, this sentence gets my vote for post of the year.
I never disputed this.
Which is why “always” is an overstatement.
Again, I never disputed this. I only disputed that you are _ always _ better off by doing so; sometimes you pick a loser.
^ Sorry, I missed page two being late to the game here, so I see you’re not disputing the rational decision here.
However… I would say your odds of being better off guessing are essientially nearing the “never”/“always” category, depending on how you view this:
The CFA exam has a binomial outcome: PASS or HACKSAW. You get ~70% or you fail.
Excel tells me the chance of passing through random guessing is 0.0000032488% or about 1 in 30 million. It’s hard to argue you’re any better off if you fail with one more mark than your peer.
It is EXTREMELY LIKELY (if not “nearly certain”) that no one will ever pass the exam by guessing while their desk neighbour fails. I doubt there will ever be 30 million people that completely guess on a CFA exam, or even close to it, there might be 10,000 EVER. This is approaching “always” and “never” type of scenarios. There is, however, a sliver of possibility, sure.
michelle never responded…
maybe she’s not a cheater, perhaps a liar, but maybe a troll too! =D
That makes no sense whatsoever. “Impossible” is not the same as “improbable”, and quantifying a statement with “always” is not equivalent to “most of the time”. We need not remove anything from the dictionary, just use the descriptive words found in there more precisely.
this conversation went from ethics to statistics to now philosophical…
bravo!
I still miss the adventure of Cobb Douglas though!
my point was that if you were to never experience enough iterations to see that one time that it was false, it is always. and i further clarified by sarcastic statement by saying that the probability actually is 100%, such that a normal distribution holds, which is should, always.
we’re using always in the context of probability. being a rational character, you will always be better off choosing to copy in the exam over guessing. whether the answer is correct or not is irrelevant to the conversation. this is especially true in this specific conversation as we will never know whether the answer was correct or not.
But are we using “better off” in the context of probability?
Are you better off if you have a greater probability of passing, but fail, or are you better off if you have a lesser probability of passing, but pass?
Arguably, you’re better off if you bet on the 21-point underdog to win, and they win.
haters gonna hate. waiters gonna wait. cheaters gonna cheat.
If you’re just talking, then using ‘always’ in such hand-waving conversational manner makes perfect sense. If you’re trying to make a more precise mathematical statement backed by some sort of numerical analysis, then you need to be a lot more careful about how you’re phrasing it.
You’re not always better off by copying because there is a nonzero probability, however small, that you can be sitting next to someone who will score less than 1/3, as S2000magician said.
You’re not always better off by copying if you qualify that statement on a risk-adjusted basis, and consider the cost of copying as bchad hinted ealier.
You’re not always better off by copying if you consider the fact that the particular question you chose to copy might be difficult, so that overall across all candidates it is not unlikely that >2/3 got it wrong. Furthermore, if everyone follows your conclusion that “you should always copy”, out of 10,000 candidates submitting asnwers to particular question, the set of candidates who actually attempted to solve that question might be a lot smaller (say 200) while the rest are propagated copied answers - the law of large numbers becomes less relevant for your analysis.
You’re not always better off by copying because you may want to consider the fact that, while the probability of guessing right is exactly 1/3, the probability of having selected the right answer by copying is not easily measurable. You can attempt to quantify it and come up with a point estimate to compare against your benchmark of 1/3, but there is uncertainty attached to your measurement which some people may be unwilling to accept. Perhaps to you, “better off” means lower expected value without any uknown unknowns.
At the end of the day, if you studied for 500 hours, you wouldn’t have to look at your neighbor’s sheet.
When I was in second year Spanish in high school we would have a weekly quiz: we were given a verb (the infinitive) and had to conjugate it in every tense and person that we’d learned.
In Spanish there is some verb tense – past perfect or some such – for which there are two sets of endings; one set is extremely common, the other is extremely uncommon. Because I knew that the girl sitting behind me had a habit of copying my quizzes, I, naturally, always used the uncommon endings.
One day, the teacher was strolling up the file of desks, stopped at her desk to look at her paper, then stopped at my desk to look at my paper, then returned to her desk (actually walked backwards: it was quite funny), picked up her paper, and announced, “You’re the only person in this room who used that set of endings . . . except HIM!”
(On another occasion I thwarted her: I wrote everything backward: right-to-left, with all the letters backward. When the teacher picked up my paper he stared at it for a while with a very puzzled look on his face, then turned it around and held it up to the light. The only thing I missed was one accent mark.)
I’m just going to sit this one out from this point on…my main point was that you shouldn’t focus on what % of questions the guy next to you gets right, but what % of the whole population (from which he’s drawn) got that particular question right. What the dude looks like sitting next to you (which is what you’ve got to go on), doesn’t really provide any useful information; however, the question itself (insofar as you can perceive its difficulty) does.