Here again is Question 1 of the 2011 Prognostication Quiz, with the number of times each answer was chosen in parentheses (also see pie chart above):What will be the least popular answer to Question 1 of the 2011 Prognostication Quiz?
a. A (7)
b. B (4)
c. C (8)
d. D (7)
e. E (15)
f. F (10)
The winning answer is therefore b. B. Congratulations to Marcus, Russell, Paul, and Ekrem for outsmarting the field on that one.
Marcus was influenced by a key game theory scene from a popular historical dramatic film:
"I rolled a six sided die for this one: I decided a 1 in 6 chance was better than trying to follow any set of logical instincts, in the theory that more than 1 in 6 of my friends might think like I do. After all, they've all seen the Princess Bride too."
This is a useful approach, since it eliminates any undue sway of underlying psychology and gives a true one-in-six chance at hitting pay dirt.
Russell plunged in and dared to guess at the underlying psychology in order to predict what would be the least popular answer:
"Many people know that in a four-choice multiple choice question that B and C are the most common answers. It's not clear how this applies to a six-choice question, but I extrapolated that there would be a subset of people who would think that the middle answers (BCDE) would be commonly picked. So I guessed that these people would pick A and F as uncommonly picked, so I avoided those. The remaining people apparently don't subscribe to the notion that the middle answers are commonly picked (or might have been applying reverse psychology) and so might have picked C and D of the remaining BCDE, so I also avoided these. That left B or E, and I chose B because there might have been people who avoided it because of the original notion that B and C are commonly picked. That last part was not well justified, but if the rest of my reasoning holds water, then I predict the second least common answer was E. If not, then I'll just agree I was lucky!"
I guess, then, that Russell was just lucky, since E was, in fact, the most popular answer.
Paul, on the other hand, remembered a little more detail from Psychology 101 and applied it in what seems to me to be the closest description of what was really going on:
"From Psychology, I learned that the most popular answers in a series always tend to be about 3/4 of the way through the list. Is you ask people to choose anything from A - D, or 1 - 4, and they are choosing at random, overwhelmingly they choose C (or 3). On a ten-point scale, they choose around 7. So I ruled out those answers. Then I also ruled out the first and the last, since those were rather obvious. All that left was 'b'!"
Indeed, most people picked E, which contains the 75% point if you assign 0 - 16% to A, 17 to 33% to B, etc.
And how did Ekrem choose his answer?
"I must confess it was entirely in the spelling! 'Bad' was a useful word that I initially almost rejected for fear of giving up on question 3. However, the larger message was too appealing to pass up."
With his entry, Ekrem decided to deliver a stern warning to a Swedish pop supergroup that if they misbehave they may be subjected to the uncommon medieval form of torture involving forced swallowing of inedible objects: BAD ABBA EAT LEVI'S. Using "bad" at the start forced him to guess that D. Ventriloquism would be the winner's talent at the Miss America pageant. This is unlikely, perhaps, but it is a noble sacrifice in the name of art.
Finally, speaking for those who were unable to avoid falling into the trap of human psychology of choosing answer E:
"I am quite proud of my reasoning on Question 1, as it is a tour de force of my dizzying intellect."
-Grant
Vizzini: But it's so simple. All I have to do is divine from what I know of you: are you the sort of man who would put the poison into his own goblet or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me.
ReplyDeleteMan in Black: You've made your decision then?
Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows, and Australia is entirely peopled with criminals, and criminals are used to having people not trust them, as you are not trusted by me, so I can clearly not choose the wine in front of you.
Man in Black: Truly, you have a dizzying intellect.
Vizzini: Wait til I get going! Now, where was I?
Man in Black: Australia.
I'd be curious about the statistics of this: are E and B sufficiently far from the average of 8-9 that this set of answers would be unlikely to arise by chance or not?
ReplyDeleteeg, if I rolled 51 six-sided dice, how often would I get at most 4 of one number, or at least 15 of another number?
-Marcus
The answer is that the number of people choosing E is actually quite consistent with everyone picking by random chance. A chi-squared test suggests that throwing 51 pairs of dice would yield a result this extreme or more extreme about one time in six (i.e. p = 0.16). That's certainly not extreme enough to publish our results in any respectable psychology journal! Maybe if we had 151 people instead of 51.
ReplyDelete