Finding Emily Jones
Posted by Nerdyy
Last week I was at a conference, and as part of the conference we had a gala reception with a whole lot of alcohol and food to be consumed. The reception was sponsored by textbook and software publishers. Typically these receptions consist of folks chilling and hanging out and yes drinking and eating; thus everyone is in very good spirits(so to speak!). However this particular one had a twist. We were forced to play a game; a game devised by one of the authors (Yes, trust a University professor to throw in some assignment in the middle of happy hour!). As it turns out the game itself was very interesting.
We all had to choose a number between 1 and 100. The person that got the number closest to 2/3 rd of the value of the average of all the numbers chosen would win the game and get a prize. OK so this just got a hell of a lot complicated, especially after having already imbibed a Manhattan (there is a picture of that somewhere!). So the first action in order to correctly find the winning number here was ... get a glass of wine! Great so now lets gather our thoughts into some logical sequence - usually in a population we can expect these type of thinkers:
(As an aside, this question was once asked as a contest in Financial Times with a cash prize, and the results showed that quite a few of the responses were 100. Was that a completely irrational response from a non trivial set of individuals - as it turns out it wasn't. Apparently a game theory professor at a British University had formed a coalition of respondents whom he convinced to submit as a a response the number 100 - no doubt with a promise of sharing the prize. Why 100 - well because this particular professor wanted to distinguish himself from what he believed would be mostly answers of 0 or 1; thus he sent in a response of 7 along with his coalition that sent in responses of 100, thus after the computations the correct answer would be somewhat removed from 0 or 1 i.e. closer to his 7. So yes - he manipulated the contest! Thus we have to be aware of potential manipulations or gamifications as well.)
At this point comes the question Who is Emily Jones (that is not her real name, just an assumed name that she used to play the game - a nom de guerre as the fancy term goes!)? As you might have guessed that was the winner of our game, with a guess of 26 which happened to be a fraction off of the correct answer. The winner could be the winner one of two ways - a random guess or a well thought out process of guessing the distribution of thinker levels in the population. Given the level of people at this conference, we can easily rule out the first. Why is it important that we find her? Well for any level of statistical analysis to succeed and be considered legitimate, it has to be the case that the researchers forecast the correct distribution of the population. Without that all you have are incomplete or incorrect estimates.
And as a conclusion - what was my guess? It was 15, so I overestimated the number of higher level thinkers or underestimated the amount of drunkenness that was prevailing in the population or more likely both!
We all had to choose a number between 1 and 100. The person that got the number closest to 2/3 rd of the value of the average of all the numbers chosen would win the game and get a prize. OK so this just got a hell of a lot complicated, especially after having already imbibed a Manhattan (there is a picture of that somewhere!). So the first action in order to correctly find the winning number here was ... get a glass of wine! Great so now lets gather our thoughts into some logical sequence - usually in a population we can expect these type of thinkers:
- Level 0 thinkers - Lets just choose a number randomly between 0 and 100 and see what happens.
- Level 1 thinkers - Given that the mean of all random numbers between 0 and 100 should be approximately 50, lets choose a number approximately closest to 2/3 rd of 50 = 33.
- Level 2 thinkers - Assume the presence of Level 1 thinkers who would choose on average 33, so choose 2/3 rd of that = 22.
- Level 3 thinkers - You get the point .. 2/3rd of 22 = 15.
- Since this was a conference full of economists, you should expect the presence of at least some game theorists who would take this sequence of thinker levels to a logical conclusion and end up at 0 or 1.
(As an aside, this question was once asked as a contest in Financial Times with a cash prize, and the results showed that quite a few of the responses were 100. Was that a completely irrational response from a non trivial set of individuals - as it turns out it wasn't. Apparently a game theory professor at a British University had formed a coalition of respondents whom he convinced to submit as a a response the number 100 - no doubt with a promise of sharing the prize. Why 100 - well because this particular professor wanted to distinguish himself from what he believed would be mostly answers of 0 or 1; thus he sent in a response of 7 along with his coalition that sent in responses of 100, thus after the computations the correct answer would be somewhat removed from 0 or 1 i.e. closer to his 7. So yes - he manipulated the contest! Thus we have to be aware of potential manipulations or gamifications as well.)
At this point comes the question Who is Emily Jones (that is not her real name, just an assumed name that she used to play the game - a nom de guerre as the fancy term goes!)? As you might have guessed that was the winner of our game, with a guess of 26 which happened to be a fraction off of the correct answer. The winner could be the winner one of two ways - a random guess or a well thought out process of guessing the distribution of thinker levels in the population. Given the level of people at this conference, we can easily rule out the first. Why is it important that we find her? Well for any level of statistical analysis to succeed and be considered legitimate, it has to be the case that the researchers forecast the correct distribution of the population. Without that all you have are incomplete or incorrect estimates.
And as a conclusion - what was my guess? It was 15, so I overestimated the number of higher level thinkers or underestimated the amount of drunkenness that was prevailing in the population or more likely both!
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