Finding Emily Jones

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:

1. Level 0 thinkers - Lets just choose a number randomly between 0 and 100 and see what happens.
2. 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.
3. Level 2 thinkers - Assume the presence of Level 1 thinkers who would choose on average 33, so choose 2/3 rd of that = 22.
4. Level 3 thinkers - You get the point .. 2/3rd of 22 = 15.
5. 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.

Well - we have already fallen into a trap because unlike a home work problem, no one asked us to find an equilibrium which would indeed be 0 or 1. We had to estimate or forecast what the actual average would be and calculate 2/3 rd of that. Thus we had to somehow figure out the approximate number of each level of thinker. We would also have to think of potentially irrational answers.

(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!

Farm Fresh

Farm Fresh

Posted by Nerdyy

... just means fresh from the farm on your deck!

An Old Love, Revisited

An Old Love, Revisited

Posted by Nerdyy

Rahul races across the bridge. Bag slung over shoulder, jacket buttons open.
"Anjali", "Anjali" he screams.
Rahul comes to the end of the bridge.
He looks toward the tent. He sees two Anjalis - his daughter, for whom he was racing across the bridge, and the OTHER Anjali - yes that one, the source of the name for his daughter.

Well No - I wasn't quite going for that type of old love in this return to posting, rather a more constant companion of old, that I had somehow forsaken for other pleasures. As a kid growing up, my first love right from the time I learned to put alphabet letters together to form words was always reading. Fantasy tales, tales about animals, tales about schools and young kids, tales about young kids solving mysteries etc. etc. would fire up my imagination until I was lazily lying down with a picnic basket full of ham sandwiches, stretched out in a meadow full of daffodils. I would conjure up travel tales for myself, and pursuit of dragon tales for myself, and flying on witches broomsticks for myself. Growing up as an only child, with very strict parents with strict rules meant that reading was my only source of escape into a fantasy world, that I always yearned to escape to in real life, except they didn't exist in any reality! As I grew into my pre-teen years I somehow convinced my mother that I would achieve a lot more productivity with my schoolwork if I could shut my door and make it more quiet in my room. Once that convincing was accomplished, I would wait every day breathlessly until I could shut my door and then secretly delve into my books during homework time. Of course the homework would be done in record time in between the pleasurable reading times! And I had to invent my own subterfuges to get around the very keen eyes of my mother; who would keep a close watch over my book reading. You see, if she saw me with 1/3rd of the book read in the afternoon, and then in the evening notice that I was 2/3rd of the way through my book, she would get naturally suspicious that I had been reading the book during my homework time! SO I ended up reading portions of the book twice to ward off any suspicions.

Adolescence passed into the teen years, in the meantime music entered my list of loves. But reading was still very important - now I had graduated into the words of Alfred, the Williams, Jane, Charles, Emily, Arthur and of course a plethora of less literary mystery and spy stories. My fantasies still raged - one day I was at war leading an armada into battle and the next I was an Interpol agent racing through multiple train stations in Europe just to make my connections in pursuit of an old Nazi, and the next day I was seducing the most beautiful woman in my imagination who just happened to be betrothed to my cousin, the Prince.

And then one day in mid August of '92 I got on a plane and flew across the globe to this brand new place - Dallas! And my fantasies had come alive. I could see daffodils in March, I could race through airports, I could visit new and exciting cities - you get the point. And reading became a lot less important. And over the years as I became busier and busier with life, it slipped completely off of my radar. But I always wondered if there would be a day that I would gravitate towards it again, and maybe rekindle the old connection we shared. Maybe all I needed was a nudge and a push towards it. And in the end, after all these years that's all it took - many nudges and pushes, some overt but mostly covert and well hidden encouragements thrown my way.

Now that I had decided that I was going to reconnect with books, the question was what should I read. I was given a book that seemed a tad to heavy and depressing, about disease and mortality, so I set it aside (and will come back to later) and took up a lighter offering. And I was hooked instantly - maybe because it kept reminding me of experiences from the very near past. And I gleefully downloaded eBooks, and ordered books from the library. So now I have this pile of books waiting to be devoured, overt and covert meanings waiting to be deciphered, romances straight and illicit waiting to be explored, and travel stories waiting to be experienced.

So I can say that my old love has ensnared me again, and I am happily reading the words of the beloved authors and poets, and delving into the fruit of knowledge offered up by this garden of eden.