Tuesday, September 9, 2014

Almost Thadingyut

It's been a while that I have written anything on this blog. There were two parts to the reason: At first, I got too busy at work during weekdays so I started writing on weekends. And then, I got chosen by one of my best friends to be her bridesmaid, which meant bridal shopping on weekends. Don't get me wrong: it's always my pleasure to accompany her. Friends or blogs? For me, it's always friends.

So it's now almost Thadingyut, which also marks the opening of nuptial season. My friend is also almost done with her wedding preparations and she is getting married in a month. Although I keep referring this wedding from the bridal side, I know both groom and bride. They have been my friends since kindergarten. They were sorta high school sweethearts although they started dating only after high school. For my friend, he was also her first love.

Then I wonder what are the chances that he is actually the best one for her given that she has never dated anyone else. (No offense, my dear friends if you happen to read this. I love you both.) You know, to be honest, I can't see how you can decide upon one person without having dated anyone else. 

There is already a well defined probability problem for my friend's case. It's known in statistics classically as a secretary problem or optimal stopping. The secretary problem is that I want to fill a single secretarial position and there are n known applicants whom will be interviewed sequentially. As soon as I am done with the interviews (or dating), the applicant is either accepted or rejected (for marriage ???) right away. When will be the best place to stop or what will I have the highest probability of selecting the best applicant?

Going back to analogy with dating and marriage: calculations are very straightforward actually. If I am happy with the first date, I will just marry him and I don't have to date the second one. Or else I have to move on with second date.

Probability of choosing the correct one at r marriage time 
 = Sum (from i = 1 to n) of P (i-th date is chosen and i-th date is the best)
 = Sum (from i = 1 to n) of P (i-th date is chosen given i-th date is the best) x P (i-th date is the best)

I will have you read the details at this wikipedia page on secretary problem. To make the long story short, you have the answer of 1/e or about 36.8%, which means that you should look for your best eligible man among the first 36.8%.

Of course, this is just a mathematical reminder to know when one should stop dating. Some people like to date forever, and I respect their choice. Also the probability of your selected one being the best partner is a whole new problem with a lot of variables in it. I am sure OkCupid has found out an answer already. 

So my friend, you are very lucky, you didn't have to look far to get the right one. He is there with you since the start. I sincerely wish you all the best.