Ten is the Magic Date Number!

http://www.msnbc.msn.com/id/23051735

This article applies many of the secretary problems to the dating world (somewhat like we touched on in class). However it puts the context of the problem in a more realistic framing, knowing that there are so many single people in the world, yet one does not want to date huge numbers before settlign down there are a few key numbers of advice that can be applied to people truly playing the dating game. The first of which is they suggest only needing to date about 10 people before looking for your perfect match (using these first ten to get an idea of what is out there). Secondly they suggest setting up some basic criteria and focusing your effort on people only within a specific ideal 25% range. These shoudl be the 25% who would be willing to date you and you'd be willing to date (aka not someone incredibly out of your league or completely not your type). These two suggestions still apply the basic concept and strategies of the secretary problem to the dating issue while keeping in mind "real world" constraints.

I think one thing the whole secretary problem model doesn't take into account is that you can also get a very good idea of what's out there based on the advice other people have. That way, you would have to do less "searching" on your own, and can rely more on the information of others, and thus find your "perfect" match sooner.

Is this article really applying the secretary problem to dating? The secretary problem is as follows:

1. There is a single secretarial position to fill.
2. There are n applicants for the position, and the value of n is known.
3. The applicants can be ranked from best to worst with no ties.
4. The applicants are interviewed sequentially in a random order, with each order being equally likely.
5. After each interview, the applicant is accepted or rejected.
6. The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.
7. Rejected applicants cannot be recalled.
8. The object is to select the best applicant. The payoff is 1 for the best applicant and zero otherwise.

While this does lead to the 37% brought up in the article, and the % does decreases and n is increased, the article suggests returning to on original date after sampling 10. This goes against the bases of the secretary problem

I think a good strategy to the marriage/dating problem would be to use a time scale than an exact number. Prof. Hartline mentioned this in class, but it just seems to make more sense than to put a number on it.

For example, you don't know how many dates you are going to run into, but say you do have a rough ideal age of marriage, say 6 years from now. Assuming you don't take any of your previous dates into account, you should roughly date for the next 2 years, then marry the person that you find to be better than all your previous dates. So the actual number of dates that you go through before you start searching for "the one" would depend on how long you date one person. Say you date a person for an average of 2 months, then that number would be 12; 3 months, 8...etc.

10 dates seems like not very many if you are going to go through 37% of your possible dating candidates before you choose the next best one. And the article also is assuming that once you've tried the 10 different dates, that you remember the best one and try to go back to them if they are still available?-- "in other words, you have to go on roughly 10 first dates, with mates who are close to your ideal. If after 10 dates there’s someone you want to go back to and he or she is available, then go for it. But give yourself those 10 first dates." It seems risky to assume that the best out of the 10 will still be available/ still want to date you after you have left them to try more people. That part of the article differs from the secretary problem where you have to hire the person immediately after the interview or they're lost for good.