Posted by: sandeepchrao | November 28, 2008

How to Find True Love

This is kind of funny, because after I finished typing this post, I saw the same exact problem posted right below mine. This is a topic I had picked to write about a couple days ago, but oh well. I think it is kind of interesting how this problem can be used in different scenarios.

Here we go…

In this game, you look for your true love by dating and having relationships with various people. Your only goal is to find the best person willing to date you.

There are a couple of rules that you must consider

  1. You can only date one person at a time
  2. A relationship either ends with you rejecting or selecting the other person.
  3. Once a person is rejected they are gone forever
  4. You want to date a fixed number of N people in your lifetime
  5. As you date people, you can only tell relative rank and not true rank

In this game you must balance the problem pf picking a mate too early, and limiting your options, with the problem of picking too late and being stuck with an “inferior” mate.

So what is the best strategy for this game…

Best Strategy

The best strategy is to always reject a certain number K of the N people you date and then select the next person that is better than the first K people that you dated. This number K will always be proportional to the number of people, N, that you plan on dating. In fact, by automatically rejecting a constant proportion of 37% of the number of people you date and finding the next best person better than the first 37%, you maximize your chance of finding true love.

You can see this with 3 people. If you reject the first person automatically, which accounts for 33% (close to 37%) of the people, than you have a 50% chance of finding true love.

Look at the possibilities…

1 2 3        Choose 2: Lose

1 3 2        Choose 2: Lose

2 1 3        Choose 1: Win

2 3 1        Choose 1: Win

3 1 2        Choose 1: Win

3 2 1        Choose 2: Lose

You can see that in 50% of the cases you will choose the best person according to the strategy we played. You will find that this will be better than any other strategy that you can play.

Now you can find true love.

To see why 37% is the correct proportion, here is the proof:

Also, here is where I got the information for my post:


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