in Computer Love

A Mathematical Solution to Choosing the Right Spouse?

I’ve always been a fan of how math and science can be applied to romance (see related articles here). So when a friend linked me to Krulwich’s article “How To Marry The Right Girl: A Mathematical Solution” on NPR, I was immediately intrigued. To summarize, Krulwich describes a dilemma in which Johannes Kepler is troubled with choosing the right wife among eleven potential mates. For the best decision-making process, Krulwich introduces ‘The Marriage Problem’ solution as explained by Alex Bellos.

The Rules

Here are the rules of the game. You have a finite number of choices. Each mate is evaluated sequentially one by one. Once you pass on a mate you cannot go back to that person. Once you’ve made an offer, the game ends. While this is a simple example of an optimal stop model, (i.e. it’s missing transaction costs for each evaluation), the results are interesting nonetheless.

The Strategy

The strategy that Krulwich highlights is relatively easy. Pass on the first 36.8% of potential mates. Next, when you meet a potential mate that’s better than ones in the first group, propose marriage. Note that you may run into a problem if the best potential mate was in the first group. Krulwich says if that happens you will at least get the second best pick (but that is untrue). Think about it, you will keep passing on people until you reach the nth potential mate in your queue. The nth mate may be riddled with character flaws or hideous (to you at least– everyone’s beautiful to someone, right?) Right. Anyhoo, what is true is you will indeed optimize your decision-making.

A Simulation

I decided to simulate the model for myself to determine the probability of outcomes. I ran the simulation for 1000 trials. The probability of landing at least an 8 hovers near 71.8% with a median score of 9.75 (see histogram above). Feel free to review or enhance my code here (myGithub).

A few caveats to my model (pardon any technical jargon): First, I used a random uniform distribution when in reality a lognormal curve would be a better fit. Thus I imagine a more precise estimated median will be closer to an 8. Second, I used the strategy described in the NPR article and didn’t go into the nuances for a complex optimal stop. The model also assumes attraction levels and other ranked traits stay constant (obviously not ideal assumptions). Finally, realize that this model illustrates optimal choice and not optimal outcome as there is a bit of game theory involved when you figure the preferences of whom you’ve chosen.

Additional

How about other applications to this model? Should you accept the first offer on your home? B-School? Job? Figure out the average amount of offers for your specified timescale and you’re on your way to optimized decision-making.