The Best Choice Problem
Whether hiring or dating, how do you know when to stop interviewing or courting?
There’s a famous math problem called the Best Choice Problem, also called the Marriage Problem. A solution was offered in the 60s by mathematician Leo Moser.
Since I’m involved in matchmaking at Wednesday Night where we setup drinks between people, I think a lot about these two questions:
At what point do you stop casually meeting people and start to seriously consider someone as a long-term partner?
At what point do you stop looking for imperfections in someone you’re dating and commit to them?
These two goals are at odds with each other. You don’t want to settle down with the first person you meet or just anyone for that matter, but your drive to search can work against you once you have potentially found someone you’re compatible with.
The simplistic answer would be: just choose someone.
Experimental studies around the Marriage Problem suggest that this is also the problem: people stop searching too soon and settle too quickly. They prematurely end their search because of the high cost of searching—examples here might include looking your best by being fit and going to the gym, buying newer clothes, buying drinks or dinner, investing time to go on dates, emotional investment of being rejected, etc.
The Marriage Problem has an elegant solution though. Given the rules, and n candidates, you can reject the first n/e candidates, where e is the natural logarithm (approximately 2.72). After that, you compare each new candidate to the previous rejected candidates and if they’re better than all of the ones before them, your odds of having successfully found the best one is 37%.
To use an example, let’s say you decide that you’ll consider meeting 25 people. You can safely reject 25/e — or 9 people. From that point forward, you can use those first 9 as a baseline to compare future dates against. Once you find someone after date #9 who is better than all the ones before them, you should commit to them. At this point, your odds of having found the best candidate is 37%.
It doesn’t matter whether you do this with 25, 50, 100, or 10,000,000 dates or job candidates. You’ll always need to reject approximately 37% of your first candidates and use them as a baseline to compare against the rest. The odds of success always converge at 37% at the optimal stopping point (in this case, where you reject the first n/e candidates).
Could we go as far as to say that our divorce rate has an effective ceiling at 67% assuming 37% of people are successfully finding their best match? Would a discrepancy between a hypothetical divorce ceiling and the current divorce rate indicate anything?
I’ve thought about whether the solution to the Marriage Problem reflects today’s dating culture in 2013. The New York Times goes into detail about how much the courtship process has changed, especially for millenials.
Previous generations had different traditions of courtship. Whether our current shift in rules are better or worse is debatable. But the trend is shifting: guys don’t usually take the girl out to dinner and a movie or buy them flowers anymore. The dating scene—at least when meeting online—is more casual and resembles something like a funnel.
In other words, dating and courtship is not a front-loaded activity anymore—it looks more like a bell curve where the y-axis is the amount of effort expended and the x-axis is time.
