Every day, our brain makes thousands of decisions, ranging from the mundane (Blue shirt or grey?) to the routine (Where to go for lunch?) to those decisions we don't even realize we're making, but are necessary for survival (Do I step out onto the street now? Now?)
Every so often, the choice is front of us a really big one, with long lasting effects. In business, this choice may be, Whom do I hire for my startup? In your career it's, Which job do I take? And in love, of course, you usually only get to choose one husband or wife.
How can you ever be certain that the choice you're making is the best option for you?
You can't, of course. If you reject the opportunity in front of you, there's no guarantee that your future options will be better for you. Even if you're not quite sure about the job you've been offered, should you take it? What if your top choice company calls next week?
...What if they don't?
In life, there's an entire class of problems that are like this. It's whenever you need to make a decision about something, where:
- You don't know what opportunities might come along in the future.
- You have an ideal timeframe or hard deadline for making the decision.
- Once you've made your decision, you're locked in or committed, at least for now.
The Secretary Problem is a famous example of this dilemma at work. Imagine you're interviewing number of secretaries for one position. The applicants are interviewed in random order, and you must make a decision about each applicant as soon as their interview is finished. Once you reject an applicant, they're gone for good.
You can base your decision on the applicants you've seen so far, but you have no idea who's coming in the door next.
At what point is it wise to stop the process and just make a decision?
This is the basis of a lesser-known mathematical theory that can help you make these types of decisions: optimal stopping theory. What it does is help maximize the probability that you'll end up with the best outcome.
So how does it work?
Based in probability theory, optimal stopping theory has a somewhat shadier pedigree than most of its mathematical brethren; it emerged as a gambling strategy. In 1875, an English mathematician from the University of Cambridge used optimal stopping theory to determine when one should stop buying lottery tickets. Let's see how it works in the hiring process above:
Say you want to fill the secretary position within eight weeks and you can interview three candidates per week. That means you have a total of 24 applicants you could potentially interview.
Optimal stopping theory says to, right off the bat, reject the first 37 percent of applicants you see. This means saying goodbye to the first nine candidates you interview, regardless of how great or terrible they seem to be.
You should then hire the next candidate that is better than the first nine you interviewed.
That is your optimal stopping point.
Now, there's a really complicated mathematical formula for determining optimal stopping point, or the time to take action in order to maximize the expected reward.
However, there's also a great deal of theory that says the optimal stopping point is the next best choice after you've seen and eliminated 37 percent of your options.
Say you hired the first person you saw. That gives you a really terrible shot at having picked the best candidate--your odds are 1 in 24, meaning you have just a 4.1 percent chance of making the right choice. You really need to see more candidates to get a sense of what else is out there.
But as you continue to see more and more candidates, the chances increase that you've already seen the best candidate and passed them over. This risk grows with every candidate you see and reject.
Optimal stopping theory applies in your own life, too. Say you're 20 years old and want to be married by the age of 30. You can date one person every six months to meet 20 people total within that time. Optimal stopping theory says you would reject the first seven people (and you might as well say goodbye, because they aren't waiting around for you) and choose the next person who is better than those first seven as the one you will marry.
If you're unemployed and want to be in a job within six months, you could set a goal for one interview a week. Out of 26 possible jobs, you should reject the first 10, then say yes to the next best one after that.
Now, of course this isn't foolproof--it's a theory! For example, your best candidate or ideal spouse or perfect job might have been in the first group to be rejected. On average, though, this theory does maximize your chance of making the best possible choice when given plentiful options. For example, when buying a house.
It's especially useful in hiring, where the cost of bad hires can be brutal. Actually, the cost of poor marriage decisions is pretty brutal, too. But I digress....
So there you have it: a mathematically proven strategy for optimal stopping in hiring, love, career, and life in general!