It’s a classic problem for any hiring manager. Namely, how do you know when you’ve found The One when interviewing for a position? Is this candidate the match your company has been dreaming of ever since you posted the job?
The secretary problem offers one solution to that question, but it also poses its own challenges.
Here’s how the secretary problem works, the problem with the secretary problem, and what your hiring managers can do to move beyond it and find the best candidate for your company.
What is the Secretary Problem?
Before we talk about what you could do better, let’s talk about the initial problem. The secretary problem.
The secretary problem, also known as the marriage problem or best choice problem, is an example of optimal stopping theory, which is concerned with choosing a time to take an action based on sequentially observed random variables in order to maximize payoff (or minimize cost).
In plain English, it’s a mathematical theory of how to make the best possible choice based on the available data when interviewing for a position.
How Does It Work?
In it’s most basic form (or if you prefer, the classic secretary problem) it goes like this.
We start by assuming the following:
- There is one secretarial position available (or whatever position you’re hiring for)
- There are n applicants for the position (the value of n is known)
- You can rank the applicants best to worst in a linear manner without any ties
- The applicants are interviewed sequentially in a random order, with any n ordering being equally likely (the applicants could come in any possible order)
- As each applicant is interviewed, you must accept them for the position (thus ending the problem) or reject them and interview the next one (if any)
- The decision to accept or reject an applicant is based solely on the ranking of applicants that have already been interviewed
- If you are interviewing a candidate, all previous candidates have been rejected and cannot be recalled
Your objective, obviously, is to select the best applicant. The question, then, isn’t which applicant is best, but rather which applicant is best based on all applicants that came before them.
And since you have no way of knowing whether a future applicant will be better or worse than the current applicant, you have to gamble on whether the applicant in front of you is, in fact, the best applicant for the position.
Dennis Lindley’s Solution
So, how do you solve the problem? There’s some dispute about who was first to solve the secretary problem, but the first official solution was published in 1961 by a British statistician named Dennis Lindley.
Lindley’s solution to the problem lies in this basic realization: if you have 10 applicants, they can all be ranked from 1 to 10 as best to worst candidates. But the candidates don’t come through your door in worst-to-best order–they’re shuffled randomly.
There’s a 1 in 10 chance that the applicant in front of you could be the best, but there’s also a 1 in 10 chance that the best applicant was the first candidate you interviewed. The interviewer has no way of knowing.
For a slightly more concrete answer, we have to return to optimal stopping theory.
By analyzing the distribution of talent, it was calculated that if you interview the first 37% of candidates, then pick the next person who is better than that initial group, you have a 37% chance of picking the best candidate (which isn’t much, but still better than the 10% chance you get by guessing randomly).
The Problem with the Secretary Problem
Lindley’s solution gives you a fairer chance–you now have a one in three chance of choosing the best overall candidate.
The problem with the secretary problem is the other two out of three, the lingering worry that the next candidate might be better after all. Unlike the secretary problem, which assumes an all-or-nothing attitude, your hiring manager’s choices are rarely that cut and dry.
Neil Bearden’s Strategy
This brings us to Neil Bearden’s strategy for solving the secretary problem, which further improves your odds for success.
In Bearden’s strategy, you use the √n method to select the highest-ranking candidate compared to the theoretically best candidate. Here’s how:
- Estimate the number of people you could interview, n (let’s say 30).
- Calculate the √n (5.477)
- Interview and reject the first √n people (the first 5.477 people). The best of them will set your benchmark.
- Continue to interview people until you find the first person to exceed the benchmark set by the previous step.
Out of a pool of 10 candidates, Bearden’s strategy will, on average, get you a candidate that’s 75% perfect; in a candidate pool of 100, the accuracy jumps to about 90%.
What You’re Left With
Using Bearden’s strategy, you can shrink your candidate pool to focus on the first 5 candidates out of the 30 interviewing for a position, candidates that will help you decide the benchmark for the best possible candidate you could be looking for.
The problem with Bearden’s strategy is simple: you have to reject the first √n candidates. In a pool of 30, that means you have to reject roughly the first five candidates.
But what if those first five candidates contained someone you really loved for the position?
We’re here to tell you that there’s an easier way. What if we said you could take those 30 candidates, whittle it down to the five you really want, and run Bearden’s strategy on those five candidates?
The key is to understand what is my employee turnover costing me and using our findings to optimize your organizational culture.
There’s an Easier Way
You want to beat the secretary problem. You want to optimize your organization and develop the tools and candidates that will set you apart in your industry.
That’s where we come in.
Our HR Data Solutions Platform offers objective data to help you make informed human decisions when interviewing for a position. We make it easy for you to find the candidates you need without jumping through a thousand hoops.
Ready to find out how we can help? Click here to get in touch.