Researchers propose a model to maximize success in professional recruitment

When it comes to hiring new staff, large companies often have to choose from hundreds of candidates, a process that requires time and resources. Can mathematics help streamline these procedures? At least in the broadest sense, probably yes.

A paper published in Journal of Statistical Mechanics: Theory and Experiment by Pavel Krapivsky, a statistical physicist at Boston University, proposes an algorithm that identifies three hiring strategies, each corresponding to different objectives a company might have.

Krapivsky drew inspiration from the famous “secretary problem” or “optimal marriage problem”. In one of its many versions, a princess must choose her future husband from a pool of 100 candidates at a grand reception. However, strict rules apply: she may meet only one suitor at a time and has limited time to get to know him.

At the end of each encounter, she must decide immediately whether to accept or reject the suitor. She cannot revisit previous candidates, nor can she ask any of them to wait while she considers others. How can the princess hope to make the best choice?

The secret lies in a number: 37, to be precise (raise your hand if you thought of 42). “If we divide 100 by 2.718, which is Euler’s number—one of the most famous in mathematical history—we get approximately 37,” explains Krapivsky.

In practical terms, this means that the princess should evaluate and reject the first 37 candidates, while keeping track of their quality. Starting with candidate number 38, she should select the first one who is better than all those she has previously met. According to Krapivsky, this strategy guarantees the best possible outcome under the given constraints.

The method is so reliable that even Johannes Kepler is rumored—though there is no solid proof—to have used it to select his second wife. “He studied in great detail the problem, spending a year doing this rather than his own great research, and then made a choice,” recounts Krapivsky.

Krapivsky reformulated the problem in a more modern context, applying it to hiring practices in large companies. The basic idea remains the same: the company has a single parameter to assess the quality of a candidate and must decide whether to hire them immediately or reject them without reconsideration. Moreover, in this model, newly hired employees cannot be dismissed.

“I don’t like firing people,” Krapivsky jokes. Unlike the secretary problem, here the stream of candidates is continuous and potentially infinite, making the model more realistic for modern workplaces where hiring decisions are made based on immediate business needs.

The study investigates three distinct hiring strategies:

• The Maximal Improvement Strategy (MIS) dictates that a candidate is hired only if their score is higher than that of any previously hired employee.
• The Average Improvement Strategy (AIS) allows a candidate to be hired if their score exceeds the average score of all current employees. The Local Improvement Strategy (LIS), on the other hand, involves each candidate being assessed by a randomly selected employee or a small hiring committee and hired only if their score surpasses that of the interviewer or all committee members.

Unlike the optimal marriage problem, there is no single best strategy—rather, the choice depends on the company’s objective. If the goal is to maximize long-term quality, MIS is the best approach, but it results in slower hiring. If the priority is to balance quality and hiring speed, AIS is a reasonable compromise. If rapid hiring is more important than quality, LIS is the most effective strategy.

“Of course, these are simplifications,” Krapivsky notes, “but they can still be useful.” A model like the one presented in the paper could, for instance, serve as the foundation for algorithms used in social networks and digital platforms.

These include not only platforms designed for job searches, such as LinkedIn, or dating apps like Tinder, which tailors future match suggestions based on past “swipes,” but also those that govern content selection, resource management, and artificial intelligence.

“A lot of these are actually based on very simple algorithms, like those that suggest what we watch on YouTube,” Krapivsky concludes.