How to solve the secretary problem

Fussy suitors

Imagine for a moment you’re about to evaluate a line-up of prospective secretaries for a position, to be interviewed in a random order with a yes/no decision to be made about each applicant immediately after you’ve seen them.

You’d likely mentally rank each applicant in order as you go along, the difficulty in this scenario being that you must make an instant decision about each candidate.

You might pick a suitable secretary very early in the process; but then there’d be no guarantees that a superior prospect wasn’t still waiting in line to be interviewed.

Choices, choices!

Optimal stopping

The solution to the problem is provided by an elegant algorithm*.

In plain English, you’d likely reject the earliest few candidates since you have little feel for the calibre of the applicants.

But then after about a third of the candidates have been seen, when you come across an individual that outshines all previous interviewees you’d offer them a job on the spot.

As implied by the example below, by stopping the process before the end you can make a solid decision, even though the best candidate not being selected remains a possibility.

The approach of leaving no stone unturned by considering every available option risks missing the boat entirely, so this is not considered to be the optimal strategy.

The Sultan’s dowry

While the above problem is abstract & theoretical in nature, we experience variations on this challenge regularly.

Each time I fly to Sydney the person organising my travel needs to make a call on airline tickets & hotel stays, at some point deciding on a deal that is attractive enough.

Whenever my wife has kindly (absent-mindedly?) left me no unleaded fuel in the Toyota – which happens surprisingly often, it must be said – I have to determine how far along the highway to risk cruising before selecting a service station.

And don’t get me started about the parking spaces at Indooroopilly Shopping Centre – if, perish the thought, I take a gamble on finding a free space close to the entrance and it doesn’t eventuate, I never hear the end of it from the attendant chorus of backseat drivers!

Conservative thinkers tend to take the earliest option, others will exhaust all opportunities in searching for the perfect spot, with most of us lying somewhere between the two extremes.

Keep the faith

Of course each time any of us makes an investment, picks a stock, deploys venture capital, or initiates a new start-up business, there’ll be a nagging doubt that a better prospect (or price) may come along sometime after we’ve taken action.

While this might appear to be anxiety-inducing, it needn’t be, provided you have a strong sense of what you’re looking for.

After all, unless you believe in the woolly concept of ‘soulmates’ you probably went through a similar process when choosing your life partner!

While real life is complex & can’t always be solved by mathematical equations – there may be other subtle factors that sway decisions – the algorithm suggests you should screen a reasonable number of candidates, make a positive choice, & then have faith in your actions.

Happy searching!

*Interview 37 per cent of the queue, then pick the next applicant that’s been the best so far (the ratio is 1/e, where e is the exponential number 2.718281828).

Glad you asked!