Science of decision-making : what is “Optimal Stopping”?

Science of decision-making is a enthralling subject which never ceases to amaze me… Especially when it involves time management.

Reading time : 4 minutes.

Saving time : an awesome lot.

You have to make an informed decision…

You should consider the science of Optimal Stopping if you have to make a timebound informed decision where you have to pick the best :

  • when hiring a new employee,
  • finding a new provider or buyer,
  • and generally with everything that involves offer and demand, down to finding a love partner or a parking spot…

Let’s imagine you are looking for the optimal rental for your new shop in town, and you give yourself one month to accomplish that task. In a context where the real estate market is rapidly shifting, you know that each offer you find will be gone by the end of the day.

So you have to make a decision on the spot, after visiting each rental. But you can’t afford to just pick the first offer you find, because you have to make a good decision as well : an informed decision. And that involves knowing what you can reasonably expect from a good rental in terms of location, price, surface area, ventilation, brightness, and so on. To know that, you need to gather information first.

So there is an inevitable tension here between the need for speed and the need for data… Simple in its layout but devilish to solve, this issue is known in recreational mathematics (yes, that’s a thing 😉 ) as the secretary problem.

What are the 2 main dangers of decision-making?

There are basically 2 ways you could make a wrong decision here :

  • Choosing too early (in case better options come up after), or…
  • Choosing too late (in case all the better options have already been shown to you)

To avoid both pitfalls, let’s analyse what you can do…

Possible strategies to handle timebound decisions making

The “better yet” rule

The “better yet” strategy suggests you take the best option so far, without consideration for the upcoming offers.

However, there’s a caveat : the larger the reviewed options pool, the harder it will be to satisfy this rule.

  • If you already saw 9 rentals there is a 1/10 chance that the next will be better than the previous ones,
  • But if you saw 99 there is a 1/100 chance it will.

So the longer you stay in the game, the more likely you are to reach the end of the decision period without having picked anything… Which is probably worse than making a suboptimal choice.

The “dry spell” criteria

Here the strategy is to pick the best option after you encountered a series of bad propositions, or “dry spell”. Essentially, it relies on the idea that these bad offers act as warnings to indicate the overall quality of the supply is tottering. Would you find a great offer at that point, you should definitely grab it!

Now, this criteria is certainly more psychology-driven than rational, as you could totally be deceived by a dry spell, lowering your expectations, then jump on the first “somehow acceptable offer” you run into. As such, I doubt its objective value when it comes to optimized decision-making.

The 37% “Look & Leap” method

This method is based on the 2 phases described above : research (“Look”) then make a decision (“Leap”). And guess what? It is endorsed by computer science.

During the Look phase, you gather data which help you define “acceptability criteria” : how many square meters, with what price, on what location.. Everything you can expect from the market at that point. Please note, during the Look phase you are not allowed to make any decision, no matter how enticing an offer might be : you could rush in too early.

And now comes back our initial concern : when should you stop looking, and allow yourself to make a decision? Where is the “Optimal Stopping” point ?

After crunching a huge amount of data, science tells us the answer : Optimal Stopping is at 37%. That is to say, you should dedicate 37% of your time Looking and the 63% remaining Leaping.

In the example above : since you have 1 month to find a rental, you should spend 11 days doing research and after that, be ready to make a move on the first best option you find.

The rejection factor

But what if you are not the only one deciding, for instance in the situation where you are looking for a partner for your company and that partner may decide to reject your offer ? Well in that case, the 37% Optimal Stopping has to be tweaked down to fit that percentage.

For instance, if you face a 50% chance of refusal, take 50% from the 37% : Optimal Stopping is now at 18.5%, meaning you should jump in way earlier in the decision process!

The losing money factor

What if you have to make a decision but every offer which passes by you lose money (because what you sell is losing value, or because of the upkeep…)? Granted that the amount lost is not trivial, you obviously have to factor that in.

Let’s imagine you’re selling your company headquarters because the upkeep is too big. You know you could get anything between 400 to 500K$ for them.

This modelization shows the lowest offer you should accept :

This is a gentle reminder that in times of distress, you should relax, knowing that maths are on your side, and accept to turn down the first offers you receive if they are not above a certain threshold 😉

And that brings us to…

The hidden time cost

Research shows that when confronted to an Optimal Stopping problem, even when there is no loss of money at each offer, most people jump in too early. Certainly impatience is to blame. So the bottom line is : you should fight your own urge to commit too quickly 😉

But I admit it psychologically makes sense : we do, after all, want a solution to our problem, and the discomfort of not having a rental / a secretary / the money from the sale of our headquarters takes a toll on us, and builds up the more we stay in the game.

It is because even when we don’t lose money for each offer, we still have to dedicate energy, and time, to this search. So at the end of the day :

Every decision, whether timebound or not, is a time-management issue.

Now as we all know, time is money. So based on this, I recommend tweaking the above graph, factoring in the amount of time you dedicate to each offer and multiplying it by how much money it yields on average.

For instance, if you determine that 1 hour of your time is worth 300$, and each offer requires 30 minutes on average, you know each offer is actually costing you 150$, and you can modelize the Optimal Stopping curve accordingly.

I hope you enjoyed this article! As for me I really like this time-management decision-making tip because it is both simple and powerful.

If you are interested in this topic, I recommend the book Algorithms to Live By: The Computer Science of Human Decisions, from which this article is largely inspired.

What do you think of the Optimal Stopping tip? Will you use it? How are you currently doing things in your organization? I’m really interested about your own practices, so let me know in the comments below!

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  1. Allan Donald says:

    I did not expect time management could become that scientific… Some food for thought for sure, here and there. Even though to be honest I probably won’t take the time to apply these to my own decision model……..

    1. Yo Nova says:

      Hey Allan, yes I understand these things require some effort to be put into effect, and can be even a little bit daunting sometimes… What matters is that you know about them so you can decide to actively (vs passively) implement or ignore them 🙂

  2. Pingback:Time-management + hypnosis = uh? - Time Master Freedom

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