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Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Imagine this scenario: you’re a boss with a string of job candidates to choose from. You have to make the final decision on each candidate at the end of each interview. If you make an offer to a candidate, you cannot interview the others; if you don’t make an offer you can never hire that candidate again.

That’s a hard decision to make. With these kinds of constraints, how are you going to maximize your chances of hiring the best candidate?

At what point in the process do you say, “Alright, I’m just going to hire the next candidate that is better than the previous ones?”

This is the “Secretary Problem,” sometimes known as the “Marriage Problem” – and mathematician Martin Gardner solved it in 1960.

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The Solution to the Formula for Making Hard Decisions

Here’s the formula’s solution: after you have interviewed 36.8% of all the candidates, just hire the next candidate that is better than the previous ones.

Essentially, the formula proves that 36.8% is the optimal stopping point. Don’t hire or marry any candidate within the first 36.8% of the group, but after that, simply choose the first one that is better than the first 36.8%.

As a practical example, if you had to interview 50 candidates, starting from the 19th candidate onward, you should hire the next candidate that is better than the first 18 ones.

Note that this doesn’t mean you will always select the absolute best candidate (you may end up with second best if the very best candidate is in the first 36.8%), but this puts the chances of you doing so at 36.8%. Pretty decent odds given the situation, I would say!

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36.8%, by the way, is the value of 1/e, where e is the base of the natural logarithm. You may or may not have recognized that little alphabet from your high school math classes.

For the mathematically-inclined who want to know exactly how the solution was derived, you can read about it here. You can also check out the more reader-friendly Wikipedia page on the Secretary Problem.

How Practical Is the Formula Really?

Like all math problems and formulas, there are always some strict constraints that don’t make it as practical as we would like.

For example, if you were going over a list of job candidates, you could most likely just interview them all and call back the best one after. No need to make a definitive offer at the end of each interview.

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However, since there is always a risk that in the interim the candidate may accept another job offer, it might be wise to follow the 36.8% rule, especially if you know the candidates are in high demand.

Making Hard Romantic Decisions Using the Formula

What about when we try to apply it to the romantic department? Well, since you (probably) can’t date a whole string of people and then go back and select the best one like in the hiring process, the problem now is that you don’t know how many candidates there are in the first place!

How you can you determine 36.8% of a number if you don’t even know what that number is?

Good news, because mathematicians have figured that one out, too, and the answer is still 36.8%! Only now, it’s 36.8% of the total time.

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Here’s how it now works: let’s say you gave yourself a certain period to find a suitable lifelong romantic partner – 5 years for example. After 36.8% of 5 years, which is about 672 days (or 1 year, 10 months, and 3 days), you should just propose to the next romantic partner who was better than the previous ones.

This is known as the unified approach, and was proved in 1984 by German mathematician F. Thomas Bruss. You can read all the mathematical details on how this was derived in his paper here.

Making hard decisions is part and parcel of life; and no mathematical formula will be able to help you with all of them. That said, it is useful to know that in certain scenarios, there is a formula we can use to maximize our chances of obtaining the most favorable outcome.

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Ian Lee

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Last Updated on October 16, 2019

Invaluable Lessons You Can Learn From Your Mistakes

Invaluable Lessons You Can Learn From Your Mistakes

Do you like making mistakes?

I certainly don’t.

Making mistakes is inevitable. Wouldn’t it be wonderful if we could be at ease with them?

Perhaps there is a way to think of them differently and see their benefits.

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Why Mistakes Feel Dangerous

Mistakes often feel dangerous. Throughout human history, our errors have often been treated as dangerous for a variety of reasons:

  • Our vulnerability. We have limited and fragile support systems. When those systems fail, people often lose their lives.
  • Real dangers. Nature can be dangerous, and making mistakes can put us at the mercy of nature and its animal residents seeking a meal.
  • Ignorance. Many cultures scapegoats someone whenever there is a failure of some kind. Scapegoating can be serious and deadly.
  • Order. Many societies punish those who do not conform to the prevailing orthodoxy and treat difference and non-conformity as a mistake. Even our brains flash an error message whenever we go against prevailing social norms.

We have a history of handling mistakes and failure in an unpleasant way. Since each of us carries our human history with us, it can be a challenge to overcome the fear of making mistakes.

If we can embrace the reality of mistakes, we can free ourselves to be more creative in our lives and dig up some interesting insights.

Why We Can’t Avoid Making Mistakes

Many people operate under the notion that making mistakes is an aberration, a mistake if you will. You can call it perfectionism but it is a more substantial problem. It is really a demand for order and continuity.

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When we think we can eliminate mistakes, we are often working from a perspective that sees the world as a fixed place. The world, however, is not so obliging. Like it or not, the world, and everything in it, is constantly changing.

Change is more constant and pervasive than we can see with our own eyes which is why we often miss it. Our bodies are constantly changing. The natural conditions of the earth change constantly as well. Everything, including economic and cultural systems have life cycles. Everything is in a constant state of flux.

We cannot see all of the changes going on around us since rates of change vary. Unfortunately, when we try to create a feeling of certainty and solidity in our lives or operate from the illusion of stability and order, we are fighting reality and our natural evolution which is built on adapting to change.

It is better to continually bend into this reality rather than fight every change we experience. Fighting it can cause us to make more mistakes. Finding the benefits in change can be useful and help us minimize unnecessary mistakes.

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Lessons Learned from Making Mistakes

Life has so many uncertainties and variables that mistakes are inevitable. Fortunately, there are many things you can learn from making mistakes.

Here is a list of ways to harness the mistakes you make for your benefit.

  1. Point us to something we did not know.
  2. Reveal a nuance we missed.
  3. Deepen our knowledge.
  4. Tell us something about our skill levels.
  5. Help us see what matters and what does not.
  6. Inform us more about our values.
  7. Teach us more about others.
  8. Let us recognize changing circumstances.
  9. Show us when someone else has changed.
  10. Keep us connected to what works and what doesn’t work.
  11. Remind us of our humanity.
  12. Spur us to want to better work which helps us all.
  13. Promote compassion for ourselves and others.
  14. Teach us to value forgiveness.
  15. Help us to pace ourselves better.
  16. Invite us to better choices.
  17. Can teach us how to experiment.
  18. Can reveal a new insight.
  19. Can suggest new options we had not considered.
  20. Can serve as a warning.
  21. Show us hidden fault lines in our lives which can lead us to more productive arrangements.
  22. Point out structural problems in our lives.
  23. Prompt us to learn more about ourselves.
  24. Remind us how we are like others.
  25. Make us more humble.
  26. Help us rectify injustices in our lives.
  27. Show us where to create more balance in our lives.
  28. Tell us when the time to move on has occurred.
  29. Reveal where our passion is and where it is not.
  30. Expose our true feelings.
  31. Bring out problems in a relationship.
  32. Can be a red flag for our misjudgments.
  33. Point us in a more creative direction.
  34. Show us when we are not listening.
  35. Wake us up to our authentic selves.
  36. Can create distance with someone else.
  37. Slow us down when we need to.
  38. Can hasten change.
  39. Reveal our blind spots.
  40. Are the invisible made visible.

Reframe Reality to Handle Mistakes More Easily

The secret to handling mistakes is to:

  • Expect them as part of the process of growth and development.
  • Have an experimental mindset.
  • Think in evolutional rather than fixed terms.

When we accept change as the natural structure of the world, our vulnerability and humanness lets us work with the ebb and flow of life.

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When we recognize the inevitability of mistakes as part of the ongoing experiment which life is, then we can relax more. In doing so we may make fewer of them.

It also helps to keep in mind that trial and error is an organic natural way of living. It is how we have evolved over time. It is better to be with our natural evolution than to fight it and make life harder.

When we adopt an evolutional mindset and see ourselves as part of the ongoing human experiment, we can appreciate that all that has been built up over time which includes the many mistakes our ancestors have made over thousands of years. Each one of us today is a part of that human tradition of learning and experimenting,

Mistakes are part of the trial and error, experimental nature of life. The more you adopt the experimental, evolutional frame, the easier it becomes to handle mistakes.

Handling mistakes well can help you relax and enjoy all aspects of life more.

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Featured photo credit: Sarah Kilian via unsplash.com

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