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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

Freelance Writer for Hire

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Last Updated on August 20, 2019

26 Useful Things to Learn Now That Will Change Your Life

26 Useful Things to Learn Now That Will Change Your Life

If you pay attention to your everyday life careful enough, you’ll know that you can learn from everything and everyone you come across. Our life is basically full of useful lessons that we should learn.

Here are 26 useful things to learn that Abhishek A. Singh shared on Quora. Let’s see how these life theories would lead you to live a different life.

1. Primacy and recency: People mostly remember the first and last things that occurred, barely the middle.

When scheduling an interview, ask the employer the time slots they do interviews and try to be the first or the last.

2. If you work in a bar or in customer service of any kind, put a mirror behind you at the counter.

In this way, angry customers who approach you will have to see themselves in the mirror behind you and the chance of them behaving irrationally will be lowered significantly.

3. Once you make a sales pitch, don’t say anything else.

This works in sales, but it can also be applied in other ways.

My previous boss was training me and just gave me pointers. I was working at a gym trying to sell memberships. He told me that once I got all the small talk out of the way and presented the prices, the first person to talk would lose.

It didn’t seem like a big deal but it actually worked. Often there were long periods of awkward silence as the person tried to come up with some excuses, but usually they bought.

4. If you ask someone a question and they only partially answer, just wait.

If you stay silent and keep eye contact, they will usually continue to talk.

5. Chew gum when you’re approaching a situation that would make you nervous, like public speaking or bungee jumping.

When we eat, our brain tell ourselves, “I would not be eating if I were danger. So I’m not in danger.” This has helped me to stay calm.

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6. People will always remember how you made them feel, not what you said.

Also, most people like talking about themselves; so ask lots of questions about them.

7. When you’re learning something new, teach it to a friend. Let them ask you questions about it.

If you’re able to teach something well, you will be sure that you’ve understood it very well.

8. If you get yourself to be really happy and excited to see other people, they will react the same to you.

It doesn’t always happen the first time, but it will definitely happen the next time.

9. The physical effects of stress — breathing rate and heart rate — are almost identical to the physical effects of courage.

When you’re feeling stressed in any situations, immediately reframe it : Your body is getting ready to be courageous, you are NOT stressed.

10. Pay attention to people’s feet.

If you approach two people in the middle of a conversation, and they only turn their torsos and not their feet, they don’t want you to join in the conversation.

Similarly, if you are in a conversation with a coworker who you think is paying attention to you and their torso is turned towards you but their feet are facing in another direction, they want the conversation to end.

11. Confidence is more important than knowledge.

Don’t be intimidated by anyone, everyone is playing a role and wearing a mask.

12. If you pretend to be something for long enough, you will eventually become it.

Fake it till you make it. Period.

13. Not to be creepy, but if you want to stare at someone unashamedly, look directly past them and wait for them to try and meet your eyes.

When they fail to do that, they’ll look around (usually nervously for a second) they won’t look at you again for some time. This is your chance to straight up stare at this person for at least 45 seconds.

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And as suggested by Brian Stutzman:

If you’re staring at someone and get caught, DON’T turn your head or your body to look away, because that just confirms that you were staring.

Just move your EYEBALLS off the person. Unlike turning your head, it’s instantaneous. And the person will think you were just looking at something behind them and that they were mistaken for thinking you were staring. Do it confidently, and ignore any reaction from the person, and you can sell it every single time.

After a second, you can even look back at them with a “Why are you staring at me?” look on your face to really cement the deal!

14. Build a network.

Become the information source, and let the information be yours. Even grabbing a beer with a former colleague once a year will keep you in the loop at the old office.

Former coworkers might have gotten a new position in that office you always wanted to work in, great! Go to them for a beer, and ask about the office. It’s all about connections and information.

15. If you are angry at the person in front of you driving like a grandmother…

Pretend it is your grandmother, it will significantly reduce your road rage.

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    16. Stand up straight.

    No slouching, hands out of pockets, and head held up high. It’s not just a cliche — you literally feel better and people around you feel more confident in you.

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    17. Avoid saying “I think,” and “I believe” unless absolutely necessary.

    These are phrases that do not evoke confidence, and will literally do you no good.

    18. When feeling anxious, clean up your home or work space.

    You will feel happier and more accomplished than before.

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      19. Always buy the first pitcher or round of drinks.

      You’d be surprised how long you could drink on the phrase “I bought the first one.”

      20. Going into an interview… be interested in your interviewers.

      If you focus on learning about them, you’ll seem to be more interesting and dynamic. (Again, people love to talk about themselves.)

      21. Pay attention parents! Always give your kid a choice that makes them think they are in control.

      For instance, when I want my son to put his shoes on I will say ,”do you want to put your star wars shoes on or your shark shoes on?”

      Pro-tip: In some cases, this works on adults.

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        22. Your action affects your attitude more than your attitude affects your action.

        As my former teacher said “You can jump and dance FOR joy, but you can also jump and dance yourself joyful.”

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        23. When a group of people laugh, people will instinctively look at the person they feel closest to in that group.

        Notice who you look at and who look at you when you laugh with a group of people!

        24. If you want to build rapport or gain someone’s trust quickly, match their body posture and position.

        If someone is sitting with her legs crossed, cross your legs. If they’re leaning away from you, lean away from them. If they’re leaning towards you, lean towards them.

        Mirroring and matching body position is a subconscious way to tell if someone trusts you or is comfortable with you. If you’re sitting with your arms crossed and you notice someone else is sitting with her arms crossed, that is a good indicator that you have/are successfully built/building rapport with that person.

        25. The Benjamin Franklin Effect (suggested by Matt Miller)

        I find the basis of the Benjamin Franklin effect is very useful and extends far beyond pencil borrowing. This knowledge is useful in the world of flirting too.

        Asking a girl in your class if you can borrow a pencil or her notes or to explain the homework will make her more likely to like you than if you let her borrow your stuff or are the one to help her. Even just asking a girl to buy you drinks (facetiously) leaves a much bigger impression than offering to or actually buying a girl a drink.

        The best part is it kills 3 birds with one stone: you get the advantages of the favor itself, the person subconsciously likes you more, and it makes them more open to future favors and conversation.

        26. Handle panic and anxiety behaviors by tapping fingers (Suggested by Jade Barbee)

        When you’re feeling stressed, worried or angry, tap each finger tip while thinking (or speaking quietly) a few specific words about what is bothering you. Repeat the same words while tapping each of your 10 fingers, including thumbs.

        For example, tap while saying, “I’m so angry with her…” Doing so will likely take the charge out of the feeling and return you to a more resourceful (better feeling) state of being. It’s called EFT (Emotional Freedom Technique) or “tapping,” and it is useful in many life situations – emotional sadness, physical pain, food cravings, traumatic memories…

        Featured photo credit: Nicole Wolf via unsplash.com

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