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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 16, 2018

16 Productivity Secrets of Highly Successful People Revealed

16 Productivity Secrets of Highly Successful People Revealed

The same old motivational secrets don’t really motivate you after you’ve read them for the tenth time, do they?

How about a unique spin on things?

These 16 productivity secrets of successful people will make you reevaluate your approach to your home, work, and creative lives. Learn from these highly successful people, turn these little things they do into your daily habits and you’ll get closer to success.

1. Empty your mind.

It sounds counterproductive, doesn’t it?

Emptying your mind when you have so much to remember seems like you’re just begging to forget something. Instead, this gives you a clean slate so you’re not still thinking about last week’s tasks.

Clear your mind and then start thinking only about what you need to do immediately, and then today. Tasks that need to be accomplished later in the week can wait.

Here’s a guide to help you empty your mind and think sharper:

How to Declutter Your Mind to Sharpen Your Brain and Fall Asleep Faster

2. Keep certain days clear.

Some companies are scheduling “No Meeting Wednesdays,” which means, funnily enough, that no one can hold a meeting on a Wednesday. This gives workers a full day to work on their own tasks, without getting sidetracked by other duties or pointless meetings.

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This can work in your personal life too, for example if you need to restrict Facebook access or limit phone calls.

3. Prioritize your work.

Don’t think every task is created equal! Some tasks aren’t as important as others, or might take less time.

Try to sort your tasks every day and see what can be done quickly and efficiently. Get these out of the way so you have more free time and brain power to focus on what is more important.

Lifehack’s CEO has a unique way to prioritize works, take a look at it here:

How to Prioritize Right in 10 Minutes and Work 10X Faster

4. Chop up your time.

Many successful business leaders chop their time up into fifteen-minute intervals. This means they work on tasks for a quarter of an hour at a time, or schedule meetings for only fifteen minutes. It makes each hour seem four times as long, which leads to more productivity!

5. Have a thinking position.

Truman Capote claimed he couldn’t think unless he was laying down. Proust did this as well, while Stravinsky would stand on his head!

What works for others may not work for you. Try to find a spot and position that is perfect for you to brainstorm or come up with ideas.

6. Pick three to five things you must do that day.

To Do lists can get overwhelming very quickly. Instead of making a never-ending list of everything you can think of that needs to be done, make daily lists that include just three to five things.

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Make sure they’re things that need to be done that day, so you don’t keep putting them off.

7. Don’t try to do too much.

OK, so I just told you to work every day, and now I’m telling you to not do too much? It might sound like conflicting advice, but not doing too much means not biting off more than you can chew. Don’t say yes to every work project or social engagement and find yourself in way over your head.

8. Have a daily action plan.

Don’t limit yourself to a to-do list! Take ten minutes every morning to map out a daily action plan. It’s a place to not only write what needs to be done that day, but also to prioritize what will bring the biggest reward, what will take the longest, and what goals will be accomplished.

Leave room for a “brain dump,” where you can scribble down anything else that’s on your mind.

9. Do your most dreaded project first.

Getting your most dreaded task over with first means you’ll have the rest of the day free for anything and everything else. This also means that you won’t be constantly putting off the worst of your projects, making it even harder to start on it later.

10. Follow the “Two-Minute Rule.”

The “Two-Minute Rule” was made famous by David Allen. It’s simple – if a new task comes in and it can be done in two minutes or less, do it right then. Putting it off just adds to your to-do list and will make the task seem more monumental later.

11. Have a place devoted to work.

If you work in an office, it’s no problem to say that your cubicle desk is where you work every day.

But if you work from home, make sure you have a certain area specifically for work. You don’t want files spread out all over the dinner table, and you don’t want to feel like you’re not working just because you’re relaxing on the couch.

Agatha Christie never wrote at her desk, she wrote wherever she could sit down. Ernest Hemingway wrote standing up. Thomas Wolfe, at 6’6″ tall, used the top of his refrigerator as a desk. Richard Wright wrote on a park bench, rain or shine.

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Have a space where, when you go there, you know you’re going to work. Maybe it’s a cafe downstairs, the library, or a meeting room. Whenever and wherever works for you, do your works there.

12. Find your golden hour.

You don’t have to stick to a “typical” 9–5 schedule!

Novelist Anne Rice slept during the day and wrote at night to avoid distractions. Writer Jerzy Kosinski slept eight hours a day, but never all at once. He’d wake in the morning, work, sleep four hours in the afternoon, then work more that evening.

Your golden hour is the time when you’re at your peak. You’re alert, ready to be productive, and intent on crossing things off your to-do list.

Once you find your best time, protect it with all your might. Make sure you’re always free to do your best uninterrupted work at this time.

13. Pretend you’re on an airplane.

It might not be possible to lock everyone out of your office to get some peace and quiet, but you can eliminate some distractions.

By pretending you’re on an airplane, you can act like your internet access is limited, you’re not able to get something from your bookcase, and you can’t make countless phone calls.

Eliminating these distractions will help you focus on your most important tasks and get them done without interruption.

14. Never stop.

Writers Anthony Trollope and Henry James started writing their next books as soon as they finished their current work in progress.

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Stephen King writes every day of the year, and holds himself accountable for 2,000 words a day! Mark Twain wrote every day, and then read his day’s work aloud to his family to get their feedback.

There’s something to be said about working nonstop, and putting out continuous work instead of taking a break. It’s just a momentum that will push you go further./

15. Be in tune with your body.

Your mind and body will get tired of a task after ninety minutes to two hours focused on it. Keep this in mind as you assign projects to yourself throughout the day, and take breaks to ensure that you won’t get burned out.

16. Try different methods.

Vladimir Nabokov wrote the first drafts of his novels on index cards. This made it easy to rearrange sentences, paragraphs, and chapters by shuffling the cards around.

It does sound easier, and more fun, than copying and pasting in Word! Once Nabokov liked the arrangement, his wife typed them into a single manuscript.

Same for you, don’t give up and think that it’s impossible for you to be productive when one method fails. Try different methods until you find what works perfectly for you.

Featured photo credit: Unsplash via unsplash.com

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