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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
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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 July 21, 2021

The Importance of Reminders (And How to Make a Reminder Work)

The Importance of Reminders (And How to Make a Reminder Work)
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No matter how well you set up your todo list and calendar, you aren’t going to get things done unless you have a reliable way of reminding yourself to actually do them.

Anyone who’s spent an hour writing up the perfect grocery list only to realize at the store that they forgot to bring the list understands the importance of reminders.

Reminders of some sort or another are what turn a collection of paper goods or web services into what David Allen calls a “trusted system.”[1]

A lot of people resist getting better organized. No matter what kind of chaotic mess, their lives are on a day-to-day basis because they know themselves well enough to know that there’s after all that work they’ll probably forget to take their lists with them when it matters most.

Fortunately, there are ways to make sure we remember to check our lists — and to remember to do the things we need to do, whether they’re on a list or not.

In most cases, we need a lot of pushing at first, for example by making a reminder, but eventually we build up enough momentum that doing what needs doing becomes a habit — not an exception.

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From Creating Reminders to Building Habits

A habit is any act we engage in automatically without thinking about it.

For example, when you brush your teeth, you don’t have to think about every single step from start to finish; once you stagger up to the sink, habit takes over (and, really, habit got you to the sink in the first place) and you find yourself putting toothpaste on your toothbrush, putting the toothbrush in your mouth (and never your ear!), spitting, rinsing, and so on without any conscious effort at all.

This is a good thing because if you’re anything like me, you’re not even capable of conscious thought when you’re brushing your teeth.

The good news is you already have a whole set of productivity habits you’ve built up over the course of your life. The bad news is, a lot of them aren’t very good habits.

That quick game Frogger to “loosen you up” before you get working, that always ends up being 6 hours of Frogger –– that’s a habit. And as you know, habits like that can be hard to break — which is one of the reasons why habits are so important in the first place.

Once you’ve replaced an unproductive habit with a more productive one, the new habit will be just as hard to break as the old one was. Getting there, though, can be a chore!

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The old saw about anything you do for 21 days becoming a habit has been pretty much discredited, but there is a kernel of truth there — anything you do long enough becomes an ingrained behavior, a habit. Some people pick up habits quickly, others over a longer time span, but eventually, the behaviors become automatic.

Building productive habits, then, is a matter of repeating a desired behavior over a long enough period of time that you start doing it without thinking.

But how do you remember to do that? And what about the things that don’t need to be habits — the one-off events, like taking your paycheck stubs to your mortgage banker or making a particular phone call?

The trick to reminding yourself often enough for something to become a habit, or just that one time that you need to do something, is to interrupt yourself in some way in a way that triggers the desired behavior.

The Wonderful Thing About Triggers — Reminders

A trigger is anything that you put “in your way” to remind you to do something. The best triggers are related in some way to the behavior you want to produce.

For instance, if you want to remember to take something to work that you wouldn’t normally take, you might place it in front of the door so you have to pick it up to get out of your house.

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But anything that catches your attention and reminds you to do something can be a trigger. An alarm clock or kitchen timer is a perfect example — when the bell rings, you know to wake up or take the quiche out of the oven. (Hopefully you remember which trigger goes with which behavior!)

If you want to instill a habit, the thing to do is to place a trigger in your path to remind you to do whatever it is you’re trying to make into a habit — and keep it there until you realize that you’ve already done the thing it’s supposed to remind you of.

For instance, a post-it saying “count your calories” placed on the refrigerator door (or maybe on your favorite sugary snack itself)  can help you remember that you’re supposed to be cutting back — until one day you realize that you don’t need to be reminded anymore.

These triggers all require a lot of forethought, though — you have to remember that you need to remember something in the first place.

For a lot of tasks, the best reminder is one that’s completely automated — you set it up and then forget about it, trusting the trigger to pop up when you need it.

How to Make a Reminder Works for You

Computers and ubiquity of mobile Internet-connected devices make it possible to set up automatic triggers for just about anything.

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Desktop software like Outlook will pop up reminders on your desktop screen, and most online services go an extra step and send reminders via email or SMS text message — just the thing to keep you on track. Sandy, for example, just does automatic reminders.

Automated reminders can help you build habits — but it can also help you remember things that are too important to be trusted even to habit. Diabetics who need to take their insulin, HIV patients whose medication must be taken at an exact time in a precise order, phone calls that have to be made exactly on time, and other crucial events require triggers even when the habit is already in place.

My advice is to set reminders for just about everything — have them sent to your mobile phone in some way (either through a built-in calendar or an online service that sends updates) so you never have to think about it — and never have to worry about forgetting.

Your weekly review is a good time to enter new reminders for the coming weeks or months. I simply don’t want to think about what I’m supposed to be doing; I want to be reminded so I can think just about actually doing it.

I tend to use my calendar for reminders, mostly, though I do like Sandy quite a bit.

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Featured photo credit: Unsplash via unsplash.com

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Reference

[1] Getting Things Done: Trusted System

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