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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 March 25, 2020

How Do You Change a Habit (According to Psychology)

How Do You Change a Habit (According to Psychology)

Habits are hard to kill, and rightly so. They are a part and parcel of your personality traits and mold your character.

However, habits are not always something over-the-top and quirky enough to get noticed. Think of subtle habits like tapping fingers when you are nervous and humming songs while you drive. These are nothing but ingrained habits that you may not realize easily.

Just take a few minutes and think of something specific that you do all the time. You will notice how it has become a habit for you without any explicit realization. Everything you do on a daily basis starting with your morning routine, lunch preferences to exercise routines are all habits.

Habits mostly form from life experiences and certain observed behaviors, not all of them are healthy. Habitual smoking can be dangerous to your health. Similarly, a habit could also make you lose out on enjoying something to its best – like how some people just cannot stop swaying their bodies when delivering a speech.

Thus, there could be a few habits that you would want to change about yourself. But changing habits is not as easy as it seems.

In this article, you will learn why it isn’t easy to build new habits, and how to change habits.

What Makes It Hard To Change A Habit?

To want to change a particular habit means to change something very fundamental about your behavior.[1] Hence, it’s necessary to understand how habits actually form and why they are so difficult to actually get out of.

The Biology

Habits form in a place what we call the subconscious mind in our brain.[2]

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Our brains have two modes of operation. The first one is an automatic pilot kind of system that is fast and works on reflexes often. It is what we call the subconscious part. This is the part that is associated with everything that comes naturally to you.

The second mode is the conscious mode where every action and decision is well thought out and follows a controlled way of thinking.

A fine example to distinguish both would be to consider yourself learning to drive or play an instrument. For the first time you try learning, you think before every movement you make. But once you have got the hang of it, you might drive without applying much thought into it.

Both systems work together in our brains at all times. When a habit is formed, it moves from the conscious part to the subconscious making it difficult to control.

So, the key idea in deconstructing a habit is to go from the subconscious to the conscious.

Another thing you have to understand about habits is that they can be conscious or hidden.

Conscious habits are those that require active input from your side. For instance, if you stop setting your alarm in the morning, you will stop waking up at the same time.

Hidden habits, on the other hand, are habits that we do without realizing. These make up the majority of our habits and we wouldn’t even know them until someone pointed them out. So the first difficulty in breaking these habits is to actually identify them. As they are internalized, they need a lot of attention to detail for self-identification. That’s not all.

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Habits can be physical, social, and mental, energy-based and even be particular to productivity. Understanding them is necessary to know why they are difficult to break and what can be done about them.

The Psychology

Habits get engraved into our memories depending on the way we think, feel and act over a particular period of time. The procedural part of memory deals with habit formation and studies have observed that various types of conditioning of behavior could affect your habit formations.

Classical conditioning or pavlovian conditioning is when you start associating a memory with reality.[3] A dog that associates ringing bell to food will start salivating. The same external stimuli such as the sound of church bells can make a person want to pray.

Operant conditioning is when experience and the feelings associated with it form a habit.[4] By encouraging or discouraging an act, individuals could either make it a habit or stop doing it.

Observational learning is another way habits could take form. A child may start walking the same way their parent does.

What Can You Do To Change a Habit?

Sure, habits are hard to control but it is not impossible. With a few tips and hard-driven dedication, you can surely get over your nasty habits.

Here are some ways that make use of psychological findings to help you:

1. Identify Your Habits

As mentioned earlier, habits can be quite subtle and hidden from your view. You have to bring your subconscious habits to an aware state of mind. You could do it by self-observation or by asking your friends or family to point out the habit for your sake.

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2. Find out the Impact of Your Habit

Every habit produces an effect – either physical or mental. Find out what exactly it is doing to you. Does it help you relieve stress or does it give you some pain relief?

It could be anything simple. Sometimes biting your nails could be calming your nerves. Understanding the effect of a habit is necessary to control it.

3. Apply Logic

You don’t need to be force-fed with wisdom and advice to know what an unhealthy habit could do to you.

Late-night binge-watching just before an important presentation is not going to help you. Take a moment and apply your own wisdom and logic to control your seemingly nastily habits.

4. Choose an Alternative

As I said, every habit induces some feeling. So, it could be quite difficult to get over it unless you find something else that can replace it. It can be a simple non-harming new habit that you can cultivate to get over a bad habit.

Say you have the habit of banging your head hard when you are angry. That’s going to be bad for you. Instead, the next time you are angry, just take a deep breath and count to 10. Or maybe start imagining yourself on a luxury yacht. Just think of something that will work for you.

5. Remove Triggers

Get rid of items and situations that can trigger your bad habit.

Stay away from smoke breaks if you are trying to quit it. Remove all those candy bars from the fridge if you want to control your sweet cravings.

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6. Visualize Change

Our brains can be trained to forget a habit if we start visualizing the change. Serious visualization is retained and helps as a motivator in breaking the habit loop.

For instance, to replace your habit of waking up late, visualize yourself waking up early and enjoying the early morning jog every day. By continuing this, you would naturally feel better to wake up early and do your new hobby.

7. Avoid Negative Talks and Thinking

Just as how our brain is trained to accept a change in habit, continuous negative talk and thinking could hamper your efforts put into breaking a habit.

Believe you can get out of it and assert yourself the same.

Final Thoughts

Changing habits isn’t easy, so do not expect an overnight change!

Habits took a long time to form. It could take a while to completely break out of it. You will have to accept that sometimes you may falter in your efforts. Don’t let negativity seep in when it seems hard. Keep going at it slowly and steadily.

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Featured photo credit: Mel via unsplash.com

Reference

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