This is the 9th day of my participation in Gwen Challenge

Author: Cola

Source: Coke’s path to data analysis

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Hello, I’m Coke

Many people suffer from fear of choice, and I am no exception. However, many choices in life can be solved by math. Today we will talk about how to cure your fear of choice.

1. Ask questions

1.1 The problem of wheat ears

Legend has it that three disciples of Ancient Greek philosopher Socrates asked their teacher how to find the ideal mate. So Socrates led his disciples to a wheat field, let them each pick a largest wheat in the wheat field, can not go back, and only pick one.

The first disciple just walked a few steps and couldn’t wait to pick what he thought was the biggest ear of wheat, only to find that there were many ears of wheat behind.

The second one looked left and right until he found that the largest head of grain had already been missed.

The third man divided the wheat field into three parts. When he walked through the first third, he only looked and did not pick. He divided the ears into three types: large, medium and small ears.

1.2 Secretary Problems

N people came to interview for the vacancy of a secretary. Each time one person is interviewed, the decision whether to hire him or not is made immediately after the interview. If the decision is not made then, he will not come back. What strategy is used to select the most suitable person to be secretary?

Similarly, there’s the dating question: How many dates before you make a decision? Renting: How many houses do you need to see before you make up your mind to rent? To solve this kind of problem, the optimal stop theory is used, that is, how to choose the time to stop watching?

2. Problem solving

2.1 The classic 37% rule

The 37% rule is a strategy: take the secretarial question as an example. Observe the top 1/ E candidates and get a sense of their ability level after each interview. Then choose the first person you meet who is better than all the previous candidates.

1/e is about 37 percent, and that’s where the 37 percent rule comes in.

Why 37 percent?

Because it has become a probability problem, suppose there are N, r individuals before the interview, we remember that one of the most outstanding people as k, then starting from the individual r + 1, as long as more than k, the choice, so we are asking is to be able to maximize the probability of success to select the best candidates can be approximate to:

Let x=r/N, then the above formula can be written as:

p=-xln(x)

The derivative of it can solve the optimal value of x, that is, P gets the maximum value when r/N is equal to 1/e, and 1/e is about 0.368, that is, the first 36.8% of the people can be regarded as a standard, and the first 63.2% of the people who meet the standard can be employed.

That is to say, if you want to interview 100 people, the first 37 people, just have a look, wait and see stage silently remember the best, from the 38th person, if he is better than the best in front of him, you can make up your mind to hire him.

According to this method, to daily life in the choice of difficulties in the phobia of small partners to improve the good theoretical guidance, how do you think?

2.2 Full information game

The 37% rule obtained by the secretary question is a very ideal situation, and based on “no information”, except for the comparison of the interviewees, they know nothing about other information, so it is also a no-information game problem.

However, in real life, especially when buying a house, renting a house and dating, people want to know all the information before making a decision, so it also belongs to the all-information game.

Taking renting as an example, we can master all the information of candidates, such as house type, layout, location, real quotation, etc., without leaving a wait-and-see stage like 37% rule, we can directly determine the threshold of renting price through known information, and make a decision when there is a house higher than the threshold value.

In fact, one of the problems everyone has when renting a house is that if I don’t sublet the house I’m renting before my rent is due next month, I’ll have to pay an extra month’s rent, which means there is a cost in waiting time.

Most likely, it will be sold at a reduced price before the deadline. The most scientific approach, however, is not to compromise and look back once the optimal stop price has been determined.

The problem of optimal stopping theory is explained in detail in the first chapter of the book Beauty of Algorithms. If you are interested, you can take a look at it. I also wrote the reading notes of this book before:How to use the algorithm change life | beauty, the map is as follows. There is compression in the uploaded picture. If you need a large hd picture, please add data_cola on wechat