Glamor Economics

Chapter 33

Chapter 5 Section 5 How to Make Decisions with Public Information——Public Knowledge

The story takes place in a village. There are 100 couples in the village, and they are all true logicians.

But there are some peculiar customs in this village: Every night, the men of the village will light a bonfire and sit in a circle for a meeting, and the topic is to talk about their wives.At the beginning of the meeting, if a man has reason to believe that his wife will always be faithful to him, then he publicly praises her virtues in the meeting.On the other hand, if a man found evidence of his wife's infidelity at any time before the meeting, he would lament and wail at the meeting and ask the gods to punish her severely.Furthermore, if a wife had ever been unfaithful, she and her lover would immediately inform all married men in the village except her husband.Although this custom is very strange, everyone abides by it.

In fact, every wife has been unfaithful to her husband.Then every husband knew that the wives of all but his own wives were illegitimate, and every night at the meeting every man praised his wife.This situation continued for many years, until one day a missionary came.The missionary attended the bonfire meeting and heard every man praising his wife. He stood up and walked to the center of the sitting circle, reminding loudly, "At least one wife in this village has been unfaithful."

For the next 99 nights, the husbands continued to praise their wives, but on the 100th night, they all screamed and wailed, and begged the gods to punish their wives severely.

This is an interesting line of reasoning: Since every man in this village knows that 99 other women have been unfaithful to their husbands, when the missionary says "at least one wife has been unfaithful", it does not necessarily follow that this The unfaithful woman is his wife, because he knows 99 women who are unfaithful to their husbands.

So this kind of reasoning continued for 99 days. In the first 99 days, every husband couldn't really doubt his wife.And on the 100th day, if no one is crying, it shows that all women are loyal to their husbands, which is obviously contrary to the fact that "at least one wife is unfaithful".Therefore, each man can deduce with certainty that his wife has cheated, and the overall inference result is: all 100 wives have cheated.

It should be said that the preacher's announcement of the fact that "at least one of his wives has been unfaithful" does not seem to increase the knowledge of these men's infidelity to the women of the village, which they all knew.But why are they all heartbroken after 100 days?The root also lies in the role of "public knowledge".

The announcement of the missionaries changed the knowledge structure of the men in the village. Originally, "at least one wife was unfaithful" was knowledge for every man, but it was not public knowledge. However, the announcement of the missionaries made this fact public. Knowledge.

From public knowledge, we can derive the "dirty face game" model:
The faces of the three students are all dirty, but none of them can see their own faces.The teacher said to them: "At least one of you has a dirty face, please raise your hand." The three students looked at each other and no one raised their hands, and then they all raised their hands to show that their faces were dirty. of.why is that?
We can restore their judgment process:

1. After the three students looked at each other, they all saw that the faces of the other two were dirty, satisfying the judgment of "at least one dirty face", so no one raised their hands.

2. None of the three students raised their hands, which means that everyone saw at least one dirty face in their eyes.The more important inference is that at least two of the three people have dirty faces.It's simple, if there's only one dirty face, someone must have raised their hand at the first step.Since all three students are equally intelligent, they all draw the same inference.This critical inference is the public knowledge generated among the three people.

3. Since "at least two dirty faces", from anyone's point of view, he has seen two dirty faces, he still can not raise his hand.

4. The three people still do not raise their hands, which means that all three people see two dirty faces, that is, all of them are dirty faces.So everyone raised their hands.

In our lives, public knowledge is very common, and having more public knowledge around us is very helpful for our choices and decisions in work and life.

[links to related words]

Public information is also called public knowledge, a concept originally proposed by logician Lewis.Simply put, the so-called public information means that not only everyone in a group knows this fact, but everyone knows that other people in the group know this fact, and everyone else knows that everyone else knows this fact.

In the case of public information, everyone knows each other's situation and reality, so some strategies are needed to achieve the goal of winning decisions.

(End of this chapter)