Glamor Economics

Chapter 77

Chapter 11 Section 4 Everyone is rational, but the result is disaster—the fallacy of rational synthesis

The swan, barracuda and prawns pulled a cart together to carry the goods. They put on the rope at the same time, "exerting so hard that the veins on their bodies were exposed", but the cart still didn't move half a step.Their strength is more than enough to pull such a small cart, but why can't they pull it?The reason is that the swan is desperately flying upwards, the prawn is desperately crawling forward, and the barracuda is determined to jump into the water... The result can be imagined.

In this story, of course the swan has to fly to the sky, the barracuda has to swim in the water, and the shrimp has to crawl forward. Those seemingly reasonable actions have caused the car to not move half a step, which involves an economic concept - The fallacy of rational composition.Regarding the concept of "fallacy of rational composition", we can also read the following short story.

There is a football field in the suburbs of a certain city. Once an important match was held in the football field, and everyone wanted to watch it.There are several roads to the football field, one of which is the closest.Wang Bo chose to take the shortest road, but found that other people also chose to take this road, so the road was very congested, so the time spent on the road was much longer than he expected.After finally arriving at the football field, the wonderful game was eye-opening, but unfortunately someone stood up in the front row, which affected his viewing effect. Wang Bo also chose to stand up, so that he could see clearly, but it caused him to stand up in the back row. People also choose to stand up and watch.The end result is that everyone is standing and watching the game.

Wang Bo is undoubtedly a rational economic man, but when everyone is a rational economic man, the fallacy of rational composition will continue to appear.In the same way, if everyone is a rational economic person, the choices or decisions made from an individual point of view are undoubtedly rational, but when everyone makes the same choice or decision based on the same considerations, rationality will occur. fallacy of composition.The choices made by the swan, barracuda, and shrimp in the fable are undoubtedly rational, but their respective rational choices do not "pull the cart", which is the fallacy of rational composition.

The prisoner's dilemma story is a typical fallacy of rational composition. In 1950, Tooke, a mathematician who served as a visiting professor at Stanford University, used the stories of two criminal suspects to construct a game model, that is, the prisoner's dilemma model, in order to illustrate the game process more vividly.

During the investigation of a theft and homicide case, the police arrested two suspects.However, they categorically denied that they had ever killed anyone, arguing that they discovered that the rich man had been killed first, and then just stole something by hand.The police lack enough evidence to prove the crimes they committed, and if at least one of the prisoners confesses to the crime, they can be convicted of the crime.

So the police isolated the two to prevent them from colluding with confessions or forming offensive and defensive alliances, and explained to them their situation and the choices they faced: if one of them pleaded guilty, the confessor would be released immediately and the other would be released. Sentenced to 8 years in prison; if both plead guilty, they will be sentenced to 5 years in prison each; 1 year imprisonment.

So, how will the two prisoners choose?

Which strategy should the prisoner choose to minimize his own personal sentence?Two prisoners are kept incommunicado and do not know the other's choice; even if they can talk, they may not be able to trust that the other will not talk back.

Then any rational prisoner in the dilemma will make such a choice:

If the other party chooses to deny it and you choose to betray, you will be released, so you will choose to betray.

If the other party chooses to betray, he must betray himself in order to get a lower sentence, so he still chooses to betray.

The two are facing the same situation, so their rational thinking will come to the same conclusion - choose to betray.Betrayal is the dominant strategy of the two strategies.Therefore, the only possible Nash equilibrium in this game is one in which both prisoners defect to each other, and they both serve the same five years.

This is the classic prisoner's dilemma in game theory, which can be represented by the following table.

Prisoner's Dilemma
Prisoner B

Prisoner A confesses
Confession -5, -5-8, 0
Deny 0, -8-1, -1
The Prisoner's Dilemma is a representative example of non-zero-sum games in game theory, reflecting that the individual's best choice is not the group's best choice.Although the predicament itself is only a model, similar situations frequently occur in reality in terms of price competition and environmental protection.

The Prisoner's Dilemma assumes that each player is self-interested, that is, they all seek to maximize their own interests and do not care about the interests of the other player.If the benefits of a strategy for a player are lower than other strategies in any case, this strategy is called "strict disadvantage", and rational players will never choose it.In addition, there is no other force intervening in individual decision-making, and participants can choose strategies completely according to their own wishes.

In terms of overall interests, if two participants cooperate and remain silent, both will be sentenced to 1 year in prison.However, according to the above assumptions, both of them are rational persons, and they only pursue personal interests.The equilibrium situation will be that both prisoners choose to defect, and the result is that the sentence for both of them is higher than that of cooperation, and the overall benefit is lower than that of cooperation.This is where the dilemma lies.

This dilemma reflects the contradiction between individual rationality and collective rationality.It is a rational choice for everyone and can get the best result, but it is irrational for the whole group, and finally leads to a result that is unfavorable to everyone in the group.In order to avoid the fallacy of rational composition, any collective should strengthen internal coordination.Not only should each individual act as a rational economic man, but the collective should also become a rational economic man. Only in this way can the interests of the collective and its internal members be maximized.

[links to related words]

Fallacy of Composition An erroneous reasoning that argues that if every part of a whole has a certain property, then the whole also has that property.For example, "If every part of this car is of good quality, then the car is of good quality."

Fallacy of Decomposition Contrary to the Fallacy of Composition, it argues that if the whole or set has a certain property, then each of its parts or elements also has that property.For example, "America is rich, so every American citizen is rich." It fails to recognize that there is no such conversion between the whole and the parts.

(End of this chapter)