Xia Zhihong: Are the university rankings people are pursuing reliable?

Recently, the ranking of Chinese colleges and universities in a certain world colleges and universities has set a new high, arousing heated discussion among netizens, and many people believe that this marks the progress of higher education in China

In fact, controversies about university rankings are not uncommon, and there are several hot search lists every year.

Xia Zhihong, Pancoe Chair Professor, Northwestern University, USA

Every year at the end of February and beginning of March, a variety of university rankings are released

Today, let’s take a look at what the rankings are all about

Let me give you an example

The so-called turnip greens, each has its own love

Each has its own reason

Of course, the rankings are also consistent

　　Ha, you can see that the ranking is either simple or obvious, or it is controversial and sometimes even absurd

　　You said that everyone knows such a simple truth

　　theorem? Don't worry, let me explain it slowly

　　First of all, what is social choice? It's very simple.

　　Well, this is very simple, it seems that the field of social choice is quite broad

　　So what is the theorem? Theorems are the conclusions that have been rigorously demonstrated in mathematics.

　　Theorem is not the same as the truth, and the truth changes with the leader

　　Wow, the theorem is so powerful, let's go to the whole theorem someday! Okay, very welcome.

　　So what is Arrow's theorem? In fact, Arrow’s theorem is very simple to say (February 21, 2018 is the first anniversary of Arrow’s death.
As I said, his coffin board may not be able to hold down): Social groups often need to make certain choices, but each Individuals have their own preferences, and they are used to arranging candidates (or things) in 1, 2, 3,.
.
.
, order
.
Of course, we hope that through a certain method, such as various voting, we can get the preferences of the group and get an overall order
.
Regrettably, Arrow said that when there are more than three candidates, there is no reasonable and non-contradictory ranking method
.

　　Does not exist, does not exist, does not exist! Say the important thing three times
.

　　Teacher Xia, for example, the curious student still looks confused
.

　　no problem! The first thing that comes to mind for food is to eat
.
Twelve students decided which restaurant to eat
.
There are three different options near the school: A (hot pot), B (Beijing cuisine) and C (Sichuan cuisine)
.
Everyone has their own preferences.
For example, Xiao Li thinks A is better than C, C is better than B, and so on.
We simply remember Xiao Li's choice as A>C>B
.
Putting everyone's thoughts together is this:

3 people: A> B> C

2 people: A> C> B

3 people: B> C> A

4 people: C> B> A

　　There was disagreement, and everyone was arguing
.
No way, vote
.
A got 5 votes, B got 3 votes, and C got 4 votes
.
Everyone went to eat hot pot
.
But I don’t know if you have noticed that 7 of the 12 students hate hot pot.
Of course, the result is very unhappy
.

　　We might as well look back at this decision-making process
.
If you change the voting method, such as deciding which restaurant to exclude first, then the one with the most negative votes is also A, and the hot pot is directly brushed (not cooked)
.

　　What's even weirder is that B (Beijing cuisine restaurant) is actually closed on the day of vacation.
If the students knew in advance, they would vote between A and C.
As a result, C would get 7 votes and A would get 5 votes
.
Everyone go to the Sichuan restaurant
.

　　It's over, you must be completely confused
.
The restaurant B cannot open, which determines whether everyone will go to restaurant A or restaurant C for dinner? If B is opened, we went to A, if B is closed, we'll go C
.

　　Ah? There seems to be something wrong.
The choice between A and C has nothing to do with B.
Let me think about it again.
.
.

　　You may have guessed again that the voting we conducted, which is our most commonly used decision-making method, is problematic
.

　　Congratulations, you can study economics
.
Let's study it together.
What better way to vote?

　　Ten years later, in the gloomy basement, you.
.
.
Forget it, it was all tears
.

　　In fact, big cows have been studying this problem for hundreds of years
.
I can tell you a series of sad stories
.
For example, you can Google the mathematics professor at Oxford University and the author of "Alice in Wonderland" Charles Lutwidge Dodgson (Charles Lutwidge Dodgson), under the pseudonym Lewis Carroll (Lewis Carroll).
), to see what kind of strange man he is
.

　　Spoiler alert: This person has a lot of research on voting theory, and has a relationship with Alice, the daughter of the dean of the academy
.
Check it out for yourself .

　　interesting……

　　Okay, let's provide another one for free.
Go to Google and check out Nicolas de Condorcet, a French academician during the French Revolution
.

　　Spoiler alert: The ending is bleak, still an unsolved case.
His empty coffin is now buried in the Halloween Temple in Paris, France
.
The body is lost, lost!

　　Okay, it's time for our protagonist Arrow to appear
.
Arrow was born in New York in 1921, a young man is a socialist, 19-year-old Columbia University graduate, 20-year-old graduate master's degree, PhD 21 years old .
.
.
.
.
.
No, just get the 30-year-old doctor
.
After ten years of sharpening the sword, the Nobel Prize doctoral dissertation was born
.
Arrow said in his doctoral dissertation that you should not go foolishly to find the perfect ranking and election method.
This simply does not exist!

　　Wait a minute, this is not quite right, with one exception
.
There is indeed an election method that is mathematically simple, crude, and perfect, without inherent contradictions, and admired by many people, that is-dictatorship
.

　　Let's give an example
.
If Teacher Zhang and his classmates go to dinner together, the teacher's wishes are C (Sichuan cuisine)> A (hot pot)> B (Beijing cuisine)
.
The classmates respect the teacher (but they are wronged), and it is hard to say anything
.
As a result, I went straight to the Sichuan restaurant, which was much less troublesome
.
This is dictatorship, that is, one person has the final say
.
This is the only way to make decisions that is not self-contradictory, Arrow said
.

　　Arrow is a big cow and has trained 12 Ph.
Ds in total, 5 of which also won the Nobel Prize, and a few others seem to deserve it
.
Look at this family, the Nobel Prize professional
.
Classmates line up to worship.
.
.

　　I was lucky enough to have dinner with Michael Spence, a student of Arrow, in 1988, before Spence won the Nobel Prize
.
His doctoral thesis is a classic of economics
.
Because I am from China, he said that his wife Ann is half of Chinese descent and is a descendant of diplomats (thanks to Mr.
Zhu Anyuan for checking, Ann’s mother’s grandfather is Liang Qichao)
.
In the late 1980s, his daughter studied abroad at Fudan University, relying on her relationship to let her live in a normal student dormitory instead of an international student dormitory
.

　　Dinner with Eric Maskin, another student of Arrow, was after Maskin won the Nobel Prize
.
Maskin talked about his very interesting academic research
.
He found that the greater the campaign pressure of US officials, the worse their decision-making ability
.
Regarding election theory, Maskin has his unique insights
.
He believes that the election should be duel, if there is a Condorcet (yes, it is the French) cycle, that is, there are situations such as A>B, B>C, C>A, and then consider using other methods to decide the victory
.

　　Closer to home
.
Since voting is so unreliable, and Arrow knew about it more than sixty years ago, why do we still enjoy it?

　　Sometimes there is no way, just talk about elections
.
We have to choose someone to lead us
.
Even Trump has elected the president.
Look at the election in the United States.
.
.
The constitution says that everyone is equal, and the one that says it has one person, one vote, but the one who gets fewer votes becomes the president.
.
.

　　Not to mention, it's all tears again.
.
.

　　Another example is the first "general election" in Taiwan in 2000
.
At that time there were three candidates: Chen Shuibian, James Soong and Lien Chan
.
The votes are as follows: Chen Shui-bian 39.
3%, James Soong 36.
8%, and Lien Chan 23.
1%
.
In fact, if there are two duels, James Soong and Lien Chan can win against Chen Shui-bian
.
But because Taiwan directly used the American election method, the one with the most votes wins in one vote, and Chen Shui-bian, who should be the least elected, wins
.

　　We know that the US election method is very bad
.
You might say, why not change to the general election method in Europe (such as France) (if no one has more than half of the votes, then vote after the candidates with low votes are eliminated)? In fact, it will be just as bad
.
There is a set of theories in economics: If the election method in the United States is changed to French, it may be better at first, but it will get worse after a while
.
People will always find ways to use the system.
.
.

　　It should be noted that Arrow's theorem only applies to ranking and ranking-related voting, but not to scoring voting
.
For example, a common election method is to give each candidate a score of 0-10, and then add up the total scores to get the total score of each candidate, and then sort by the total score
.
If there is no fixed total score limit for each voter during the scoring process, this election method can avoid some inherent contradictions (for example, as we mentioned before, the existence of B will affect the choice between A and C), But this method also has serious problems
.
First, it violates the principle of equality for all.
Second, it is easy to be exploited by dishonest people, such as deliberately lowering the score of competitors (strategic voting)
.
Economists have done a lot of research in this area
.

　　In short, there is no voting method that can be applied in any situation
.
Of course, if everyone has a large degree of consensus, our commonly used methods still have a certain degree of credibility
.

　　It's time for us to talk about university rankings
.
Ranking is also a kind of voting, which is more complicated, subjective, and easier to manipulate
.
Under normal circumstances, not only are people voting in the rankings, but also various other indicators, such as published articles, funding, quality of teachers, quality of students, majors, key laboratories, and so on
.
Each indicator can also be regarded as a voter, and they can be used to rank or score schools
.
Most of the popular rankings now use school reputations, which are scored or ranked by experts
.
These indicators are weighted and combined to get the so-called ranking
.
It is worth noting that the various indicators are actually not comparable, and there is too much room for operation on how to weight them
.

　　Give a simple example:

　　The score of the romantic partner = height x 0.
12 + wealth x 0.
18 + skin whiteness x 0.
213 -|weight-100|x 0.
32 -age x 0.
2.
.
.

　　Students who study physics may be crying, how can things of different dimensions add up randomly? Yes, that's how the ranking comes
.

　　By changing various algorithms, basically, whoever I want to score high will score high
.
Therefore, Zhang San’s school will definitely rank very high according to Zhang San’s ranking, and Li Si’s sponsorship will also increase the ranking of Li Si’s school
.

　　To put it bluntly, the effect of ranking is like this: God has given us a colorful multidimensional world, with fat, thin, thin, graceful and graceful, but we abruptly want to turn her into a black and white line, which is convenient for size comparison
.

　　Those who have good things get together, rank the university, and earn some money from simple-minded people.
It doesn't hurt
.
A good ranking can sometimes be used as a reference, after all, it reflects a certain aspect of the index
.
But what is really useful should be the data collected behind the rankings
.
These data, if credible, provide a better three-dimensional portrait of each school
.

　　The problem is that rankings have been abused for a long time, and seriously abused
.
The ranking ranks schools and ranks students
.
If you fail to enter the so-called "first-rate" school, it seems that the whole person is not good
.
Students no longer pursue individuality, schools no longer pursue characteristics, and society develops towards mediocrity
.

　　We should spend more time to understand the characteristics of each university
.
What a university needs is good teachers and friends to stimulate your interest and perfect your life.
Can you see these in the rankings? The commonly used indicators for ranking are how many teachers, how many majors, how many key laboratories, and so on.
How much does this have to do with you? What you want is a teacher who suits your major, suits your laboratory, and stimulates your interest
.

　　Not all students are suitable for research
.
If your interest is excavators, Lanxiang Technical School is of course much stronger than Tsinghua University
.

　　Only with characteristics can there be originality, and only with originality can the country be strong
.

　　The good news is that Chinese universities are developing in a diverse and distinctive direction
.
The establishment of the private West Lake University and the rapid development of the high-start Southern University of Science and Technology have brought vigorous vitality to our education
.

　　Well, let's make an agreement.
Next time someone uses rankings to fool you, you will ask him how radishes compare with vegetables? Or a foreign one: Apples and Oranges.