Welcome to the site of Ranking

I decided to write a non-fiction book with the title and subtitle RANKING – The reality, illusion and manipulation of objectivity.  The book discusses the Hows and Whys of our love and fear of making ranks and being ranked through many real life examples to be viewed from three different angles (reality, illusion and manipulation) of objectivity. Ranking converts scientific theories to everyday’s experience by raising and answering such question as:

  • Are college ranking lists objective?
  • How to rank and rate states based on their fragility, corruption or even happiness?
  • How to find the most relevant web pages?
  • How to rank employees?

Life and society is really complex, consequently our message is not so simple such as ”Ranking is good!” or ”Ranking is bad!”. Since we permanently rank ourselves and others and are also being ranked, the message is twofold: how to prepare the possible most objective ranking and how to accept that ranking does  not necessarily reflects our real values and achievements. The reader will understand our difficulties to navigate between objective and subjective and gets help to identify and modify her place in real and virtual communities by combining our human intelligence with computational techniques.


Against the myth: I Bounded rationality

While probably not even the most dogmatic mainstream economist believed that ”hyperrational” utility maximizing agent is a plausible model for describing human behavior, and the rational choice theory was attacked from different angles, still a new more realistic paradigm is gradually being emerged. Herbert Simon, who worked far from the mainstream, somewhat unexpectedly got the Nobel prize in economics in 1978, for introducing and propagating the concept of bounded rationality. A satisfactory, even not optimal solution is good. He coined the term satisficing by combining the words satisfy and suffice. We have to accept that our ability of making decisions is limited by a number of constraints, such as the complexity of a problem, limits on resources (most importantly, time and money), limited available information, our limited cognitive skills, values, influence by our feelings etc. As I learned in the soccer field in my childhood, ”there is no better position than a good one”.

There is a nice mathematical problem, officially called as the ”optimal stopping problem”. It helps to to answer when to stop dating and choose a long-term mate. The problem is analogue if an employer is trying to find a suitable new office manager from a range of applicants, so it is also known as the secretary problem. Let’s assume that you have a number of possible mates. I don’t want to tell this number, but if your name is not Don Giovanni, is much less than thousand and three (”Ma in Spagna son gia mille e tre”). As opposed to Don Giovanni, you suppose to have one relationship in one time. You should decide whether or not He’s The One, She’s The One. Much more often than not, you can’t go back to one of the people that you have rejected earlier. You might make two types of mistakes. You may bring a decision to settle down early, and and you will think in the future that maybe you missed the chance to meet the real queen of your life. Alternatively, it may happen that you wait too long to commit, and all the good
ones might be gone. So, here is the big question: when to stop? Math gives an answer for the magic number: 37%.51 The recipe You have the highest chance of finding Mrs. or Mr. Right, you should date and reject the first 37 percent of your potential mates. The rules has a second part. Pick the next person who is better than anyone you have ever dated earlier. (Yes, the algorithm does not guarantee for sure that you will not reject a wonderful option, so you need balance balances the risk of stopping too soon against the risk of stopping too late. Returning from romantic relationships to social science: with the words of the political scientist Bryan D Jones:

As Herbert Simon . . . notes, homo politicus is not irrational. He seems to behave
purposefully, adopting strategies that are relevant to general goals, given the limits
of cognitive capacity and the complexity of the political world. But these facets to
try to make it impossible to maximize and often inappropriate maximize. Homo
politicus seems to Simon to operate according to the model of bounded rationality,
that is, adopting means that are relevant to goals within environmental and cognitive processing limits.


How do people choose? The myth of rationality

We like to believe that we are rational, and what is called as the neoclassical theory of economics is based on the assumptions, that humans have fixed preferences, and these preferences are called transitive. Fixed preferences mean if you prefer key lime pie to caramel fudge cheesecake on Monday, you will do it on Tuesday too. (This book is not about healthy diet desserts). Transitivity means, for example, if you decide about the dessert to complete your dinner in a fine-dining restaurant, if you prefer key lime pie to caramel fudge cheesecake, and these cheesecake to chocolate mousse, than you will prefer this pie to the chocolate mousse, too. So, the choice of a dessert is a rational activity, but in a restricted sense of the world. We would not tell somebody that she is crazy by still choosing chocolate mousse to key lime pie.

Neoclassical economic theories are based on the concept that we are rational in a sense
that during decision making humans are maximizing our expected gain (say, pleasure or profit) expressed by the utility function. However, if we want to make a quantitative analysis, say to maximize the utility function for the dessert selection, we should be able to assign numerical values to our desire to consume pie, cheesecake or mousse. The rational choice theory47 madepossible to represent and solve problems of choice in a formal manner, and was the basis of many results in decision theory, game theory, and microeconomics. Rational choice theory is based on absurdly simple assumptions, as that more is always better, and people have full information, an use this information rationally. In addition people are not affected by their emotion, as fear or envy. So, more or less the model assumes that people are emotionless robots, who don’t make computational errors. In a famous publication (6325 citations in the Google Scholar today (June 7h, 2018)) the celebrated economist Milton Freedman48 argues that it is possible to offer useful prediction tools for economists even based on oversimplified assumptions.

How social decision emerge in the society of homo economicus? Before starting to give any answer, let’s clarify the differences between two types of theories. They are called descriptive and normative, respectively. The first attempts to answer the question ”How does the world work?”, while the second is interested in the problem of ”How the world should work?”. Responses for the second question arrived both from mathematics and moral philosophy, and I would like to believe that the best ones come from the combination of the two. In the world of the society of self-rational people Pareto optimality state corresponds to the allocation of resources from which it is impossible to improve any individual’s utility without making at least one individual worse
off. Welfare economics promised to find the state that creates the highest overall level of social satisfaction among its members. Technically, the problem is to give a complete and transitive ranking of all social alternatives.
As always in with ranking and rating problems, there are two possibilities. First, it is possible to give a an ordered list of preferences. Economists use the terminology of ordinal utility function for an individual to rank all possible ”states”. It tells that an individual prefers possible state X to possible state Y , but it is meaningless to ask how much better she prefers the first option. Second, a cardinal utility function assigns a number to characterize the attractivity of any state, so it it is possible to express the magnitudes of how much an individual prefers X to Y . Here is a recurring problem, how to assign numbers to qualities? In a very very reduced sense the state of the world is nothing else, but a set of products to buy. One way to put numbers on goods
utility is to ask what price people are willing to pay for a good. If you are ready to pay $27,000 for a Toyota Camry Hybrid, you can say that this product has a 27; 000 utils (the abstract unit of utility). But it is a very naive picture.

How to construct a cardinal social welfare function (SWF) from the utility functions of individuals? Identifying the utilities of individuals one might define SWF as their sum of the individual utilities. In this case the goal of maximizing the SFW means maximizing the individual incomes. Any thoughts about income distribution were totally neglected. A very skew distribution, where a small portion of people (”1%”) owns the majority of wealth may maximize the SWF defined this way. Others may prefer a ”social state” with more total income even if itis unevenly distributed. As a third, and influential option, one may define SWF based on the average of individual utilities.
John Rawls (1921—2002), a leading political and moral philosopher of the last century identified classical and average utilitarianism ”as the Principal Opponent: and suggested to define SWF based on the utility of worst-off individual. So, maximizing SWF would mean maximizing the income of the poorest person in society without taking into account the income of other individual.49
Amartya Sen, the legendary Indin economist, proposed a form of SWF, which penalizes
economic inequality50. Sen adopted the concept of Gini coefficient (G). G is zero in case of perfect equality, (assuming everyone has the same income), and coefficient of 1, in there is a maximal inequality (e.g., ideally where only one person has all the income and all others have none, the Gini coefficient will be one.) His SWF is defined as the average per capita income of a country, is multiplied with a number(1-G). A good normative theory could be applied to the real world, and we will return to an application to show the ranked lists of countries based on Sen’s SWF will in 6.3.1.

Under the spell of the objectivity

The notion of ”objective reality” refers to anything that exists as it is independent of any
conscious awareness, perception. ”Subjective reality” is related to anything depending upon some conscious awareness. Objectivity is associated with concepts such as reality, truth and reliability. Ranking of the tallest buildings in the world are easy, since it is based on verifiable facts, and we have a result what everybody will accept. (Well, we learn how to believe or not believe to secondary or ternary information sources. I have not measured the heights of the towers myself, but I am ready to accept that the actual source of information found on the web (44) is reliable:

1. Burj Khalifa, United Arab Emirates – 2,717 Feet
2. Shanghai Tower, China – 2,073 Feet
3. Makkah Royal Clock Tower, Saudi Arabia – 1,972 Feet
4. Ping An International Finance Centre, China – 1,965 Feet
5. Lotte World Tower, South Korea – 1,819 Feet
6. One World Trade Center, United States – 1,776 feet

Actually all the other web-pages show the same result.
The rank of most influential people of all time shown by the Ranker site shows:

1. Jesus Christ
2. Albert Einstein
3. Isaac Newton
4. Leonardo da Vinci
5. Aristotle
6. Muhammad

This list is far from being objective. What about Napoleon, Hitler, Stalin, Churchill, Darwin etc. ? The ranked list of tall buildings is objective, and it approaches well what we accept as ”truth”. We feel that trying to create an objective ranking has a higher value, than a subjective one. A person who argues based on a subjective viewpoint sees things only from their own perspective, loaded with all biases. Of course, subjective is not identical to random. When you read the list of the six most influential people you were not surprised by seeing any of the names, even if you missed somebody else. Seeing on this list the name of Péter Érdi you might think, that the list is random, extremely subjective or most likely manipulated.
Philosophers gave up the attractive concept of absolute objectivity, still mathematicians
study the problem of the science of objective ranking45. Nobody is perfect, there is no individual can be fully unbiased.

Social dominance orientation

Social dominance orientation (SDO) measures social and political attitudes. Measurement is a procedure, when a number is assigned to an object, event, attitude etc. It is measured by a so-called Lickert scale, what social psychologists use base to generate scales from responses to statements. A frequently used version permits five answers (strongly disagree; disagree; neither agree nor disagree; agree, strongly agree). To generate a scale, numbers are assigned to each answer (from 1 to 5). Here are some textbook examples, you may check your attitude:
Western civilization has brought more progress than all other cultural traditions.
Lower wages for women and ethnic minorities simply reflect lower skill and education levels.
Patriotism is the most important qualification for a politician.
If not executed, murderers will commit more crimes in the future.
SDO measures attitude for inequality between social groups. While measurement refers to the present, it also predicts future behavior. ”SDO also predicts support for group-relevant social policies that uphold the hierarchical status quo, such as support for wars of aggression, punitive criminal justice policies, the death penalty and torture, and opposition to humanitarian practices, social welfare, and affirmative action” 38 .
How does our brain help us to know our social rank? Do you remember how you spent the first days in your newest job? I would guess many of us collected information about the formal and informal relationships among people. We learn soon the formal hierarchical relationship. It might be useful to uncover the structure of the gossip network. (It was easy to notice that a colleague having his office adjacent to mine seemed to know everything from everybody in our small campus. So for me it is a viable strategy to visit him occasionally to update myself about recent (and future) local events.
Modern neuroscience has combined brain imaging devices and computational techniques to uncover some mechanisms about how people’s brain processes information on social hierarchy 39 .
An exciting field, social neuroscience uncovers the brain regions and neural mechanisms
related to reflecting ranks and dominance. Studies have shown that a brain region called the dorsolatereal prefrontal cortex might play a significant role in the prevalence of employment discrimination against women or ethnic minorities, which is directly related to the conservative and hierarchy-enhancing attitudes indexed by the social dominance orientation (SDO) scale.
So what? Assuming neural determinism, may an ultraconservative guy may tell ”it is not me, only my prefrontal cortex”. I leave the story here and let the Reader to think on it.

Social structures: Hierarchical versus Network Organization


Hierarchy is the very general organization principle that characterizes our physical, biological and social systems.21 Such systems are structured in layers or levels. An excellent example for the success of interdisciplinary science is an explanation of the evolution of complex hierarchical human societies through combining the collection and analysis of traditional historical data with mathematical modeling. The core of the hypothesis is that there are two main governing factors, warfare and the so-called “multi-level selection,” which have propelled human evolution for centuries. 22 According to anthropological scholars, human society evolved from small-scale, relatively egalitarian tribes to the complex social entities of advanced industrialized nations through a multilevel selection mechanism combining competition and cooperation. Historically, tribal social groupings resulted in competition for scarce resources, and tribes had incentives to act selfishly for the benefit of their group members. However, historians and anthropologists have noted that during periods of intensive competition, like wartime, tribal groups have tended towards cooperative practices. Increased cooperation among group members induces firmer social
cohesion, drives technological progress (including military and organizational applications), and results in population expansion. Due to cognitive bounds that limit the number of social relationships any single person can maintain, evolutionary mechanisms have promoted demarcating social groups along cultural, linguistic, religious, and other lines, and constructing ever-larger social hierarchies that have grown to encompass societies of quite literally billions of people.
These interdisciplinary studies show (i) that both altruism (benefiting others at a cost to
ourself) within a community, and hostility (toward individuals outside of our own ethnic, racial communities) are common human behaviors; and (ii) the intersection of the two (called ”parochial altruism”) 23 led to an evolutionary mechanism well-labeled with the slogan ”cooperate to compete” to generate large-scale hierarchical social structures.

Some social hierarchies

Social hierarchies can be traced throughout history, and here are illustrative examples:
Toga and rank Roman society was strongly hierarchical. Among the patricians there were wealthy landowners, politicians, as consels, senators, judges. They could veto on laws. Among the most famous patrician families you can find Julia (Julius Caesar), Cornelia, Claudia, Fabia, and Valeria. The plebians, i.e. the ordinary citizens had to pay tax. A common job was to be shop owner. The plebians cannot participate in government. (One of Rome’s most famous senator, Cicero, however, was a plebeian). The freedmans may have jobs, as craftsmen and traders, while they were free from slavery, they had little rights. Slaves, had not any rights, they worked in mines, farming, road construction etc. During many years of work they could save up to pay to get out of slavery. The hierarchical organization was well-reflected by the types of toga worn.24 Figure 3.1 shows that the color of the toga is a symbol of social status.

The strict social hierarchy of the Aztecs Aztec society was structured by social, political, and religious hierarchies. The election system ensured continuity: emperors were usually chosen from among the brothers or sons of the deceased rule, and they were elected by a high council of four nobles who were related to the previous ruler. The nobles had many privileges, including
full educations and fancier clothes. They might have held government offices, but craftsmen, or even servants, could belong to the nobles. There was some class mobility, since servants with distinction could move up in the ranks. The commoners were farmers, artisans, merchants, and low-level priests. Slaves typically had more rights than we would often think. They had the right to form a family and even to buy their freedom. (Actually, poor and free people could sell themselves as slaves.) 25. Fig. 3.2 illustrates their social structure.

Hierarchies in the Medieval Europe The feudal system in the Medieval Europe implemented a strict ”pecking order”, everyone from the pope to the king to the peasant knew his or her place in the hierarchy.26 The King was on the top of the hierarchy, he had the maximal power. The system is based on the belief that God owns the land, and the King, who rules with the God’s wish, could use this land. So, the King grants the land to nobles for military services. Nobles granted further the land to peasants, to who made the agricultural work, and
other services. Land and privileges were subdivided based on the hierarchy shown at Fig. 3.3.

Symbolic actions of social status
”It’s believed that bowing in Japan started sometime
during the Asuka and Nara periods (538-794 AD) with the introduction of Chinese buddhism. According to those teachings, bowing was a direct reflection of status—if you met a person of higher social standing, you would put yourself in the more “vulnerable” position of a bow, much like a friendly dog rolling over on its back, to prove that you didn’t harbor any ill will towardthem.”27

How does our brain help us to know our social rank?
Do you remember how you spent the first days in your newest job? I would guess many of you collected information about the formal and informal relationships among people. Modern neuroscience has combined brain imaging devices and computational techniques to uncover some mechanisms about how people’s
brain processes information on social hierarchy. 28 An exciting field, social neuroscience uncovers the brain regions and neural mechanisms
related to reflecting ranks and dominance. A brain region called dorsolatereal prefrontal cortex might play a significant role in the prevalence of employment discrimination against women or ethnic minorities, which is directly related to the conservative and hierarchy-enhancing attitudes indexed by SDO scale. So what? Should an ultraconservative guy should tell, ”it is not me, only
my prefrontal cortex”. I leave the story here and let the Reader to think on it.