Péter Érdi: RANKING. The Unwritten Rules of the Social Game We All Play

Zero was not always on the number scale. The concept of zero emerged from the the contemplation of void by the Buddhists. While the notion of emptiness has negative connotation according to the Western psychology, the Buddhists don’t identify emptiness to the concept of nothing. 2
The number zero was discovered or invented in India. (”Invented” implies that zero is a
human construction, while ”discovered” assumes that while the symbol is created by human, the concept existed without any human activity.) It appeared in the Bakhshali manuscript, denoted by a point. While symbols as placeholders were used earlier by the Babylonians and Mayans, this script seems to be the first, where the symbol represents ”nothing”. Zero as a number is the result of the Buddhists deep introspection. The manuscript is located in the University of Oxford’s Bodleian Libraries, and it was a big excitement among the historians of mathematics in 2017, when radiocarbon dating of the documents showed that zero appeared in the 3rd or 4th century, four-five hundreds years earlier, that it was assumed 3. Zero arrived to Europe only around 1200, when the Italian mathematician traveled back from North-Africa, and now the whole digital age is based on the difference between ”nothing” and ”something”.
Integrative studies in cognitive science combined human developmental psychology, animal cognition and neurophysiology, and the results suggested zero emerges through four stages: first, sensory ”nothing”, i.e. the lack of any stimulus; second, the categorical ”something”, still qualitative; third, nothing is characterized quantitatively by empty sets; and finally there is a transition from an empty set to the number zero. 4 Present day cognitive neuroscience investigates the neural mechanisms of representing empty sets and zero.
Zero and non-zero, nothing and something are basic categories in our digital age. So, we
should think three times (referring to another magical number), when we declare: ”my pain is zero”.

2 https://www.huffingtonpost.com/lewis-richmond/emptiness-most-misunderstood-word-in-buddhism_b_2769189.html; Kaplan, R: The Nothing that Is: A Natural History of Zero. Oxford Univ. Press, 2000; Amir D.
Aczel: Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. St. Martin’s Press, 2015.
3 see e.g. https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-

4 Nieder A: Representing Something Out of Nothing: The Dawning of Zero. Trends in Cognitive Science,
20(830-842), 2016 Nov.

The human brain generally does not have the ability of remembering long lists of unstructured items. We don’t remember well for a series of numbers, of nonsense words, or lengthy list of goods to shop in the supermarket. One of the pioneers of the memory research, Hermann Ebbinghaus made memory studies around 1885 on himself and tried to memorize nonsense syllables. Time to time he tested his memory, and realized that it decayed exponentially, and the performance of his memory is quantitatively can be characterized by what is called ”forgetting curve”. He also found that the his performance depended on the the number of items, it was more difficult to memorize long lists of items.

There are big exceptions. Some people literally are able to remember list of nonsense items for decades. Alexander Luria (1902–1977), a Soviet neuropsychologist studied a journalist, called Solomon Shereshevski, who apparently had a basically infinite memory. He was able to memorize long lists, mathematical formulae, speeches, poems, even in foreign languages etc.  He was able to recall of these lists of nonsense syllables 14 years later as well that the day he had learned them. His performance did not depend on the length of the items, what Ebbinghaus observations and theory suggested,

Shereshevski was diagnosed with synaesthesia, which is a neurological condition, when different senses are coupled. When he realized his ability, he performed as a mnemonist. His ability implied disorders in his everyday life, it was difficult to him to discriminate between events that happened minutes or years ago.

Contents
1 Prologue: My Early Encounters with Ranking 1
1.1 How to lead the popularity list? Own a soccer ball! . . . . . . . . . . . . . . . . . 1
1.2 Rating and ranking of soccer players: the illusion of objectivity . . . . . . . . . . 2
1.3 A not-so beautiful tale: An example for intentional biased ranking from a Hungarian
folktale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Lessons learned: The reality, illusion and manipulation of the objectivity . . . . . 3
2 Comparison, ranking, rating and lists 5
2.1 Comparison: ”thief of joy” or driving force towards future successes? . . . . . . . 5
2.2 From Ali’s ”I am the greatest” to ”the grass is always greener on the other side of
the fence” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 When to use ranking and rating? . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 From the ranking of mathematicians to the rating of chess players . . . . . . . . . 10
2.5 From the Ten Commandments to the Top Ten Mania . . . . . . . . . . . . . . . . 11
3 Social ranking in animal and human societies 17
3.1 Pecking order in chicken community . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Dominance, prestige, hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 The tragedy of being the SECOND best . . . . . . . . . . . . . . . . . . . . . . . 22
4 Choices, Games, Laws and the Web 25
4.1 Choices: individual, social and algorithmic . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Rock–paper–scissor: games and laws . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 The fortune-making algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 The Ignorant and the Manipulator 33
5.1 (Not only) cognitive bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2 ”When the World Is Led by a Child” . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3 The importance and the difficulties of measuring society . . . . . . . . . . . . . . 34
6 Ranking games 41
6.1 Players and strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 Nobody likes, everybody uses: college ranking . . . . . . . . . . . . . . . . . . . . 41
6.3 Is there any ”best” country in the world? . . . . . . . . . . . . . . . . . . . . . . . 43
6.4 About the results of the game: stability, reversal, statistics . . . . . . . . . . . . . 47
iii
7 Struggle for reputation 49
7.1 Reputation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2 Ranking game what scientists play . . . . . . . . . . . . . . . . . . . . . . . . . . 50
7.3 Rating artists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7.4 Nobel and Oscar the candidates and the winners . . . . . . . . . . . . . . . . . . 52
7.5 How (not) to rig an election? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.6 The dark side of a success story: the search engine manipulation effect and its
possible impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
8 You can choose something (somebody) if you know it (her/him): recommendation
systems 57
8.1 Algorithms: friends or foes? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
8.2 The music what you like: Cantometrics and the Music Genome Project . . . . . . 59
9 Epilogue: Ranking, rating and everything else. The mystery of the future:
how to combine human and computational intelligence? 61
9.1 Rules of the ranking game: where we are now? . . . . . . . . . . . . . . . . . . . 61
9.2 Algorithms humans use and create/control . . . . . . . . . . . . . . . . . . . . . . 62
9.3 Controling the web: Who has the last word? The human or the computer? . . . . 62

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An excellent summary

• 1. History of social choice theory
  • 1.1 Condorcet
  • 1.2 Arrow and his influence
  • 1.3 Borda, Carroll, Black, and others
• 2. Three formal arguments for majority rule
  • 2.1 The concept of an aggregation rule
  • 2.2 A procedural argument for majority rule
  • 2.3 An epistemic argument for majority rule
  • 2.4 A utilitarian argument for majority rule
• 3. Preference aggregation
  • 3.1 Arrow’s theorem
  • 3.2 Non-dictatorial preference aggregation rules
  • 3.3 The Gibbard-Satterthwaite theorem
• 4. Welfare aggregation
  • 4.1 Measurability and interpersonal comparability of welfare
  • 4.2 The possibility of welfare aggregation
  • 4.3 Other topics
• 5. Judgment aggregation
  • 5.1 The ‘doctrinal paradox’ and the ‘discursive dilemma’
  • 5.2 The conditions for inconsistent majority judgments
  • 5.3 A general model and a simple impossibility result
  • 5.4 More general impossibility and possibility theorems
  • 5.5 Non-dictatorial judgment aggregation rules
• 6. Other topics

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 transitive. 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 we are maximizing our expected gain expressed by the utility function. However, if we want to make a mathematical 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 theory made possible 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. While probably the 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 the new paradigm is being emerged slowly. 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. 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 (such as time and money), limited available information, our limited cognitive skills, values, influence by our feelings etc. 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.”

Cognitive bias makes us ”predictably irrational”, by using with a fashionable expression. (Dan Ariely). It frequently blocks people from making rational decisions, even they try to do their best. But what is rationality behavior? Is it true that we always behave in favor of our narrow economic interest? A counterexample is the Ultimatum Game There are two players, the proposer and the responder, who have to agree on how to split a certain amount of money. The proposer makes an offer. The responder has two possibilities, to accept or reject. If she accepts, the deal has been done, If she rejects neither player gets even a single penny. Rationality would require to accept any positive offer, even the smallest one. In this case, the proposer would obtain the overwhelming majority of the entire sum. Studies with humans across different cultures showed that often the responders reject offers below 30% . Still we may say the expected utility concept
works, but we should take into account the psychological benefit for being able to reject an offer just to penalize the miserly proposer.

Richard Thaler, Amos Tversky and Daniel Kahneman not only revolutionized behavioral
economics, but also wrote best-seller books. The takeaway is that we should understand and accept that we humans are evolutionary wired to make errors in judgment (including ranking) and we need a nudge to make decisions that are in our own best interest. The understanding our own fallibility can help us to bring better decisions. The behavioral economists’ approach enhances the rational choice model.

 

“Close to a quarter of adults in American eat fast food *every single day*. The popularity of the drive-through window is a good indicator that we like to eat on the go, or at least that we are too busy to stop for a meal. It’s not surprising then, that fast food restaurants are in every city in America. “

Read Ranking the Places with the Most (and Least) Fast Food in America