Ferenc Jánossy (1914-1997), an engineer-turned economist from a legendary Hungarian family (he was the step son of George Lukács (1885-1971), one of the founders of the philosophy of ”Western Marxism”), wrote a book in Hungarian with the title ”The measurability and a new measuring method of economic development level”, and it was a revelation at that time. Jánossy explained his approach clearly:

”The first issue is how qualitatively different objects can be compared quantitatively. Every child knows that an elephant is bigger than a sparrow. They would agree without the least doubt that the cow is smaller than the elephant, but bigger than the sparrow. Ranking animals according to size, they would place the cat between the cow and the sparrow without any hesitation. But suddenly the child is faced by the problem of the horse. Where should the horse go? Is it bigger or smaller than the cow? When comparing objects of different characteristics, ranking is no longer so simple because taking into consideration various features may lead to various ranking results. (The horse is taller, yet shorter than the cow.)..”

Generalizing the above game Jánossy finds that the greater the qualitative difference between two items the greater is the quantitative difference needed to make the ranking reliable according to size. Qualitative difference is limiting the quantitative comparability – this is what Jánossy calls the ’criterion of comparability’. Obviously, the critical limit depends on the features compared. (If ranking is only according to height, then the horse-cow dilemma does not even arise.) Ranking, however, is not the aim but only the means, therefore the basis of the comparison cannot be changed to make ranking easier. A clear definition of the organizing principle may lower the critical limit but cannot eliminate it.

The next question is how to move from ranking to measuring. How to make a quantitative statement, or rather under what conditions could be quantitatively described that Sweden is more advanced than Turkey. If any one feature is not additive or cannot be traced back to some additive feature, it cannot be measured. If a feature is measurable, then the comparison of two objects can be decomposed into two steps of “numerical measurements along a fixed scale”. Which means that the critical limit of measurability matches the given absolute scale and the limit of comparability of the object. If the examined feature of the objects can be measured along an absolute scale, the critical limit can be expressed numerically.

This is an example to gave the hint that ranking and rating needs appropriate methods, and the methods have limits! It is very vital to accept the existence of the limits of comparability!

László Arany (1844-1898), the son of the celebrated poet, and the “Shakespeare of ballads”, János Arany (1817-1882), collected Hungarian folktales. One of these tales taught children, how decisions supposed to bring collectively can be manipulated by the strongest participant.

A number of animals escaped from their homes, and fell into a trap. They were not able to escape, and became very hungry. There wasn’t any food around, so the wolf suggested a solution: ”Well, my dear friends! What to do now? We should eat soon, otherwise we starve to death. I have an idea! Let us read the names of all of us, and the most ugly one will be eaten.” Everybody agreed, (I have never understood, why). The wolf  assigned himself to be the judge, and counted:
”Woolf-boolf o! So great!, fox-box also great, my dear-my beer very great, rabbit-babbit also great, cock-bock also great, my hen-my-ben, you are not great.. and they ate the hen… so on…next time cock-bock became food… (thanks to Judit Zerkowitz for the translation from Hungarian).

This is a great example of demonstrating how objectivity is manipulated if one of the voters controls an election.

Fareed Zakaria just mentioned in his GPS at CNN  a list of countries ranked by their passport index.  Countries  ranked by their total visa-free score:

Singapore becomes most powerful passport in the world.

“Paraguay helps Singapore overtake Germany for the top spot. Montreal, October 24, 2017 – Paraguay removed visa requirements for Singaporeans, propelling Singapore’s passport to the top of Passport Index’ most powerful ranking with a visa-free score of 159. Historically, the Top 10 most powerful passports in the world were mostly European, with Germany having the lead for the past two years. Since early 2017, the number one position was shared with Singapore, which was steadily going up. Other Asian passports in the Top 20 include those of South Korea, Japan and Malaysia. According to The Hon. Philippe May, Managing Director of Arton Capital’s Singapore office, “For the first time ever an Asian country has the most powerful passport in the world.” “It is a testament of Singapore’s inclusive diplomatic relations and effective foreign policy,” shared May. …”

 

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I must have been maybe ten, eleven years old, still remember well to a paradoxical title of a journal article : ‘Let the objective numbers speak!” I enlighten you, why was it paradoxical. At the ends of the soccer seasons the sport newspaper evaluated the performance of the players for each of the eleven positions, from goalkeepers to left wingers. The article, in addition to the verbal appraisal, contained eleven ranked lists, one for each position; players from each team were ranked based on their seasonal scores, Fig.  shows. How these scores were constructed? Please note: soccer is not baseball, there is no objective measure to score the players. A journalist apprentice was delegated to every game, and he (surely he) gave a score to each player after each game. Any player, who was sending off from the field, got a score ”one”. A very few players in each season received a score ”ten” for their extraordinary performances. The majority of the scores was in the ”five” to ”eight” interval. More or less the meaning of ”five” was ”somewhat below average”, and ”eight” indicated ”excellent” (but not brilliant). After each game as we walked with my Dad, to the tram stop to get a ride from the suburb called Újpest, where our stadium has been located, to our apartment in ”Újlipótváros”, we also gave our own scores to each players of our team. I was impatiently waiting the morning paper to compare their scores with mines. At the end of the season, when I read about ”objective numbers”, I knew well that they reflected ranks on the objective average of their subjective grades. This observation suggested, that ranking based on subjective rating generates the illusion of objectivity only. The scores were not random, they reflected the best estimations of the journalists, but beyond dispute they were subjective.

 

‘The only guy who seems to have escaped the rankings game is Adam. He got into the record books without trying: Before him there was nobody. Eve had to settle for runner-up, and look what happened when she tried to get ahead by snacking on a piece of fruit…”

I am reading about what people wrote about the ranking game.  Stephen Joel Trachtenberg is president emeritus  of George Washington University published in 2011 a witty article .

“The ancient Greeks picked up the game, fashioning bits of gold, silver and bronze to represent win, place and show. Earning an Olympic medal meant, and still means, you are the best of the best, the top dog in your chosen category of competition. It is absolute and objective, not relative and subjective. The best sprinter gets the gold because she is fast, not because she is popular…”

Thank you, Prof. Trachtenberg!

Adopted from the site

1. See failure as a beginning, not an end

2. Never stop learning

3. Assume nothing, question everything

4. Teach others what you know

5. Analyze objectively

6. Practice humility

7. Respect constructive criticism

8. Give credit where it is due –

9. Take initiative

10. Ask the tough questions early

11. Love what you do, or leave

Mark Cuban threw shade at Forbes’ rich list after Wilbur Ross lied about being a billionaire

(I am not sure whether my friends in Pest and Buda or even in Debrecen know MC…  My daughter and wife like to watch Sharks, so I have heard about him.

Here is the new QS World University Rankings (thanks for Gyuri Bazsa for writing me).

if you click to Methodology, you see again the magic numbers  and categories.

Academic reputation (30%)

Employer reputation (20%)

Faculty/student ratio (15%)

Papers per faculty (10%)

Web impact (10%)

Staff with a PhD (5%)

Citations per paper (5%)

International faculty (2.5%) and international students (2.5%).

Lomonosov is still the first. Written on ~ November 7th, 2017.

Caterina De Bacco, Daniel B. Larremore, Cristopher Moore  published a new algorithm with the title A physical model for efficient ranking in networks.  The model is based on binary interactions among the entities. As often in  physical models, interactions via edges are considered as mechanical springs, and the optimal rankings of the nodes are minimizes the total energy (or “energy”) of the system. They show some examples for identifying  prestige, dominance, and social hierarchies in human and animal communities.

Further studies will tell how efficient is the new algorithm.

 

 

Algorithms are maybe objective. A famous example now known how PageRank gives different results by changing the numerical value of what is cold the ”damping factor”. PageRank is based on an assumption how a web-surfer behaves. For a while the surfer will click to links she is seeing in a certain page, but get bored with the actual page she visits, and then jump to another page randomly (as with directly typing in a new URL rather than following a link on the current page). The original algorithm assumed that the probability of being bored is 0.15, so the numerical value of the damping factor was set as 1-0.15=0.85. So, setting the damping factor for other numbers we may get different ranking. The phenomenon is called rank reversal. Rank reversal is a change in the rank ordering depending on some not important, or many times irrelevant factors. While I find the paper of Seung-Woo Son, Claire Christensen, Peter Grassberger, Maya Paczuski PageRank and rank-reversal dependence on the damping factor  excellent, my opinion does not count much, during almost six years its citation number is just six.

On a somewhat different note it is reasonable to expect that the ranking of any two candidates, A and B, should be preserved even if one more candidate C enters the race. In the theory of election systems it is called the ”rank reversal rule”. This rule was infamously violated in the US election in 2000, when Ralph Nader captured a few per cent of the vote in Florida, giving the election to George W. Bush (over Al Gore). As all we know Gore would have won if Nader was not in the race.