The Influence Index

On January 23, 2026, Fuad Aleskerov turned 75. He is Head of the Department of Mathematics at the Faculty of Economic Sciences and Director of the International Centre of Decision Choice and Analysis. In an interview with the HSE News Service, the scholar spoke about Florentine families of the Renaissance, influence indices in economics, and the usefulness of coalitions in politics.

‘There Is Nothing for Him to Do Here—He Knows Everything’

I was born in Baku, into the family of a well-known oil industry specialist and the head of a department at the Institute of Oil and Chemistry. As far as I can remember, everything around me in childhood was connected with knowledge and culture. From the age of five I was taken to the conservatoire and to theatres, and this has remained an integral part of my life ever since. I recently worked out that in the past I used to attend three or four concerts and performances a month, whereas now I go to six or eight.
Until the fourth year of school, before I gave it up, I studied music at a conservatoire school: first I played the violin, then the piano, and then the cello. I was strongly encouraged to continue, and now I sometimes regret that they did not persuade me to stay. Another passion of mine was chess. My father, who at first used to beat me, once gave me a book; I studied it, and after that I stopped losing to him and fell in love with chess for life, seriously so—I read three-volume works on openings. It was only in my second year at the Faculty of Mechanics and Mathematics, when the volume of knowledge I was receiving became so large that I had to choose between mathematics and chess, that I gave up a chess career.

‘Only Moscow, and Only the Faculty of Mechanics and Mathematics’

In the ninth grade, which was then the penultimate one, a funny incident occurred. My parents were summoned to the school and told: ‘There is nothing for him to do here—he knows everything. Let him take the exams externally and go to university.’ I was not against the idea in principle; the only thing was to decide where to apply. For a while I wanted to become a sinologist. Then a surgeon, like my cousin, who later became a well-known neurosurgeon. My cousin always said he would be a surgeon and used to dissect cockroaches and frogs at the dacha to see how everything inside them was arranged. At that point I would step aside so as not to watch—what kind of surgeon would I have made? So, when asked what I wanted to be, I said ‘a lawyer.’ We had lawyers in our family. When my parents heard that, they said nothing. My father simply subscribed me to the Bulletin of the Supreme Court, and after the fourth issue I realised that I no longer wanted to be a lawyer. I followed in my parents’ footsteps and enrolled at the Institute of Oil and Chemistry. By my second year it became clear that this was not for me, and at the exam in theoretical mechanics my examiner, a well-known academician at the time, said: ‘There is nothing for you to do here. Only Moscow, and only the Faculty of Mechanics and Mathematics.’

That is how I ended up at the Faculty of Mechanics and Mathematics of Moscow State University. Studying there was far more interesting. I remember once taking an advanced algebra course exam for six hours, whereas exams usually lasted three or four hours. There were six students on the course. Everyone else had already passed, but they did not leave—they stood by the door while I was answering last. After the lecturer said, ‘Right, well, you have answered all the questions…,’ they started applauding. I received a grade of ‘good,’ however, with the comment: ‘By the third year one should already know the standard proofs, rather than invent them again.’ And I did know them.

But for me it was a special pleasure to come up with new proofs of classical theorems.

Of course, I was offended, but I was so tired that I did not argue.

I Could Not Even Imagine That Human Behaviour Could Be Described Using Mathematics

I went on to postgraduate study not at MSU but at the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, under my teacher Mark Aizerman, and to this day I believe that I gained from that choice.

I was offered two possible topics. The first was optimal control, which I already knew. The second was choice theory. A book by Boris Mirkin on this subject had just been published at the time. When I started reading it, I was amazed. I could not even imagine that human behaviour could be described using mathematics. We were not taught anything like that at the Faculty of Mechanics and Mathematics. Later, after I had defended my PhD thesis on ‘Interval Choice,’ Mark Aizerman gave me photocopies of three pages from Kenneth Arrow’s book on the impossibility of collective choice. And once again I was astonished. It is, after all, perfectly obvious that there are elections involving several candidates, but the idea that this story could be described using mathematical formulae had never occurred to me. We began working in this area and achieved a great deal. A book on this topic was published in the Kluwer Mathematical Library series.

I am still working at the Institute of Control Sciences. I rose from an intern to head of a laboratory—this was my teacher’s wish. And when he passed away, I went abroad to work. I taught in the United States, and later at Boğaziçi University in Istanbul. We travelled a great deal, and whenever possible I took photographs. Many of them can be seen in the corridor next to my office in Building T in the HSE campus building on Pokrovsky Bulvar. And when it was time for my daughter to start school, we returned to Moscow.

For me, Moscow is truly a beloved city. It is the only city to which, when I return, my soul sings.

Network Models in Renaissance Florence

I was recently asked how many fields of science I have publications in. I counted and was surprised myself—32! I once joked that I am like a dinosaur, walking along and ‘eating’ everything ‘tasty’ that I see. Take networks, for example, which I have been actively working on for the past ten years. This topic has its own backstory, which I like to tell students. One day I received a call from a deputy chair of the Russian Central Bank with a problem: they had created a network of interbank lending using classical methods, but the result turned out to be wrong. I was asked to look into it, and I realised what the issue was: classical methods do not take vertex parameters into account. Let me give my favourite example involving a bank loan. If I borrow a million from Sberbank and do not repay it, the head of Sberbank, German Gref, will stop greeting me, but Sberbank will not collapse because of it. But if I take the same amount from a small bank and fail to repay it, the bank will be in serious trouble. That is, one needs to take vertex parameters into account—yet for some reason nobody was doing this. Even though the pioneer of this field, Max Newman, explicitly wrote that we should.

Another example: imagine that you and I each take 500,000 from a small bank. If one of us repays the money and the other does not, the bank will still survive; but if neither of us repays it, the bank will fail. So group effects also need to be taken into account. Yet this question had not even been posed. As a result, we managed to create an entire series of so-called ‘centrality indices’ that take all of this into account, and we are now actively working with networks.

In general, however, this can be applied in many different fields. For instance, I have always been interested in the period of the European Renaissance. When I first developed network-based models, I immediately thought about how they could be applied to that era. One of my favourite papers is therefore devoted to the question of which Florentine family of the Renaissance period was the most influential. I even wrote to Italian historians suggesting a joint project, but they did not reply. Later, when it turned out that all the necessary data was available in open sources, my PhD student Anna Semenova and I did the work ourselves. In it, we take into account such parameters as marriage ties, family wealth, and representation in the Signoria. This work is still awaiting publication.

Tornadoes, Influence Indices, and Law-Abiding Behaviour

Here is another story, this time from meteorology. Commissioned by a large foreign trading company, we carried out a project on predicting consumer behaviour (this was the first time I encountered big data). I came up with the idea of applying a superposition of choice functions, and it worked extremely well. Later, on a completely different occasion, I found myself at a conference in Greece. After my talk, an American professor spoke about the accuracy of tornado prediction being 57%. Using our methods, we achieved an accuracy of 61%. At the time, to be honest, this figure annoyed me. I felt we had wasted our time. But then they showed me a paper stating that 57% was the best result achieved up to that point, and that every additional half per cent was a major achievement. There is an idea for how to improve it further, but this would require more detailed data, which unfortunately cannot yet be obtained. And yet the stakes are enormous—both money and human lives.

Some time ago I produced a series of works on influence indices. There is such a concept as ‘influence in electoral groups.’ Let me give a simple example for clarity. Imagine a parliament of 99 people. There are three parties with 33 members each. A simple majority is 50. Clearly, no single party can push through its decision, but any two can—and, of course, all three together can. Now let us imagine a different distribution: 48, 48, and 3. But 48 still cannot win on its own, can it? From this point on, we become interested in coalitions, where a party with three members turns out to be just as influential as those with 48. There is one more important point. Classical indices calculate this influence purely combinatorially, in the sense of ‘whoever joins whoever.’ But when we were writing a book on the distribution of influence in the State Duma, I thought this was wrong. Because an extreme left party and an extreme right party will never form a coalition. I therefore devised an entire series of new indices, published in leading journals, which also take into account whom we are prepared to form a coalition with. Incidentally, together with my PhD student Rita Kamalova and my friend Prof. Manfred Holler, we wrote a paper on party influence in the Reichstag of the Weimar Republic. The methods I proposed there vividly demonstrate how, against the background of the two main forces failing to reach agreement with each other, Hitler came to power. Had they managed to form a coalition, they would have governed the country for another hundred years.

It is always better to form coalitions so as not to open the way for extreme forces.

There is no sense in which I consciously choose where and on what I would like to work. Problems find me themselves. Thus, in 1984 I received a call from the Institute of Endocrinology: they had around 20,000 experiments but did not know how to analyse them. We took the data and statistically proved a striking result: high blood pressure is not a risk factor for diabetes. The thing is that whenever I work in a field that is new to me, I start by studying that field. And so, while reading a medical encyclopaedia published in 1956, I discovered that long before us our greatest endocrinologist, Vasily Baranov, had come to the same conclusion. I still remember the quotation: ‘…I have no convincing evidence, but judging by my understanding of this disease, high blood pressure is not a risk factor for diabetes.’ 1956! And thirty years later, we proved it statistically.

During the pandemic there were tasks of a different kind. We continued working, and I had the opportunity to observe people in the metro. Alas, even during the toughest times no more than 20% of people were wearing masks, and only about 5% were wearing gloves. I (wearing a mask and gloves myself) counted honestly. It then occurred to me to introduce a parameter such as law-abiding behaviour into the calculations. At the time, figures for new infections were being published almost daily. I approached sociologists, assuming that everything had of course already been calculated, but it turned out that it had not. And so, drawing on my own understanding of how the world works and on what I had taken from the literature, I produced an expert assessment for 60 countries. It worked very clearly. I gave four plenary talks on this topic at various conferences, including a medical one, and who knows—perhaps this work of mine will still prove useful.

Our most recent model is connected with biology. It is a model of apoptosis. It turns out that at the genetic level, when a biological system lacks sufficient food, genetic mechanisms are activated and some of the cells are sacrificed to nourish the remaining ones. Then, when nutrition becomes sufficient again, the colony flourishes. To my mind, this is simply fantastic! And I like the fact that each of my projects is linked to new discoveries.

The Soul Should Sing

Is it important to me that a solution should have practical value? It is hard to say. Take the problem of the superposition of choice functions, for example. Initially it was solved as a purely theoretical problem, but twenty years later we realised that the superposition could be applied to searching in big data—and it worked. I use this example to show students that knowledge is never useless. Or take the classic case of Boolean algebra. The concept was devised by the mathematician George Boole in 1847 as a purely theoretical construct. Now it is used throughout computer science. So much for practicality.

Do you know which of my articles is the most cited at present? The one about how to write and defend a dissertation.

Once I decided to give such a lecture and thought that about fifteen people would attend, but nearly a hundred turned up. Afterwards, three journals approached me with requests to publish it. There is even an English version.

I have many students, and I love them very much. And I love teaching. When you explain something new and see their eyes light up, it is a wonderful feeling. Not every serious undertaking has to be reduced to a formula. I tell students: ‘Read the philosophers. There is not a single formula there, yet the ideas are absolutely brilliant!’ And it is also important to listen to yourself. When you are doing something, your soul should sing. And if it does not, it is better to stop. I am a very happy person. I have always had remarkable teachers—at school, at Moscow State University, and at the Institute of Control Sciences of the Russian Academy of Sciences. At HSE University I spent a lot of time talking with Evgeny Yasin, Lev Lyubimov, Revold Entov, and other colleagues. It was a tremendous pleasure, and I learnt a great deal from them. With no less pleasure, I learn from my students and PhD candidates.

January 23