Anatol Borisovich Rapoport (; ; May 22, 1911January 20, 2007) was an American mathematical psychologist. He contributed to general systems theory, to mathematical biology and to the mathematical modeling of social interaction and

stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...

models of contagion.

Biography

Rapoport was born in Lozova, Kharkov Governorate,

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

(in today's Kharkiv Oblast,

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

) into a secular Jewish family. In 1922, he moved to the United States, and in 1928 became a naturalized citizen. He started studying music in

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

and continued with

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

conducting Conducting is the art of directing a musical performance, such as an orchestral or Choir, choral concert. It has been defined as "the art of directing the simultaneous performance of several players or singers by the use of gesture." The primary d ...

and composition at the

Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...

Hochschule für Musik where he studied from 1929 to 1934. However, due to the rise of Nazism, he found it impossible to make a career as a pianist. He shifted his career into

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, completing a Ph.D. in mathematics under Otto Schilling and Abraham Adrian Albert at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

in 1941 on the thesis ''Construction of Non-Abelian Fields with Prescribed Arithmetic''. According to ''

The Globe and Mail ''The Globe and Mail'' is a Newspapers in Canada, Canadian newspaper printed in five cities in Western Canada, western and central Canada. With a weekly readership of more than 6 million in 2024, it is Canada's most widely read newspaper on week ...

'', he was a member of the American Communist Party for three years, but quit before enlisting in the U.S. Army Air Forces in 1941, serving in

Alaska Alaska ( ) is a non-contiguous U.S. state on the northwest extremity of North America. Part of the Western United States region, it is one of the two non-contiguous U.S. states, alongside Hawaii. Alaska is also considered to be the north ...

and

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

during World War II.Ron Csillag, "Anatol Rapoport, Academic 1911–2007." ''The Globe and Mail'' (Toronto), January 31, 2007, p. S7 After the war, he joined the Committee on Mathematical Biology at the University of Chicago (1947–54), publishing his first book, ''Science and the Goals of Man'', co-authored with semanticist S. I. Hayakawa in 1950. He also received a one-year fellowship at the prestigious Center for Advanced Study in the Behavioral Sciences at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

. From 1955 to 1970, Rapoport was Professor of Mathematical Biology and Senior Research Mathematician at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

, as well as founding member, in 1955, of the Mental Health Research Institute (MHRI) at the University of Michigan. In 1970, during the

Vietnam War The Vietnam War (1 November 1955 – 30 April 1975) was an armed conflict in Vietnam, Laos, and Cambodia fought between North Vietnam (Democratic Republic of Vietnam) and South Vietnam (Republic of Vietnam) and their allies. North Vietnam w ...

, Rapoport moved to

Toronto Toronto ( , locally pronounced or ) is the List of the largest municipalities in Canada by population, most populous city in Canada. It is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a p ...

"to live in a country that was not committed to a messianic role—a small peaceful country with no aspiration to major power status". He was appointed professor of mathematics and psychology at the University of Toronto (1970–79). The university appointed him professor emeritus in 1980. He lived in bucolic Wychwood Park overlooking downtown Toronto, a neighbour of

Marshall McLuhan Herbert Marshall McLuhan (, ; July 21, 1911 – December 31, 1980) was a Canadian philosopher whose work is among the cornerstones of the study of media studies, media theory. Raised in Winnipeg, McLuhan studied at the University of Manitoba a ...

. On his retirement from the University of Toronto, he became director of the Institute of Advanced Studies (Vienna) until 1983. University of Toronto appointed him professor of peace studies in 1984, a position he held until 1996, but continued to teach until 2000. In 1984 he co-founded

Science for Peace Science for Peace is organization of scientists, engineers, social scientists and scholars working together to promote peace worldwide. It was co-founded by mathematical psychologist Anatol Rapoport, and physicist Eric Fawcett, both former professo ...

, was elected president and remained on its executive until 1998. In 1954 Anatol Rapoport co-founded the Society for General Systems Research, along with the researchers Ludwig von Bertalanffy, Ralph Gerard, and Kenneth Boulding. He became president of the Society for General Systems Research in 1965. Anatol Rapoport died of pneumonia in Toronto. He was survived by his wife Gwen, daughter Anya, and sons Alexander and Anthony.

Work

Rapoport contributed to general systems theory, to mathematical biology, and to the mathematical modeling of social interaction and

models of contagion. He combined his mathematical expertise with psychological insights into the study of

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, social networks, and

semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...

. Rapoport extended these understandings into studies of psychological conflict, dealing with nuclear disarmament and international politics. His autobiography, ''Certainties and Doubts: A Philosophy of Life'', was published in 2001. An article celebrating his legacy and thinking includes a career overview alongside testimonials by scholars and family that provide a glimpse of Anatol Rapoport, the scientist and the person. Philosopher and physicist Mario Bunge called Rapoport a

polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...

whose work Bunge found congenial because of its applicability to real-life problems, its use of mathematics, and its "avoidance of holistic blabber".

Game theory

Rapoport had a versatile mind, working in

psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...

biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...

social network A social network is a social structure consisting of a set of social actors (such as individuals or organizations), networks of Dyad (sociology), dyadic ties, and other Social relation, social interactions between actors. The social network per ...

analysis, and peace and conflict studies. For example, he pioneered in the modeling of parasitism and symbiosis, researching cybernetic theory. This went on to give a conceptual basis for his lifelong work in conflict and cooperation. Among many other well-known books on fights, games, violence, and peace, Rapoport was the author of over 300 articles and of "Two-Person Game Theory" (1966) and " N-Person Game Theory" (1970). He analyzed contests in which there are more than two sets of conflicting interests, such as war, diplomacy, poker, or bargaining. His work led him to peace research, including books on ''The Origins of Violence'' (1989) and ''Peace, An Idea Whose Time Has Come'' (1993). In the 1980s, he won a computer tournament which was based on Robert Axelrod's '' The Evolution of Cooperation'' and was designed to further understanding of the ways in which cooperation could emerge through

evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...

. The contenders had to present programs that could play iterated games of the prisoner's dilemma and these were pitted against each other. Rapoport's entry, Tit-for-Tat, has only four lines of code. The program opens by cooperating with its opponent. It then plays exactly as the other side played in the previous game. If the other side defected in the previous game, the program also defects; but only for one game. If the other side cooperates, the program continues to cooperate. According to ''Peace Magazine'' author/editor Metta Spencer, the program "punished the other player for selfish behaviour and rewarded her for cooperative behaviour—but the punishment lasted only as long as the selfish behaviour lasted. This proved to be an exceptionally effective sanction, quickly showing the other side the advantages of cooperating. It also set moral philosophers to proposing this as a workable principle to use in real life interactions." His children report that he was a strong chess player but a bad poker player because he non-verbally revealed the strength of his hands.

Social network analysis

Rapoport was an early developer of

analysis. His original work showed that one can measure large networks by profiling traces of flows through them. This enables learning about the speed of the distribution of resources, including information, and what speeds or impedes these flows—such as race,

gender Gender is the range of social, psychological, cultural, and behavioral aspects of being a man (or boy), woman (or girl), or third gender. Although gender often corresponds to sex, a transgender person may identify with a gender other tha ...

socioeconomic status Socioeconomic status (SES) is a measurement used by economics, economists and sociology, sociologsts. The measurement combines a person's work experience and their or their family's access to economic resources and social position in relation t ...

, proximity, and

kinship In anthropology, kinship is the web of social relationships that form an important part of the lives of all humans in all societies, although its exact meanings even within this discipline are often debated. Anthropologist Robin Fox says that ...

. This work linked social networks to the diffusion of innovation, and by extension, to

epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and Risk factor (epidemiology), determinants of health and disease conditions in a defined population, and application of this knowledge to prevent dise ...

. Rapoport's empirical work traced the spread of information within a school. It prefigured the study of degrees of separation by showing the rapid spread of information in a population to almost all—but not all—school members (see references below). His work on random nets predates the random graphs as defined by the Erdős–Rényi model and independently by Edgar Gilbert. Rapoport is also the originator of the theory behind the interpretation of bias in social networks, which pertains to the extent to which a network deviates from a random base model. He introduced what is now known as "preferential attachment mechanism" in biased networks. It is a stochastic process that involves connected nodes that snowball into more connections. Rapoport also published an article that outlined a probabilistic approach to animal sociology, which is one of the earliest efforts at modeling simple social structures.

Conflict and peace studies

According to Thomas Homer-Dixon in the ''Toronto Globe and Mail'', Rapoport "became anti-militarist quite soon after

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. The idea of military values became anathema". He was a leading organizer of the first teach-ins against the

at the University of Michigan, a model that spread rapidly throughout North America. He told at a teach-in: "By undertaking the war against Vietnam, the United States has undertaken a war against humanity…This war we shall not win". (''Ann Arbor News'', April 1967). He said he was an abolitionist, rather than a total pacifist: "I'm for killing the institution of war". In 1968, he signed the " Writers and Editors War Tax Protest" pledge, vowing to refuse tax payments in protest against the Vietnam War. As a result of his opposition to the Vietnam War, J.Edgar Hoover considered Rapoport a Communist, and organized FBI agents to write letters to the president of the University of Michigan, the Governor of Michigan and others. This smear campaign drove him from Ann Arbor to the University of Toronto. Rapoport returned to the University of Toronto to become the founding (and unpaid) Professor of Peace and Conflict Studies programme, working with George Ignatieff and Canada's

organization. As its sole professor at the start, he used a rigorous, interdisciplinary approach to the study of peace, integrating mathematics, politics, psychology, philosophy, science, and sociology. His main concern was to legitimize peace studies as a worthy academic pursuit. The Trudeau Centre for Peace and Conflict Studies continued to flourish at the University of Toronto under the leadership of Thomas Homer-Dixon, and, from 2008, under Ron Levi. When Rapoport began, there was one (unpaid) professor and twelve students. In 2007, there were three paid professors and ninety students. Rapoport's students report that he was an engaged and inspiring professor who captured their attention, imagination and interest with his wide-ranging knowledge, passion for the subject, good humor, kind and generous spirit, attentiveness to student concerns, and animated teaching style. In 1981 Rapoport co-founded the international

non-governmental organization A non-governmental organization (NGO) is an independent, typically nonprofit organization that operates outside government control, though it may get a significant percentage of its funding from government or corporate sources. NGOs often focus ...

. He was recognized in the 1980s for his contribution to world peace through nuclear conflict restraint via his game theoretic models of psychological conflict resolution. He won the Lentz International Peace Research Prize in 1976. Professor Rapoport was also a member of the editorial board of the ''Journal of Environmental Peace'' published by the International Innovation Projects at the University of Toronto.

Publications

Books

* 1950, ''Science and the Goals of Man'', Harper & Bros., New York * 1953, ''Operational Philosophy: Integrating Knowledge and Action'', Harper & Bros., New York * 1960, ''Fights, Games, and Debates'', University of Michigan Press, Ann Arbor * 1965, ''Prisoner's Dilemma'', The University of Michigan, Ann Arbor, MI. (co-author; Albert M. Chammah) * 1966, ''Two-Person Game Theory: The Essential Ideas'', Ann Arbor, MI, The University of Michigan Press. (reprinted by Dover Press, Mineola, NY, 1999). * 1969, ''Strategy and Conscience'', Shocken Books, New York, NY. (first published in 1964) * 1970, ''N-Person Game Theory. Concepts and Applications'', University of Michigan, Ann Arbor, MI. (reprinted by Dover Press, Mineola, NY, 2001). * 1974, ''Conflict in Man-made Environment'', Harmondsworth, Penguin Books. * 1975, ''Semantics'', Crowell.This book about general semantics is similar to S.I. Hayakawa's '' Language in Thought and Action'' with more technical (mathematical and philosophical) material. * 1986, ''General System Theory. Essential Concepts and Applications'', Abacus, Tunbridge Wells. * 1989, ''The Origins of Violence: Approaches to the Study of Conflict'', Paragon House, New York. * 1989, ''Decision Theory and Decision Behaviour'', Kluwer Academic Publishers. * 1992, ''Peace: An Idea, Whose Time Has Come'', University of Michigan Press, Ann Arbor, MI. * 2000, ''Certainties and Doubts: A Philosophy of Life'', Black Rose Books, Montreal, 2000. His autobiography. * 2001, ''Skating on Thin Ice'', RDR Books, Oakland, CA. * (English version: ).

Selected articles

* 1948, "Cycle distributions in random nets." ''Bull. Math. Biophysics'' 10(3):145–157. * 1951, with Ray Solomonoff, "Connectivity of random nets." ''Bull. Math. Biophysics'' 13:107–117. * 1953, "Spread of information through a population with sociostructural bias: I. Assumption of transitivity." ''Bulletin of Mathematical Biophysics'', 15, 523–533. * 1956, with Ralph W. Gerard and Clyde Kluckhohn, "Biological and cultural evolution: Some analogies and explorations". ''Behavioral Science'' 1:6–34. * 1957, "Contribution to the Theory of Random and Biased Nets." ''Bulletin of Mathematical Biology'' 19:257–77. * 1960 with W.J. Horvath, "The theoretical channel capacity of a single neuron as determined by various coding systems". ''Information and Control'', 3(4):335–350. * 1962, "The Use and Misuse of Game Theory". ''Scientific American'', 207:108–114. * 1963, "Mathematical models of social interaction". R. D. Luce, R. R. Bush, & E. Galanter (Eds.)
''Handbook of Mathematical Psychology'', Vol. II
pp. 493–579. New York, NY: John Wiley and Sons. * 1974, with Lawrence B. Slobodkin, "An optimal strategy of evolution". ''Q. Rev. Biol''. 49:181–200 * 1979, "Some Problems Relating to Randomly Constructed Biased Networks." ''Perspectives on Social Network Research'':119–164. * 1989, with Y. Yuan, "Some Aspects of Epidemics and Social Nets." Pp. 327–348 in ''The Small World'', ed. by Manfred Kochen. Norwood, NJ: Ablex.

About Rapoport

* * * * *