Michel Louis Balinski (born Michał Ludwik Baliński; October 6, 1933 – February 4, 2019) was an
applied mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
One ...
,
economist
An economist is a professional and practitioner in the social science discipline of economics.
The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are ...
,
operations research analyst and
political scientist
Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and l ...
. As a
Polish-American, educated in the United States, he lived and worked primarily in the United States and France. He was known for his work in optimisation (combinatorial, linear, nonlinear), convex polyhedra, stable matching, and the theory and practice of electoral systems, jury decision, and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the
C.N.R.S. at the École Polytechnique (Paris). He was awarded the
John von Neumann Theory Prize
The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS)
is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operati ...
by INFORMS in 2013.
Michel Louis Balinski died in
Bayonne
Bayonne (; eu, Baiona ; oc, label= Gascon, Baiona ; es, Bayona) is a city in Southwestern France near the Spanish border. It is a commune and one of two subprefectures in the Pyrénées-Atlantiques department, in the Nouvelle-Aquitain ...
,
France. He maintained an active involvement in research and public appearances, his last public engagement took place in January 2019.
Early life
Michel Balinski was born in
Geneva, Switzerland, the grandson of the Polish
bacteriologist
A bacteriologist is a microbiologist, or similarly trained professional, in bacteriology -- a subdivision of microbiology that studies bacteria, typically pathogenic ones. Bacteriologists are interested in studying and learning about bacteria, ...
and founder of
UNICEF,
Ludwik Rajchman.
Brought up by his mother Irena (Rajchman) Balinska and his grandparents, they were living in France when the Nazis invaded in 1940. They fled via Spain and Portugal to the United States. He graduated from the Edgewood School in Greenwich CT in 1950, earned a B.A. degree cum laude in mathematics at
Williams College in 1954 and a M.Sc. in economics at the
Massachusetts Institute of Technology in 1956. He completed a Ph.D. in mathematics at
Princeton University in 1959 under the supervision of
Albert W. Tucker.
Career
After completing his Ph.D. Balinski remained at
Princeton University as a research associate then lecturer in mathematics. From 1963 to 1965 he was associate professor of economics at the
Wharton School of the University of Pennsylvania. He was then appointed to the Graduate School of the
City University of New York, first as associate professor then (as of 1969) professor of mathematics. One of his doctoral students at the City University was another noted mathematician, Louis Billera, through whom he has many academic descendants. In 1978 he was appointed professor of organization and management and of administrative sciences at
Yale
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the worl ...
.
In parallel with his academic work, Balinski engaged in consulting as of the time he was a graduate student at Princeton. A participant in the beginnings of what became the consulting firm Mathematica, he was a senior consultant with the firm from 1962 to 1974. He also acted as a consultant elsewhere, including the
Rand Corporation
The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed ...
, Mobil Oil Research, the
ORTF (Office de Radiodiffusion-Télévision Française), the Mayor's office of the City of New York (as member of the Operations Research Council), and Econ, Inc. From 1975 to 1977 he was chairman of System and Decision Sciences at IIASA (International Institute for Applied Systems Analyses) at Laxenburg, Austria.
In 1980 Balinski settled in France, becoming Directeur de Recherche de classe exceptionnelle of the CNRS (
Centre National de Recherche Scientifique) at the Laboratoire d’Econométrie of the
Ecole Polytechnique in 1983. Concurrently he was Leading Professor of Applied Mathematics and Statistics and of Economics at
Stony Brook University
Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system' ...
(1983–1990), where he founded and was the first Director of the Institute for Decision Sciences (that has since become the Center for Game Theory in Economics).
Upon becoming director of the Laboratoire d’Econométrie (1989 to 1999), he co-founded and co-directed the joint Ecole Polytechnique/Université de Paris 1 masters program "Modélisation et méthodes mathématiques en économie: optimisation et analyse stratégiques," and its successor the joint Ecole Polytechnique/Université Pierre et Marie Curie (Paris 6) masters program "Optimisation, jeux et modélisation en économie."
He was a visiting professor at other institutions, including the Ecole Polytechnique Fédérale de Lausanne (1972–1973), the Université Scientifique et Médicale de Grenoble (1974–1975), the
Universidad de Chile
The University of Chile ( es, Universidad de Chile) is a public research university in Santiago, Chile. It was founded on November 19, 1842, and inaugurated on September 17, 1843. in
Santiago (1994), and
INSEAD in Fontainebleau (1997–1998).
[Michel Balinski receives the 2013 John von Neumann Theory Prize](_blank)
, École Polytechnique, retrieved 2013-11-27.
Balinski was the founding editor-in-chief of the journal ''
Mathematical Programming'' in 1971, one of the founders of the
Mathematical Optimization Society in 1970, and president of that society from 1986 to 1989.
Research contributions
Balinski's Ph.D. thesis concerned the
vertex enumeration problem In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation ...
, the
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
ic problem of listing all vertices of a
convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the w ...
or finding all optimal solutions of a
linear program
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming i ...
, and some of his subsequent work continued to concern
polyhedral combinatorics. The thesis includes the fundamental theorem, published in 1961, that the skeletons of polytopes in "n"-space viewed as graphs are "n"-connected, meaning that at least "n" edges must be removed to disconnect the graph of the remaining vertices and edges; it is known as
Balinski's theorem
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex polyhedra and higher-dimensional convex polytopes. It states that, if one forms an undirected ...
. He also proved the
Hirsch conjecture
In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge- vertex graph of an ''n''- facet polytope in ''d''- dimensional Euclidean space has diameter no more than ''n'' − ''d' ...
for several different classes of polytopes associated with the transportation problem, showed that the diameter of the skeleton of the assignment polytope viewed as a graph is 2, and found the polytope whose vertices are the stable matchings of the university admissions problem.
His contributions to linear and nonlinear optimization include a primal/dual simplex method that incorporates a natural proof of termination and leads to a self-contained, elementary but rigorous, constructive account of the theory and the basic computational tool of linear programming; the use and economic interpretation of dual prices; and a proof that prices in von Neumann's model of an expanding economy are marginal values. His work in integer programming includes the formulation and analysis of the fixed cost transportation problem; one of the first computationally successful practical uses of Gomory's cutting plane algorithm (1968, truck deliveries with cost functions in part concave, in part convex); and an extensive survey paper on integer programming which was awarded INFORM's
Lanchester Prize in 1965.
Together with Mourad Baïou, he developed a new formulation of stable matchings and generalizations in terms of graphs, providing a unified notation and tool leading to new proofs of known results and new results; notably, a characterization of the university admissions polytope, and a generalization of matching opposites (e.g., men and women, students and universities) to matching opposites in real numbers (e.g., time spent together).
In 1970, he published one of the earliest papers on the
closure problem and its applications to transportation planning.
Electoral systems
Balinski has made important contributions to the theory of electoral systems, namely, representation and apportionment on the one hand, and voting on the other. His 1982 book with H. Peyton Young has had direct practical application in apportioning the seats of assemblies to regions in several countries (including the UK). He conceived and developed with others "
biproportional apportionment
Biproportional apportionment is a proportional representation method to allocate seats in proportion to two separate characteristics. That is, for two different partitions each part receives the proportional number of seats within the total numb ...
" that has been adopted (as of 2014) in five of Switzerland's cantonal elections. His 2010 book with Rida Laraki proposes a new theory and method of voting called "
majority judgment
Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating.
Unlike other vo ...
" where voters evaluate the merit of each candidate in a well-defined ordinal scale (instead of voting for one or several candidates, or rank-ordering them) and majorities determine society's evaluation of each candidate and thereby its rank-ordering of them all. This, they prove, overcomes the most important drawbacks of the traditional theory of voting (including
Arrow's impossibility theorem
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...
).
Awards and honors
Phi Beta Kappa
The Phi Beta Kappa Society () is the oldest academic honor society in the United States, and the most prestigious, due in part to its long history and academic selectivity. Phi Beta Kappa aims to promote and advocate excellence in the liberal ar ...
, Williams College 1954;
Frederick W. Lanchester Prize, INFORMS 1965;
I.B.M. World Trade Corporation Fellow 1969–1970;
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisco ...
, Mathematical Association of America 1976; Honorary Master of Arts, Privatum, Yale University 1978; Special Service Award, Mathematical Optimization Society, 1982; Honorary Doctorate (Ehrendoktors, Mathematisch-Naturwissenshaftlichen)
Universität Augsburg, 2004;
[Laudatio](_blank)
Friedrich Pukelsheim, University of Augsburg
The University of Augsburg (german: Universität Augsburg) is a university located in the Universitätsviertel section of Augsburg, Germany. It was founded in 1970 and is organized in 8 Faculties.
The University of Augsburg is a relatively you ...
, retrieved 2013-11-27. Murat Sertel Lecturer (inaugural lecture), 8th International Meeting of the Society for Social Choice and Welfare, Istanbul, July 2006; Messenger Lecturer, Cornell University, September 2007; IFORS Distinguished Lecturer, INFORMS National Meeting, Washington, D.C., October 2008; George H. Hallet Award, 2009;
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisco ...
, Mathematical Association of America, 2009; Celebration of Michel Balinski's 78 years at the 23rd International Conference on Game Theory, SUNY Stony Brook, July 2012;
John von Neumann Theory Prize
The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS)
is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operati ...
, INFORMS, 2013;
INFORMS
The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger ...
Fellow, 2014.
[INFORMS award recipients: Michel L. Balinski](_blank)
retrieved 2013-11-27.
Selected publications
Books
*''Fair Representation: Meeting the Ideal of One Man, One Vote'', Michel L. Balinski and
H. Peyton Young, Yale University Press, 1982. 2nd edition, Brookings Institution Press, Washington, D.C., 2001. Japanese translation, Chikura-Shobo Publishing Co., Tokyo, 1987. .
iven the George H. Hallet Award, 2009, "[Fora book published at least 10 years ago that has made a lasting contribution to ... representation and electoral systems."]
*''Le Suffrage Universel Inachevé'', Michel Balinski, Editions Belin, 2004, .
*''Majority Judgment: Measuring, Ranking, and Electing'', Michel Balinski and Rida Laraki, MIT Press,
2010, .
Articles
*.
*.
*. Reprinted in ''Mathematics of the Decision Sciences'' (1968), in ''Proceedings of the Princeton Symposium on Mathematical Programming'', 1970, and in ''50 Years of Integer Programming 1958–2008'' (2010). Given the 1965
Lanchester Prize
*
*
*.
*
*. Given the 1976
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisco ...
*
*
*
*
*
*.
*
*.Given the
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisco ...
*.
*
References
External links
Biography of Michel Balinskifrom the Institute for Operations Research and the Management Sciences
*
Ludwik Rajchman – Grandfather of Michel Balinski, Founder of
UNICEFMichel Balinski's websiteMessenger LecturesApportionment: Balinski and Young’s ContributionMajority Judgment: Measuring, Ranking and ElectingA Biography of Michel Balinskiin the book: A Mathematical View of Our World.
IFORS Distinguished Lecture George H. Hallet Award 2009Remembering Michel BalinskiIn Memoriam: Michel Balinski (1933-2019)
{{DEFAULTSORT:Balinski, Michel L.
1933 births
2019 deaths
20th-century American mathematicians
Williams College alumni
MIT School of Humanities, Arts, and Social Sciences alumni
Princeton University alumni
Princeton University faculty
University of Pennsylvania faculty
City University of New York faculty
Yale University faculty
Stony Brook University faculty
American operations researchers
Econometricians
American political scientists
American people of Polish descent
21st-century American mathematicians
John von Neumann Theory Prize winners
Fellows of the Institute for Operations Research and the Management Sciences