Michel Balinski

Born: October 6, 1933

Brief Biography

Balinski Fellow Election Portrait

Michel Louis Balinski is a major figure in operations research, mathematics, economics, and political science, best known for bringing OR methodology to bear on the electoral process. Balinski was born in Geneva, Switzerland to a family actively involved in international relations. His father was a Polish diplomat at the League of Nations and his grandfather, Ludwik Rajchman, was the founder of UNICEF, the United Nations Children’s Fund. The Balinskis and Rajchmans fled the growing Nazi threat, leaving France via Spain and Portugal and reaching the United States in 1940. He earned his bachelor’s degree in mathematics at Williams College and a master’s in economics from the Massachusetts Institute of Technology. Balinski went on to Princeton University and studied under Albert W. Tucker and Ralph E. Gomory, earning a PhD in mathematics in 1959.

Balinski spent his first five postgraduate years at Princeton University, the consulting firm Mathematica, and the University of Pennsylvania. In 1965, he was appointed a professor of mathematics at the Graduate Center of the City University of New York. During his time at CUNY, he served as chairman of the System and Decision Sciences area at the International Institute for Applied Systems Analysis in Austria, spent sabbatical years at the Ecole Polytechnique Fédérale de Lausanne and l’Université de Grenoble, and a year as an IBM World Trade Corporation Fellow in Paris. Balinski then relocated to Yale for several years before taking a permanent position as Directeur de recherche de classe exceptionnelle of the CNRS (its top research title, the equivalent of a chaired professorship) at the Ecole Polytechnique in Paris, where for a decade he was Director of the Laboratoire d’Econométrie. Concurrently, from 1983 to 1990, he was Leading Professor of Applied Mathematics and Statistics and of Economics at SUNY Stony Brook, where he was founder and first Director of the Institute for Decisions Sciences (which later became The Center for Game Theory).

Balinski has made important contributions to linear and nonlinear programming, combinatorial optimization, and stable matching problems. In 1961, he proved “Balinski’s theorem” – a graph-theoretic property of the skeleton of multi-dimensional polytopes – and developed an algorithm for finding all vertices of a convex polyhedron. In 1970, he published one of the earliest papers on the closure problem (a graph-theoretic problem with applications in transportation planning, strip mining, defense, and scheduling jobs in a job shop). His 1965 Management Science article, “Integer Programming: Methods, Uses, Computation” was awarded INFORMS’s Frederick W. Lanchester Prize.

For all of his contributions to traditional OR, Balinski is best known for his research and publications on electoral systems. His 1982 book with H. P. Young has had direct practical application in apportioning the seats of assemblies to regions in several countries (including the UK). He conceived and developed “biproportional apportionment” that has been adopted (as of 2014) in five of Switzerland’s cantonal elections. His 2011 book with Rida Laraki proposes a new theory and method of voting called “majority judgment” 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). He has twice won the Mathematical Association of America’s Lester R. Ford Award for articles on voting, one in 1975 with H.P. Young on apportionment, the other in 2009 on how to avoid gerrymandering.

Balinski has been a dedicated member of the Mathematical Programming Society (today’s Mathematical Optimization Society). He was one of the six founding members and was the founder and first editor-in-chief of its journal, Mathematical Programming (1970-1980). He went on to serve as MPS president for three years in the late 1980s.

Though he has since retired from active teaching, Balinski continues to be active in research and has earned accolades from the OR community. In 2013, the Institute for Operations Research and the Management Sciences (INFORMS) awarded him the John von Neumann Theory Prize, one of the highest honors an operations researcher can receive. He was celebrated for having “made major theoretical and practical contributions in both traditional and nontraditional areas of OR,” most importantly “in the domain of electoral decisions, namely, representation and apportionment on the one hand, and voting on the other.” The following year he was elected an INFORMS Fellow. Balinski is also a recipient of the George H. Hallett Award given by the APSA for his influential book with Young, Fair Representation: Meeting the Ideal of One-Man One-Vote (1982, 2001). In 2004, Balinski received an honorary doctorate in mathematics from the University of Augsburg.

Other Biographies

Wikipedia Entry for Michel Balinski

International Federation of Operational Research Societies. Michel Balinski. Accessed March 30, 2015. (link)

Balinski ML (2013) John von Neumann Theory Prize Acceptance Remarks.   Accessed June 13, 2017 (link)


Williams College, BA 1954

Massachusetts Institute of Technology, MS 1956

Princeton University, PhD 1959 (Mathematics Genealogy)


Academic Affiliations
Non-Academic Affiliations
  • RAND Corporation
  • French National Center for Scientific Research (CNRS)
  • International Institute for Applied Systems Analysis
  • Mathematica, Inc

Key Interests in OR/MS

  • Economics of Social Choice
Application Areas

Awards and Honors

Frederick W. Lanchester Prize 1965

Mathematical Association of America Lester R. Ford Award 1976 & 2009

American Political Science Association George H. Hallet Award 2008

John von Neumann Theory Prize 2013

Institute for Operations Research and the Management Sciences Fellow 2014

Professional Service

Mathematical Programming Society (Mathematical Optimization Society), President/Chair 1986-1989

Selected Publications

Balinski M. L. (1961) On the graph structure of convex polyhedral in n-space. Pacific Journal of Mathematics 11: 431-434.

Balinski M. L. (1965) Integer Programming: Methods, Uses, Computation. Management Science, 12(2): 253-313.

Balinski M. L. & Baumol W. J. (1968) The dual in nonlinear programming and its economic interpretation. The Review of Economic Studies, XXXV: 237-256.

Balinski M. L. & Tucker A. W. (1969) Duality theory of linear programs: a constructive approach with applications. SIAM Review, 11: 347-377.

Balinski M. L. (1970) On a selection problem. Management Science, 17(2): 230-231.

Balinski M. L. & Young H. P. (1975) The quota method of apportionment. The American Mathematical Monthly, 82: 701-730.

Balinski M. L. & Young H. P. (1982) Fair Representation: Meeting the Ideal of One Man, One Vote. Brookings Institution Press: Washington, DC.

Balinski M. L. & Demange G. (1989) An axiomatic approach to proportionality between matrices. Mathematics of Operations Research, 14: 700-719.

Balinski M. L. & Sönmez T. (1999) A tale of two mechanisms: student placement. Journal of Economic Theory, 84: 73-94.

Baïou M. & Balinski M. L. (2002) The stable allocation (or ordinal transportation) problem. Mathematics of Operations Research, 27: 662-680.

Balinski M. L. (2004) Le suffrage universel inachevé. Editions Belin: Paris.

Balinski M. L. (2008) Fair Majority Voting (or How to Eliminate Gerrymandering). The American Mathematical Monthly, 115(1): 97-113.

Balinski M. L. & Laraki R. (2011) Majority Judgment: Measuring, Ranking, and Electing. MIT Press: Cambridge, MA.

Balinski M. L. & Laraki R. (2014) Judge: Don’t Vote!. Operations Research, 62: 483-511.

Additional Resources

Balinski M. L. (2007) Representing, electing and ranking. Messenger Lectures, September 25-27. Abstracts and References, Slides, Videos and Biographical Information. Cornell University, Ithaca New York (courtesy of Louis Billera). 

Balinski M. L. (2012) Le jugement majoritaire : une nouvelle théorie du vote. Lecture, February 29. Video. Collège de France, Paris, France. (link)

Balinski M. L.  Google website.  Accessed December 28, 2016 (link)