Michel Balinski

Michel Louis Balinski
From left: Michel Balinski, Friedrich Pukelsheim, Steven Brams, Oberwolfach 2004
Born	(1933-10-06)October 6, 1933 Geneva, Switzerland
Residence	France
Nationality	Polish
Fields	Mathematics
Alma mater	Princeton University
Doctoral advisor	Albert W. Tucker
Doctoral students	Louis Billera
Notable awards	John von Neumann Theory Prize (2013)

Michel Louis Balinski (born 1933) is a mathematician, econometrician, operations researcher, and political scientist.

Life and work

Balinski was born in Geneva; he was the son of a Polish diplomat at the League of Nations and the grandson of Polish bacteriologist and UNICEF founder Ludwik Rajchman. His family fled the Nazis to France, Portugal, and finally the U.S., where he grew up speaking French natively at home. He earned a bachelor's degree in mathematics from Williams College in 1954, a master's degree in economics from the Massachusetts Institute of Technology, and finally his Ph.D. in mathematics again from Princeton University in 1959 under the supervision of Albert W. Tucker.

He taught at Princeton University, the Wharton School of the University of Pennsylvania, the City University of New York, Yale University, and Stony Brook University. One of his doctoral students at the City University was another noted mathematician, Louis Billera, through whom he has many academic descendants. He moved to France in 1980 where, at the École Polytechnique, he directed the Laboratoire d'Econométrie for ten years. He retired in 1999, and continues to be a Directeur de Recherche de classe exceptionnelle émérite.

He was one of the founders of the Mathematical Optimization Society in 1970, and in 1971 he founded and became editor-in-chief of the journal Mathematical Programming, the official journal of the society; he also chaired the society from 1986 to 1989.

Research contributions

Balinski's Ph.D. thesis concerned the vertex enumeration problem, the algorithmic problem of listing all vertices of a convex polytope or of a linear program, and some his subsequent work continued to concern polyhedral combinatorics. Balinski's theorem, which he published in 1961, gives a lower bound on the graph-theoretic connectivity of every convex polytope. It shows that, for an n-dimensional polytope, at least n vertices must be removed in order to disconnect the graph of the remaining vertices and edges. He also proved the Hirsch conjecture for a class of polytopes arising in combinatorial optimization problems.

In 1970, he published one of the earliest papers on the closure problem and its applications to transportation planning.

His 1982 book with Peyton Young concerns the apportionment paradox, and his more recent book with R. Laraki concerns majority judgment methods of avoiding this and similar electoral paradoxes by asking voters for evaluations of candidates rather than rank-orderings of them.

He has also made important contributions to linear programming and integer programming, and to the stable marriage problem and other matching problems.

Awards and honors

In 1965 he won the Frederick W. Lanchester Prize of the Institute for Operations Research and the Management Sciences (INFORMS) for his survey paper on integer programming. His book on electoral theory, Fair Representation: Meeting the Ideal of One Man, One Vote, won the George H. Hallett Award of the American Political Science Association in 2008. He won a Lester R. Ford Award (shared with H. P. Young) in 1976 and unshared in 2009. He is the 2013 winner of the INFORMS John von Neumann Theory Prize.

In 2004 he was given an honorary doctorate by the University of Augsburg.

Selected publications

Books

• Fair Representation: Meeting the Ideal of One Man, One Vote, M. L. Balinski and H. Peyton Young, Yale University Press, 1982, and Brookings Institution Press, 2001, ISBN 9780815716341.
• Majority Judgment: Measuring, Ranking, and Electing, M. L. Balinski and Rida Laraki, MIT Press, 2010, ISBN 9780262015134.

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).
• .