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 bachelors degree in mathematics from Williams College in 1954, a masters 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 émérité.
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.
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.
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.
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 is the 2013 winner of the INFORMS John von Neumann Theory Prize.
- 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.
- Balinski, M. L. (1961), "An algorithm for finding all vertices of convex polyhedral sets", J. Soc. Indust. Appl. Math. 9: 72–88, doi:10.1137/0109008, MR 0142057.
- —— (1961), "On the graph structure of convex polyhedra in n-space", Pacific Journal of Mathematics 11 (2): 431–434, doi:10.2140/pjm.1961.11.431, MR 0126765.
- —— (1965), "Integer Programming : Methods, Uses, Computation", Management Science 12: 253–313, doi:10.1287/mnsc.12.3.253, JSTOR 2627582. 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).
- —— (1970), "On a selection problem", Management Science 17 (3): 230–231, doi:10.1287/mnsc.17.3.230.
- Laudatio, Friedrich Pukelsheim, University of Augsburg, retrieved 2013-11-27.
- Michel Louis Balinski at the Mathematics Genealogy Project
- Michel Balinski receives the 2013 John von Neumann Theory Prize, École Polytechnique, retrieved 2013-11-27.
- Wolfe, Philip, The Mathematical Programming Society, Mathematical Optimization Society, retrieved 2013-11-27.
- Ziegler, Günter M. (1995), "Section 3.5: Balinski's Theorem: The Graph is d-Connected", Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag.
- INFORMS award recipients: Michel L. Balinski, retrieved 2013-11-27.
- Hochbaum, Dorit (2004), "50th Anniversary Article: Selection, Provisioning, Shared Fixed Costs, Maximum Closure, and Implications on Algorithmic Methods Today", Management Science 50 (6): 709–723, doi:10.1287/mnsc.1040.0242.