Michel Balinski

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Michel Louis Balinski (born October 6 or October 7, 1933 in Geneva ; † February 4, 2019 ) was an American mathematician , economist and political scientist , known for his contributions to the theory of elections and mathematical optimization .


From left: Michel Balinski, Friedrich Pukelsheim , Steven J. Brams , Oberwolfach 2004

Balinski is the son of a Polish diplomat with the League of Nations and grandson of Ludwik Rajchman . During the time of National Socialism, his family fled via France to the United States, where he grew up bilingual - French was spoken in the family. He studied at Williams College with a bachelor's degree in 1954 and at the Massachusetts Institute of Technology with a master's degree in 1956. He received his doctorate in 1959 from Princeton University with Albert W. Tucker (An algorithm of finding all vertices of convex polyhedral sets). He was then an instructor and then a lecturer at Princeton and from 1963 Associate Professor of Economics at the University of Pennsylvania . In 1965 he became an associate professor and later professor of mathematics at the City University of New York . From 1978 to 1980 he was a professor at Yale University and from 1983 to 1989 at the State University of New York at Stony Brook and at the same time at the École polytechnique (laboratory for econometrics) and did research for the CNRS . In 1999 he retired.

In the 1960s he advised Mobil Oil Research, the City of New York and the Rand Corporation, among others . From 1975 to 1977 he was at the IIASA in Laxenburg, 1972/73 visiting professor in Lausanne and 1974/75 in Grenoble.


Since his dissertation he has dealt with the combinatorics of polyhedra. Balinski's theorem (1961) makes statements about the network property of graphs that correspond to convex polyhedra in three and more dimensions and generalizes a theorem by Ernst Steinitz (1922) that polyhedron graphs of three-dimensional polyhedra are precisely the 3-connected plane graphs . Balinski proved that in d dimensions ( ) the graph is at least d-connected, i.e. if you remove (d-1) any nodes, the graph remains connected.

In 1982 he and Peyton Young proved that there are always paradoxes of seat allocation in electoral systems when three or more parties compete and the quota condition applies ( Balinski and Young's rule of impossibility ). In 1970 he was one of the first with JMW Rhys to look at the closure problem . B. can be formulated as a transport problem in networks.

He also made important contributions to linear and nonlinear optimization and mathematical economics.

He was a US citizen.

Awards and honors


  • On the graph structure of convex polyhedra in n-space, Pacific J. Math., Vol. 11, 1961, pp. 431-434
  • Integer Programming: Methods, Uses, Computation, Management Science, Volume 12, 1965, 253–313 (received the Lanchester Prize)
  • with H. Peyton Young : Fair Representation: Meeting the Ideal of One Man, One Vote, Yale University Press 1982, Brookings Institution Press 2001 ISBN 9780815716341 .
  • with Rida Laraki: Majority Judgment: Measuring, Ranking, and Electing, MIT Press, 2010,

Individual evidence

  1. Life data according to American Men and Women of Science , Thomson Gale 2004.
  2. Michel Balinski informs.org, accessed May 7, 2019
  3. Michel Balinski in the Mathematics Genealogy Project (English) Template: MathGenealogyProject / Maintenance / id used. Published in J. Soc. Indust. Appl. Math., Vol. 9, 1961, pp. 72-88
  4. Bogomolny The constitution and paradoxes, Cut the Knot 2002
  5. Balinski On a selection problem , Management Science, Volume 17, 1970, pp. 230-231.
  6. Rhys A selection problem of shared fixed costs and network flows , Management Science, Volume 17, 1970, pp. 200-207.
  7. ^ Frederick W. Lanchester Prize. (No longer available online.) Informs.org ( Institute for Operations Research and the Management Sciences ), archived from the original on October 2, 2015 ; accessed on February 16, 2016 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.informs.org