In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex...

methodology can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution...

disconnect the graph of the remaining vertices and edges; it is known as Balinski's theorem. He also proved the Hirsch conjecture for several different classes...

Viviani's theorem (Euclidean geometry) Alexandrov's uniqueness theorem (discrete geometry) Balinski's theorem (combinatorics) Bang's theorem (geometry)...

if and only if it has an orientation that is strongly connected. Balinski's theorem states that the polytopal graph (1-skeleton) of a k-dimensional convex...

segments. The 3-connectivity of a polyhedral graph is a special case of Balinski's theorem that the graph of any k {\displaystyle k} -dimensional convex polytope...

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the...

polytope forms a k-vertex-connected graph (Balinski's theorem). As a partial converse, Steinitz's theorem states that any 3-vertex-connected planar graph...

at the sum of the vectors in S. is a n-vertex-connected graph, by Balinski's theorem. is planar (can be drawn with no crossings) if and only if n ≤ 3....

obtained from the vertices and edges of polytopes (their 1-skeleta). Balinski's theorem states that the graph obtained in this way from any d-dimensional...

In a polygon, two edges meet at each vertex; more generally, by Balinski's theorem, at least d edges meet at every vertex of a d-dimensional convex polytope...

planar graph. Additionally, by Balinski's theorem, it is a 3-vertex-connected graph. According to Steinitz's theorem, these two graph-theoretic properties...

historian and professor at Harvard University Michel Balinski 1954, known for Balinski's theorem; mathematician and economist, winner of the John von...

many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments...

judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting...

method of rounding suffers one or more paradoxes, as proven by the Balinski–Young theorem. The mathematical theory of apportionment identifies what properties...

allowing the house size to vary, satisfies strong monotonicity in this sense. Balinski and Young proved that an apportionment method is VRM if-and-only-if it...

than 2 or 3, or giving party C any other than 0 or 1 seat. The Balinski–Young theorem proved in 1980 that if an apportionment method satisfies the quota...

situations called cyclic ties. Rated voting systems are not subject to Arrow's theorem. Whether such methods are spoilerproof depends on the nature of the rating...

impossibility theorem, a theorem on the limitations of ranked-choice voting Gibbard's theorem, a generalization of the Gibbard-Satterthwaite theorem applicable...

Webster's method and Huntington-Hill perform well even without quota-caps. Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal...

voting rules, highest medians are not subject to Arrow's impossibility theorem. However, critics note that highest median rules violate participation...

first-round vote needed to survive earlier rounds. By Black's median-voter theorem, the candidate who appeals most to the median voter will be the majority-preferred...

Victoriano (2016-09-01). "The whole and its parts: On the coherence theorem of Balinski and Young". Mathematical Social Sciences. 83: 11–19. doi:10.1016/j...

Social Choice and Welfare. 59 (2): 305–333. doi:10.1007/s00355-022-01397-4. Balinski, Michel; Laraki, Rida (2020-03-01). "Majority judgment vs. majority rule"...

is minimized when the weight of C is maximized. By the max-flow min-cut theorem, a minimum cut, and the optimal closure derived from it, can be found by...

to maximize one's satisfaction with the election's results. Gibbard's theorem shows that no voting system has a single "always-best" strategy, i.e. one...

1007/978-3-319-64707-4_7, ISBN 978-3-319-64707-4, retrieved 2024-05-10 Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal...

1007/978-3-319-64707-4_9, ISBN 978-3-319-64707-4, retrieved 2024-05-10 Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal...

1007/s00355-020-01269-9. S2CID 226196615 – via Springer Link. Smith, Warren D. "On Balinski & Laraki's "majority judgment" median-based range-like voting scheme"....