Landau set

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In voting systems, the Landau set (or uncovered set, or Fishburn set) is the set of candidates such that for every other candidate , there is some candidate (possibly the same as or ) such that is not preferred to and is not preferred to . In notation, is in the Landau set if , , .

The Landau set is a nonempty subset of the Smith set. It was discovered by Nicholas Miller.


  • Nicholas R. Miller, "Graph-theoretical approaches to the theory of voting", American Journal of Political Science, Vol. 21 (1977), pp. 769–803.
  • Nicholas R. Miller, "A new solution set for tournaments and majority voting: further graph-theoretic approaches to majority voting", American Journal of Political Science, Vol. 24 (1980), pp. 68–96.
  • Norman J. Schofield, "Social Choice and Democracy", Springer-Verlag: Berlin, 1985.
  • Philip D. Straffin, "Spatial models of power and voting outcomes", in "Applications of Combinatorics and Graph Theory to the Biological and Social Sciences", Springer: New York-Berlin, 1989, pp. 315–335.
  • Elizabeth Maggie Penn, "Alternate definitions of the uncovered set and their implications", 2004.
  • Nicholas R. Miller, "In search of the uncovered set", Political Analysis, 15:1 (2007), pp. 21–45.
  • William T. Bianco, Ivan Jeliazkov, and Itai Sened, "The uncovered set and the limits of legislative action", Political Analysis, Vol. 12, No. 3 (2004), pp. 256–276. [1]