voting system An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections m ...

s, the Landau set (or uncovered set, or Fishburn set) is the set of candidates

x

such that for every other candidate

z

, there is some candidate

y

(possibly the same as

x

z

) such that

y

is not preferred to

x

and

z

is not preferred to

y

. In notation,

x

is in the Landau set if

\forall \,z

\exists \,y

x \ge y \ge z

. The Landau set is a nonempty subset of the

Smith set In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats ever ...

. It was discovered by Nicholas Miller.

References

*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. . . Voting theory {{applied-math-stub