Fishburn Set

In voting systems, 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 $x$ or $z$) 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. 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

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