Landau set

In voting systems, the Landau set (or uncovered set, or Fishburn set) is the set of candidates ${\displaystyle x}$ such that for every other candidate ${\displaystyle z}$, there is some candidate ${\displaystyle y}$ (possibly the same as ${\displaystyle x}$ or ${\displaystyle z}$) such that ${\displaystyle y}$ is not preferred to ${\displaystyle x}$ and ${\displaystyle z}$ is not preferred to ${\displaystyle y}$. In notation, ${\displaystyle x}$ is in the Landau set if ${\displaystyle \forall \,z}$, ${\displaystyle \exists \,y}$, ${\displaystyle x\geq y\geq z}$.

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