Landau set: Difference between revisions
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In [[voting system]]s, the '''Landau set''' (or '''uncovered set''', or '''Fishburn set''') is the set of candidates ''x'' such that for every other candidate ''y'', there is some candidate ''z'' (possibly the same as ''x'', but distinct from ''y'') such that ''y'' is not preferred to ''x'' and ''z'' is not preferred to ''y''. |
In [[voting system]]s, the '''Landau set''' (or '''uncovered set''', or '''[[Peter Fishburn|Fishburn]] set''') is the set of candidates ''x'' such that for every other candidate ''y'', there is some candidate ''z'' (possibly the same as ''x'', but distinct from ''y'') such that ''y'' is not preferred to ''x'' and ''z'' is not preferred to ''y''. |
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The Landau set is a nonempty subset of the [[Smith set]]. It was discovered by Nicholas Miller. |
The Landau set is a nonempty subset of the [[Smith set]]. It was discovered by Nicholas Miller. |
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Revision as of 04:47, 4 December 2009
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In voting systems, the Landau set (or uncovered set, or Fishburn set) is the set of candidates x such that for every other candidate y, there is some candidate z (possibly the same as x, but distinct from y) such that y is not preferred to x and z is not preferred to y.
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. [1]
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