Abstract
Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
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Literature
Birkhoff, Garrett. 1948.Lattice Theory. (Revised edition.) AMS Colloquium Publication.
Richardson, Moses. 1958.Fundamentals of Mathematics. (Revised edition.) New York: Macmillan and Co.
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Robison, G.B. Abstract power structures (APS) and related bumping orders. Bulletin of Mathematical Biophysics 29, 207–216 (1967). https://doi.org/10.1007/BF02476894
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DOI: https://doi.org/10.1007/BF02476894