The measurement of ranks and the laws of iterated contraction

Authors:
Matthias Hild;Wolfgang Spohn
Affiliations:
Darden Graduate School of Business Administration, PO Box 6550, Charlottesville, VA 22906, USA;Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany
Venue:
Artificial Intelligence
Year:
2008

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Abstract

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.