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. © 2008 Elsevier B.V. All rights reserved.
Hild, M., & Spohn, W. (2008). The measurement of ranks and the laws of iterated contraction. Artificial Intelligence, 172(10), 1195–1218. https://doi.org/10.1016/j.artint.2008.03.002