Measuring Ranks via the Complete Laws of Iterated Contraction

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper gives a complete axiomatization of that behavior, i.e., a complete set of laws of iterated contraction. It does so by showing how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multi-plicative constant and thus how to measure ranks on a ratio scale