The law of categorical judgment (corrected) extended: a note on Rosner and Kochanski (2009)

Rosner and Kochanski (2009) noticed an inconsistency in the mathematical statement of the Law of Categorical Judgment and derived "the valid equation, the Law of Categorical Judgment (Corrected)" (p. 125). The purpose of this comment is to point out that the law can be corrected in many different ways, leading to substantially different equations. The different versions have different consequences for the predicted distributions of the responses and, hence, for fitting real data. Some of these consequences are unexpected and sometimes undesirable. Researchers should be aware of the different possibilities as they may lead to pronouncedly different accounts of given data.