Counting and timing models in psychophysics and the conjoint Weber's law

J. C. Falmagne, G. Iverson, and S. Marcovici ((1979). Psychological Review, 86, 25–43) proposed a generalization of Weber's law, which they called the conjoint Weber's law. Empirically, the law sometimes holds. When it fails, the data satisfy a relation that Falmagne et al. identify as the conjoint Weber's inequality. This paper investigates the ability of counting and timing models of psychophysics to predict Weber's law and the conjoint Weber's law. It is shown that although the timing model naturally predicts both laws to hold, all reasonable counting models predict them to fail. Instead, counting models naturally predict Weber's inequality and the conjoint Weber's inequality.