On Three Measures of Explanatory Power with Axiomatic Representations

Jonah N. Schupbach and Jan Sprenger ([2011]) and Vincenzo Crupi and Katya Tentori ([2012]) have recently proposed measures of explanatory power and have shown that they are characterized by certain arguably desirable conditions or axioms. I further examine the properties of these two measures, and a third measure considered by I. J. Good ([1960]) and Timothy McGrew ([2003]). This third measure also has an axiomatic representation. I consider a simple coin-tossing example in which only the Crupi-Tentori measure does not perform well. The Schupbach-Sprenger and Good-McGrew measures are based on different notions of explanatory power, but both are tenable.