We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Ríos Insua (Theory Decis 33:83–100, 1992) and Alon and Lehrer (J Econ Theory 151:476–492, 2014) is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott (J Math Psychol 1:233–247, 1964), relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.
Cancellation axioms Comparative probability Qualitative probability Incomplete relations
Alon, S., & Lehrer, E. (2014). Subjective multi-prior probability: A representation of a partial likelihood relation. Journal of Economic Theory, 151, 476–492.CrossRefGoogle Scholar
Fine, T. L. (1973). Theories of probability. New York: Academic Press.Google Scholar
Kraft, C., Pratt, J., & Seidenberg, A. (1959). Intuitive probability on finite sets. The Annals of Mathematical Statistics, 30(2), 408–419.CrossRefGoogle Scholar
Ríos Insua, D. (1992). On the foundations of decision making under partial information. Theory and Decision, 33(1), 83–100.CrossRefGoogle Scholar
Savage, L. J. (1954). The foundations of statistics. New York: Wiley.Google Scholar
Scott, D. (1964). Measurement structures and linear inequalities. Journal of Mathematical Psychology, 1(2), 233–247.CrossRefGoogle Scholar