Theory and Decision

, Volume 80, Issue 1, pp 159–166 | Cite as

A note on cancellation axioms for comparative probability

  • Matthew Harrison-Trainor
  • Wesley H. Holliday
  • Thomas F. IcardIII


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 



The first author was partially supported by the Berkeley Fellowship and an NSERC PGS-D award. The authors wish to thank an anonymous referee for helpful comments.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Matthew Harrison-Trainor
    • 1
  • Wesley H. Holliday
    • 2
  • Thomas F. IcardIII
    • 3
  1. 1.Group in Logic and the Methodology of ScienceUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Philosophy and Group in Logic and the Methodology of ScienceUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of Philosophy and Symbolic Systems ProgramStanford UniversityStanfordUSA

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