The theory of games against nature relies on complete preferences among all conceivable acts (case 1). Aumann and Drèze (Am Econ J Microecon 1(1):116,(2009) consider situations where preferences are defined only for a given set of acts (case 2).We extend these results to situations where (i)...

This paper contributes to the axiomatization of additive rules for ranking sets of objects under the psychological principle of categorization. Firstly we proceed with the case where the elements in the sets are categorized into at most three groups, namely good (with value 1), neutral (with...