Generalized individual desirability relations are defined relying on a) effectivity functions (EFs) b) Galois lattices of EFs and c) opportunity rankings as defined on EFs. It is argued that such desirability relations enable an enlargement of the scope of game-theoretic approaches to the...

It is argued that if opportunity sets are properly embedded in an interactive environment then the lattice of set-inclusion order filters of opportunity sets is the most suitable domain for opportunity rankings. A simple characterization of the cardinality-based preorder in terms of certain...