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...

A parameterized characterization of height-based total extensions of Principal filtral opportunity rankings is provided and shown to include as a special case a version of the well-known Pattanaik-Xu characterization of the cardinality-based ranking

A parameterized characterization of height-based total extensions of principal filtral opportunity rankings is provided and shown to include, as a special case, a version of the well-known Pattanaik-Xu characterization of the cardinality-based ranking