Preferences over location-scale family

This paper extends the work on location-scale (LS) family with general n random seed sources. First, we clarify and generalize existing results in this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Second, we introduce and study some general non-expected utility functions defined over the LS family. Special care is taken in characterizing the shapes of the indifference curves induced by the location-scale expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first- and second-order stochastic dominances, the mean-variance rule, and a newly defined location-scale dominance.