Invariance axioms for preferences: applications to social choice theory

I investigate the role played by the combination of two invariance axioms for preferences in utility theory; namely, those of zero-independence and scale-independence, respectively. I provide a characterization of the preference relations on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n}}$$\end{document} that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n}}$$\end{document}. This result is then applied in social choice theory to characterize those social welfare functions that satisfy IIA and PI. Other characterizations involving the usual Pareto concepts are also provided.