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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathbb{R}^{n}}$$</EquationSource> </InlineEquation> that satisfy these two axioms as those which are either trivial, or what I call a two-serial total preorder on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\mathbb{R}^{n}}$$</EquationSource> </InlineEquation>. 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. Copyright Springer-Verlag 2013