Pivato, Marcus - In: Theory and Decision 77 (2014) 1, pp. 31-83
Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathcal{X }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="script">X</mi> </math> </EquationSource> </InlineEquation> be a set of outcomes, and let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathcal{I }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="script">I</mi> </math> </EquationSource> </InlineEquation> be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$(\succcurlyeq )$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mo>≽</mo> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mathcal{X }^\mathcal{I }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="script">X</mi> </mrow> <mi mathvariant="script">I</mi> </msup> </math> </EquationSource> </InlineEquation> admits an additive...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>
