We define generalized (preference) domains <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal{D}$</EquationSource> </InlineEquation> as subsets of the hypercube {−1,1}<Superscript> D </Superscript>, where each of the D coordinates relates to a yes-no issue. Given a finite set of n individuals, a profile assigns each individual to an element of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal{D}$</EquationSource> </InlineEquation>. We prove that, for any domain <InlineEquation ID="IEq3"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></superscript></equationsource></inlineequation>