We show that if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function. We also show that, if people's utility functions are generated according...

Given a large enough population of voters whose utility functions satisfy certain statistical regularities, we show that voting rules such as the Borda rule, approval voting, and evaluative voting have a very high probability of selecting the social alternative which maximizes the utilitarian...

We introduce a ranking of multidimensional alternatives, including un- certain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of...

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of...

What is the meaning of "majoritarianism" as a principle of democratic group decision-making in a judgement aggregation problem, when the propositionwise majority view is logically inconsistent? We argue that the majoritarian ideal is best embodied by the principle of "supermajority efficiency"...

We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In...

A ``difference preorder'' is a (possibly incomplete) preorder on a space of state changes (rather than the states themselves); it encodes information about preference intensity, in addition to ordinal preferences. We find necessary and sufficient conditions for a difference preorder to be...

We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural...

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>

Sequential majority voting over interconnected binary propositions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, under what circumstances this happens for some sequence of the voting process. It turns out that the class...