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 sufficiently large population satisfying certain statistical regularities, we show that it is often possible to accurately estimate the utilitarian social welfare func- tion and identify the welfare-maximizing social alternative, even if we only have very noisy data about individual...

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...