Elections and the Representation of Preferences over Infinite Sets

Voting theory has always focused on mechanism design, but this paper shows that voting theory is also a useful tool in the field of preference representation. Both the lexicographic order on n-dimensional Euclidean space and the threshold of detectable difference relation are pairwise majority voting aggregates of utility functions. Pareto dominance on n-dimensional Euclidean space and the threshold of detectable difference relation are pairwise unanimous voting aggregates of utility functions. Separability conditions are established for voting aggregates, and used to show that the lexicographic order is not a pairwise unanimous voting aggregate of utility functions, and Pareto dominance is not a pairwise majority voting aggregate of utility functions.