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...

This paper takes voting theory out of the realm of mechanism design and studies elections as tools for representing preferences: every preference relation on a set of n elements is the outcome of pairwise voting by approximately 2 log2n voters with transitive preferences. Results like this one...