A bi-preference interplay between transitivity and completeness: Reformulating and extending Schmeidler’s theorem

Consumers’ preferences and choices are traditionally described by appealing to two classical tenets of rationality: transitivity and completeness. In 1971, Schmeidler proved a striking result on the interplay between these properties: On a connected topological space, a nontrivial bi-semicontinuous preorder is complete. Here we reformulate and extend this well-known theorem. First, we show that the topology is not independent of the preorder,...