Economists have used the term “nonbinary” to describe both choice functional nonbinariness (choice functions that cannot be rationalized as the maximizing outcome of a binary preference relation) and structural nonbinariness (the structure of the model dictates that pairs of alternatives do not belong to the domain of the social choice function). Here we have described necessary and sufficient conditions for oligarchy and dictatorship results in social choice models that are nonbinary in both senses.
