Social choice and the topology of spaces of preferences

Social choice theory is concerned with providing a rationale for social decisions when individuals have diverse opinions. Voting is an obvious way in which societies aggregate individual preferences to obtain social ones. The procedure of voting registers individual comparisons between alternatives, called ordinal preferences, rather than intensities of preferences among these alternatives, called cardinal preferences, and this is one source of so-called paradox of social choice. It is the purpose of this paper to study the paradox of social choice and to show that it arises, in part, because of the topological structure of spaces of ordinal preferences.