Do impossibility results survive in historically standard domains?

One of the major assumptions common to all impossibility results in social choice theory is that of ”full” or rich enough domain. Thus, a major stream of attempts has focused on how to restrict the domains of social choice functions in order to escape impossibilities, without paying much attention to the question of whether there exist actual societies with such restricted domains of preference profiles, however. The notion of an unrestricted domain is based on the assumption that the individuals form their preferences independent of each other. If one replaces this assumption by one under which individual preferences are clustered around a ”social norm” in a unipolar standard society, the question of how this kind of restricted domain restriction influences the existence of a Maskin monotonic, surjective and nondictatorial social choice function becomes important. We employ the so-called Manhattan metric to measure the degree of how clustered a society around a social norm is. We then try to characterize what degrees of clustering around a social norm allow us to escape impossibility results, in an attempt to shed some light on the question of whether impossibilities in social choice theory arise from assuming the existence of historically impossible societies.