  This article explicitly constructs and classifies all arrovian voting systems
on three or more alternatives. If we demand orderings to be complete, we have,
of course, Arrow's classical dictator theorem, and a closer look reveals the
classification of all such voting systems as dictatorial hierarchies. If we
leave the traditional realm of complete orderings, the picture changes. Here we
consider the more general setting where alternatives may be incomparable, that
is, we allow orderings that are reflexive and transitive but not necessarily
complete. Instead of a dictator we exhibit a junta whose internal hierarchy or
coalition structure can be surprisingly rich. We give an explicit description
of all such voting systems, generalizing and unifying various previous results.
