  Actual individual preferences are neither complete (=total) nor antisymmetric
in general, so that at least every quasi-order must be an admissible input to a
satisfactory choice rule. It is argued that the traditional notion of
``indifference'' in individual preferences is misleading and should be replaced
by `equivalence' and `undecidedness'. In this context, ten types of majority
and minority arguments of different strength are studied which lead to social
choice rules that accept profiles of arbitrary reflexive relations. These rules
are discussed by means of many familiar, and some new conditions, including
`immunity from binary arguments'. Moreover, it is proved that every choice
function satisfying two weak Condorcet-type conditions can be made both
composition-consistent and idempotent, and that all the proposed rules have
polynomial time complexity.

Combinatorics