  Methods for choosing from a set of options are often based on a strict
partial order on these options, or on a set of such partial orders. I here
provide a very general axiomatic characterisation for choice functions of this
form. It includes as special cases axiomatic characterisations for choice
functions based on (sets of) total orders, (sets of) weak orders, (sets of)
coherent lower previsions and (sets of) probability measures.
