  Top monotonicity is a relaxation of various well-known domain restrictions
such as single-peaked and single-crossing for which negative impossibility
results are circumvented and for which the median-voter theorem still holds. We
examine the problem of testing top monotonicity and present a characterization
of top monotonicity with respect to non-betweenness constraints. We then extend
the definition of top monotonicity to partial orders and show that testing top
monotonicity of partial orders is NP-complete.
