  This paper investigates best-worst choice probabilities (picking the best and
the worst alternative from an offered set). It is shown that non-negativity of
best-worst Block-Marschak polynomials is necessary and sufficient for the
existence of a random utility representation. The representation theorem is
obtained by extending proof techniques employed by Falmagne (1978) for a
corresponding result on best choices (picking the best alternative from an
offered set).
