A probability weighting function w(p) is a prominent feature of several nonexpected utility theories, including prospect theory and rank-dependent models. Empirical estimates indicate that w(p) is regressive with respect to the diagonal (w(p) > p for small p, and w(p)< p for large p), s-shaped (concave near p = 0, convex near p = 1), and asymmetrical (intersecting the diagonal at about p = l/3). The paper provides axioms for several families of weighting functions, including a "compound invariant" form, w(p) = exp{-{-ln p}[superscript alpha]}, 0 < alpha < 1, which is regressive, s-shaped, and which has invariant fixed and inflection points at p = 1/e.
