If a vector-valued function has convex range and one of its components is related to the others by a Pareto-like condition, that component must be affine w.r.t. the others; sign restrictions on the coefficients follow from suitably strengthening the unanimity condition. The theorem is applied to social choice and decision theories.
Demeyer, B., & Mongin, P. (1995). A Note On Affine Aggregation. Economics Letters, 47(2), 177-183. https://doi.org/10.1016/0165-1765(94)00531-6 (Original work published 1995)