  We characterize a rich class of valuated matroids, called R-minor valuated
matroids that includes the indicator functions of matroids, and is closed under
operations such as taking minors, duality, and induction by network. We exhibit
a family of valuated matroids that are not R-minor based on sparse paving
matroids. Valuated matroids are inherently related to gross substitute
valuations in mathematical economics. By the same token we refute the Matroid
Based Valuation Conjecture by Ostrovsky and Paes Leme (Theoretical Economics
2015) asserting that every gross substitute valuation arises from weighted
matroid rank functions by repeated applications of merge and endowment
operations. Our result also has implications in the context of Lorentzian
polynomials: it reveals the limitations of known construction operations.
