Negative Probabilities: What Are They For?

An observation space S is a family of probability distributions < P-i : i is an element of I > sharing a common sample space Omega in a consistentway. A grounding for S is a signed probability distribution P on Omega yielding the correct marginal distribution P-i for every i. A wide variety of quantum scenarios can be formalized as observation spaces. We describe all groundings for a number of quantum observation spaces. Our main technical result is a rigorous proof that Wigner's distribution is the unique signed probability distribution yielding the correct marginal distributions for position and momentum and all their linear combinations.