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Studying the extent to which realism is compatible with quantum mechanicsteaches us something about the quantum mechanical universe, regardless of thevalidity of such realistic assumptions. It has also recently been appreciatedthat these kinds of studies are fruitful for questions relating to quantuminformation and computation. Motivated by this, we extend the ontological modelformalism for realistic theories to describe a set of theories emphasizing therole of measurement and preparation devices by introducing `hidden variables'to describe them. We illustrate both the ontological model formalism and ourgeneralization of it through a series of example models taken from theliterature. Our extension of the formalism allows us to quantitatively analyzethe meaning contextuality (a constraint on successful realistic theories),finding that - taken at face-value - it can be realized as a naturalinteraction between the configurations of a system and measurement device.However, we also describe a property that we call deficiency, which followsfrom contextuality, but does not admit such a natural interpretation. Looselyspeaking, deficiency breaks a symmetry between preparations and measurements inquantum mechanics. It is the property that the set of ontic states which asystem prepared in quantum state psi may actually be in, is strictly smallerthan the set of ontic states which would reveal the measurement outcome psiwith certainty.

Ontological models and the interpretation of contextuality