Mathematical models are just formalized metaphors.
They both are (literary/mathematical) devices where meaning is conveyed by borrowing the literal meaning of the metaphor/model to describe the localized meaning in the context the metaphor/model is applied to. They are therefore both internally consistent, and their validity relies on whether they are appropriately applied to a localized context.
E.g. 1 “Elections work like a political market” is to use the model of the market as metaphor.
E.g. 2 “The international system is a like a game” is to invoke game theory as an appropriate model, or the “game (of thrones?!?)” as an appropriate metaphor.
They don’t sound so “sciency” anymore.