Magari algebras and Plott choice functions

I wanted to talk about an unexpected and as yet unexplained connection between two identities: the Loeb identity from provability theory and Plott's "path independence" condition from rational choice theory. Not being an expert in provability theory, I will focus my talk more on choice functions. Plott's choice functions are a remarkable mathematical structure that generalizes the concept of a partial order in a somewhat unexpected direction. Because of this, such functions appear in various places - in nonmonotonic logic, stability theory, combinatorics. And under various guises - as convex geometries, as sparse spaces, as Kolmogorov pre-topologies, as generalized Magary algebras.