Similarly, the most general form of rational decision theory or rational choice theory is based on lattices. That makes intuitive sense, since preference relations ~are~ partially ordered sets. Then, analyzing rational (vs. for example boundedly rational choice behavior) is equivalent to analyzing lattice optimization problems (monotonicity).

Then, parameterizing the choice situation and / or introducing strategic dependecies between actors leads to analyzing sub/supermodular correspondences on these sets. In fact, the most general version would make use of quasi-supermodularity. I think Milgrom&Roberts 94 show that this is the most general way, one can think of coherent (rational) decision theory.