Basically you are talking about expected utility theory without the independence axiom. See
Mark Machina “Choice Under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1 (Summer 1987) 121-154. Alex -- Alexander Tabarrok Department of Economics, MSN 1D3 George Mason University Fairfax, VA, 22030 Tel. 703-993-2314 and Director of Research The Independent Institute 100 Swan Way Oakland, CA, 94621 Tel. 510-632-1366