The classical account of decision-making derives from seminal work done by Frank P. Ramsey (Truth and probability. In: Braithwaite R (ed) The foundation of mathematics and other logical essays (1931). Routledge and Kegan, London, 1926a; Math Ga 13:185–194, 1926b) and later on by Von Neumann and Morgenstern (Theory of games and economic behavior (2nd edn). Princeton University Press, Princeton, 1947). This work culminates later on with the influential account of Leonard Savage (The foundations of statistics. Wiley, New York (2nd ed. in 1972, Dover), 1954), Ascombe and Aumann (Ann Math Stat 34:199–205, 1963) and de Finetti (Annales de l"Institut Henri Poincare 7:1–68, 1974). We can recapitulate here in a compact form the classical presentation by Von Neumann and Morgenstern. Define a lottery as follows: If A₁, … , A_m is a partition of the possible outcomes of an experiment with α_j = Pr(A_j) for each j, then the lottery (α₁, … , α_m) awards prize z_j if A_j occur. We can assume that the choice of the partition events does not affect the lottery. We can then introduce some central axioms for preferences among lotteries.