I.A.1.4.1 The Four Basic Axioms

Question 1

Transitivity of Choice (A1)

Answer 1

All possible outcomes of the decision under consideration can be ranked in order of preference; that is, if among three outcomes A, B, & C, we strictly prefer A to B and B to C then we ought to strictly prefer A to C

Question 2

Continuity of Choice (A2)

Answer 2

If among three outcomes A, B, & C we strictly prefer A to B and B to C, then B is the certain equivalent of some lottery between A and C, that is there exists a unique probability p for which we should be indifferent between receiving B or playing a lottery offering A with probability p and C with probability 1-p

Question 3

Independence of Choice (A3)

Answer 3

Our preference order between two lotteries should not be affected if these lotteries are part of the same wider range of possibilities

Question 4

Stochastic Dominance (A4)

Answer 4

Between two lotteries offering the same two possible outcomes, we out to prefer the lottery offering the larger probability of yielding the preferred outcome

Question 5

Principle of maximum expected utility (Maximum EU)

Answer 5

The lottery with the largest expected utility ought to be preferred over others. (The 4 axioms A1-A4 are sufficient to establish the concept of utility and lead to this unique decision criterion)