Axiom of independence
In economics, the axiom of independence represents a central assumption about rational decision-making. According to the axiom of independence, the order of preference over two alternatives A and B does not change when a third alternative C is introduced. The axiom of independence is assigned to the system of axioms which established the Bernoulli principle . It is an important assumption about the behavior of a Bernoulli rational decision maker. According to the axiom of independence, the order of preference of a decision maker regarding two alternatives is independent of whether he judges these individually or in the context of other alternatives in a more complex election situation.
definition
Let L1, L2 and L3 be different lotteries. If a preference order is now established for the lotteries L1 and L2 (ie one of the following alternatives L1> L2, L1 ≥ L2, L1 ~ L2, L2> L1, L2 ≥ L1), then this preference order must remain in place if both lotteries L1 and L2 are expanded in the identical way by a probability p∈ (0,1) with L3.
So if, for example, L1> L2, then the following must also apply:
p L1 + L3 (1-p)> p L2 + L3 (1-p) , where p∈ (0,1)