Consistent Risk Acceptance Criteria through Networks

In decision theory projects are usually evaluated in terms of their riskiness, and often decision under risk is intended as the one-shot-type binary choice of accepting or not accepting the risk. This paper elaborates on the concept of risk acceptance, and aims at developing a theoretical framework based on networks theory. In doing this, the interconnections between the random quantities involved in the decision are taken into account. The conditions to be satisfied in order for the risk-acceptance criterion to be consistent with the axiomatization of standard expected utility theory are also explored. In accordance with existing literature, we obtain that a risk evaluation problem can be meaningful even if it is not consistent with the standard axiomatization of expected utility. Some illustrative examples are also provided.