Irrational Properties of Risk Attitude in Decision Making

The aim of this study was to investigate the irrationality in decision making on risk attitude. More concretely, the likelihood of reflection effect in decision making was investigated and compared between two conditions (the reflection effect from the risk seeking choice to the risk aversive choice and that from the risk aversive choice to the risk seeking choice). Second, the condition (p-value (probability of gain or loss) in for the reversal of choice (change of risk attitude) was identified and compared between gain and loss domains. In such a way, the irrational property in decision making on risk attitude was pointed out. On the basis of such an approach, it was discussed how decision making on choosing one of the two prospects (A) ($Y, p) and (B) ($X,1) should be systematically treated in order to generalize the behavior of changing risk attitude under the condition of a smaller value of p and (Y is by far larger than X). Moreover, it was also pointed out that the derivation of the property of weighting function in prospect theory using a simple demonstrative decision making paradigm cannot be generalized and is not proper for verifying and deriving this property. The results were as follows: (1) While the reflective effect from the risk seeking choice to the risk aversive choice readily occurred when the occurrence probability of the larger gain was low, the reflective effect from the risk aversive choice to the risk seeking choice was unlikely and didn't readily occur. (2) The larger change (increment or decrement) of p-value was necessary to change the risk attitude (from risk aversive to risk seeking, and vice versa) in the loss domain than in the gain domain. (3) Only Equations (2) and (4) are insufficient for the generalization of characteristics of the weighting function. (4) For the systematical generalization of the change of risk attitude, the characteristics of the following prospects must be explored in more detail: Prospect (A) ($Y,p) and Prospect (B) ($X,1), where p is a smaller probability, and (Y is by far larger than X).