Abstract
Yang and Qiu proposed an expected utility-entropy (EU-E) measure of risk, which reflects an individual’s intuitive attitude toward risk. Luce et al. have derived the numerical representations under behavioral axioms about preference orderings among gambles and their joint receipt, which further demonstrates the reasonability of the EU-E decision model as a normative one. In the paper, combining normalized expected utility and entropy together, we improve the EU-E measure of risk and decision model, and then propose the normalized EU-E measure of risk and decision model. The normalized EU-E measure of risk has some normative properties under certain conditions. Moreover, the normalized EU-E decision model can be a proper descriptive model to some extent. Using this model, two cases of common ratio effect and common consequence effect, which are the examples of certainty effects, can be explained in an intuitive way.
Highlights
The measure of risk, and decision making under risk have always been important issues in the field of decision sciences, finance, economics and psychology, etc
If all states of nature have the same distribution, the normalized entropy of the states is the same for every state of nature corresponding to each action; in this case the risk ordering is determined by the normalized expected utility component
By combining normalized expected utility and entropy together, we propose the normalized expected utility-entropy (EU-E) measure of risk
Summary
The measure of risk, and decision making under risk have always been important issues in the field of decision sciences, finance, economics and psychology, etc. In EU-E measure of risk, the expected utility reflects the decision maker’s subjective preference; the entropy measures the objective uncertainty of its corresponding states. The EU-E measure of risky action effectively incorporates the decision maker’s subjective preference and the objective uncertainty regarding the states of nature by the risk tradeoff factor This measure of risky action is the weighted linear average of the expected utility and entropy. Both EU-E and EM-EU representation may not provide the proper description for risky choice To deal with these kinds of risky actions, normalized entropy is a better way to measure the relative uncertainty of the risky actions with different numbers of state of nature. We demonstrate the reasonability of the normalized EU-E decision model as a descriptive model or a normative decision model involving risk
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