Utility Difference before Expectation Calculation

Risk Aversion

Prudence

Temperance

Probability of options is x² (ambiguity), and probability of people’s mind is y² (subjective probability)

Variable

$\begin{array}{l}-\epsilon \times \left(1-y^2\right)\{x^2{y}^2\\ +\left(1-x^2\right)\left(1-y^2\right)\\ +2x\sqrt{1-x^2}\\ \times y\sqrt{1-y^2}\cos \left(\theta \right)\}\end{array}$

Constant

$\begin{array}{l}k\times \left(1-2y^2\right)\{x^2{y}^2\\ +\left(1-x^2\right)\left(1-y^2\right)\\ +2x\sqrt{1-x^2}\\ \times y\sqrt{1-y^2}\cos \left(\theta \right)\}\end{array}$

Variable

$\begin{array}{l}-\epsilon 2\times \left(1-2y^2\right)\{x^2{y}^2\\ +\left(1-x^2\right)\left(1-y^2\right)\\ +2x\sqrt{1-x^2}\\ \times y\sqrt{1-y^2}\cos \left(\theta \right)\}\end{array}$