Utility Paradox of Risk Decision : The Correlation between Risk/Wealth and Value/Weighting Function

Decision under risk is one of the most important topics in economics. The underlying assumption of traditional theory models suggests that weighting function and value function are independent, i.e., value functions are constant under any risk, and weighting functions are constant under any value. This study tests subjects' valuations of different lotteries and insurances, which have different risks and gains or losses. We find a paradox under traditional independent framework: according to independent framework, under the same risk (value), the subject's valuation of one prospect that has a certain value (risk) to another should be constant across different risks (values), but our results reject the assumption both aggregately and individually. We propose and test the new dependent framework: value function is affected by risk, and weighting function is affected by value. This finding can help us understand and analyze risk decisions from a new perspective