Abstract
Traditional stochastic dominance rules are so strict and qualitative conditions that generally a stochastic dominance relation between two alternatives does not exist. To solve the problem, we firstly supplement the definitions of almost stochastic dominance (ASD). Then, we propose a new definition of stochastic dominance degree (SDD) that is based on the idea of ASD. The new definition takes both the objective mean and stakeholders’ subjective preference into account, and can measure both standard and almost stochastic dominance degree. The new definition contains four kinds of SDD corresponding to different stakeholders (rational investors, risk averters, risk seekers, and prospect investors). The operator in the definition can also be changed to fit in with different circumstances. On the basis of the new SDD definition, we present a method to solve stochastic multiple criteria decision-making problem. The numerical experiment shows that the new method could produce a more accurate result according to the utility situations of stakeholders. Moreover, even when it is difficult to elicit the group utility distribution of stakeholders, or when the group utility distribution is ambiguous, the method can still rank alternatives.
Highlights
In some real-life decision situations, such as some public projects, decision makers (DMs) are just agents of all stakeholders
Levy’s [20] and Tzeng’s [21] definitions of almost first degree stochastic dominance (AFSD) and almost second degree stochastic dominance (ASSD), we further supplement the definitions of almost second degree inverse stochastic dominance (ASISD), and almost prospect stochastic dominance (APSD)
To overcome the defects in traditional SD rules, we firstly supplement the definitions of ASISD
Summary
In some real-life decision situations, such as some public projects, decision makers (DMs) are just agents of all stakeholders. Leshno and Levy [11] noticed that such strict rules relate to “all” utility functions in a given class, including extreme ones that presumably rarely represents stakeholders’ preference. They proved that SD rules may fail to show dominance in cases where almost everyone would prefer one gamble to another. To better apply the SD rules, the method to measure the stochastic dominance degree (SDD) is necessary [13] To solve these problems, scholars have made many attempts. The new definition contains four kinds of SDDs corresponding to four risk preference styles It can measure the degree of SD and ASD, and has clear economic meaning.
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