A New Stochastic Dominance Degree Based on Almost Stochastic Dominance and Its Application in Decision Making

Abstract

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.

Profitability of farm-scale management strategies against the boll weevil in the tropics: case study from the Colombian Caribbean

“…Finally, given that we are comparing the outcomes of discrete strategies (actions), we used Stochastic Dominance (SD) as a measure of their efficiency. SD allows assessing risk when it is impossible to elicit utility functions for the decision makers involved (Gandhi et al 1981;Levy 2016;Genest et al 2016;Wu et al 2017). This approach provides support for the decisionmaking process of farmers and identifies knowledge gaps that can be considered for further research by consultants.…”

“…However, an option that provides higher benefits and higher risks is preferred by risk seekers. This preference is called inverse second-order stochastic dominance (ISSD) (Aaberge et al 2013;Wu et al 2017;Spiegel et al 2018).…”

“…6). Simulation results were plotted as cumulative distribution functions (CDF) and the control strategies ranked using the hierarchical rules of stochastic dominance (Leshno and Levy 2004;Wu et al 2017;Jiang et al 2018). The proactive strategy, the option with the higher mean, exhibits a wider dispersion than reactive control.…”