Before revision:  The  \alpha,[a,b]-convex decreasing stochastic orders  allow us to derive  comparative statics results for  applications in economics and operations research that could not be derived using previous stochastic orders  .
After revision:  The \alpha,[a,b]-convex decreasing stochastic orders allow us to derive comparative statics results for applications in economics and operations research that could not be derived using previous stochastic orders . In particular, our comparative statics results are useful when an increase in the lottery's riskiness increases the agent's optimal action, but an increase in the lottery's expected value decreases the agent's optimal action. For this kind of situation, we provide a tool to determine which of these two forces dominates -- riskiness or expected value .