In this letter, we show that the results presented by Jindapon and Neilson (2007) for changes in risk à la Ekern (1980) can be generalized to mean-preserving stochastic dominance changes, with appropriate and simple additional conditions on the utility function.
Denuit, M., & Eeckhoudt, L. (2013). Improving your chances: A new result. Economics Letters, 118(3), 475-477. https://doi.org/10.1016/j.econlet.2012.12.016 (Original work published 2013)