Although “Lehman Sisters” may have acted quite differently from “Lehman Brothers,” the differences in outcomes may often be substantially smaller than the differences observed in the average behavior of males and females

Do Gender Preference Gaps Impact Policy Outcomes? Ranehill, Eva, and Weber, Roberto A. University of Gothenburg, Department of Economics, Working Papers in Economics #713. https://ideas.repec.org/p/hhs/gunwpe/0713.html

Abstract: A large body of evidence documents systematic gender differences in a variety of important economic preferences, such as risk-taking, competition and pro-sociality. One potential implication of this literature is that increased female representation in decision-making bodies may significantly affect organizational and policy outcomes. However, research has yet to establish a direct connection from gender differences in simple economic choice tasks, to voting over policy and to the resulting outcomes. We conduct a laboratory experiment to provide a test of such a connection. In small laboratory “societies,” people repeatedly vote for a redistribution policy and engage in a real-effort production task. In this environment, we observe a substantial difference in voting behavior, with women voting for significantly more egalitarian redistribution policies. This gender difference is large relative to other differences based on observable characteristics and is partly explained by gender gaps in economic preferences and in beliefs about relative performance. Gender voting gaps persist with experience and in environments with varying degrees of risk. We also observe policy differences between male- and female-controlled groups, though these are considerably smaller than the mean individual differences—a natural consequence of the aggregation of individual preferences into collective outcomes. Thus, we provide evidence for why substantial and robust gender differences in preferences may often fail to translate into differential policy outcomes with increased female representation in policymaking.

Check also: Individual risk preferences and the demand for redistribution. Manja Gärtner, Johanna Mollerstrom and David Seim. Journal of Public Economics, v 153, September 2017, Pages 49-55. http://www.bipartisanalliance.com/2017/08/individual-risk-preferences-and-demand.html