Many studies document 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 alter 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. Women persistently vote for more egalitarian redistribution. This gender difference is large relative to other voting differences based on observable characteristics and is partly explained by gender gaps in preferences and beliefs. 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.