This view of the political process has, however, been challenged by empirical papers that seemed to suggest that if candidates or parties care about certain outcomes and cannot credibly commit to moderate policies, there will be divergence in the policies implemented by elected officials, viz, gender does affect behaviour and outcomes.
A recent NBER paper looks at the impact of gender in the context of city leaders in the US (where there has been an upsurge in female participation in politics). Till 1970, a negligible number of women participated in US mayoral elections. Since then, the percentage of females who won mayoral elections has rised from about 2% in 1970 to more than 15% in recent years.
The paper makes a distinction between women in chief executive positions at the local level and participation in legislature. There is a reason for this. Mayors have executive power that could facilitate the reallocation of resources in a city to serve one's political preferences.
Legislators, on the other hand, have to negotiate with other representatives (and possibly the executive) to pass legislation, so the impact of an added female legislator may not be as effective, or it may be noticeable only when large participation shocks are observed.
Perhaps for this reason, the paper finds there is no impact of having a female chief executive on the size of local government, the composition of its expenditures, or local crime rates. The gender of the political leader also does not seem to affect the short- or long-run policy choices of US cities, corroborating the median voter view of the political process described by Downs.
Many features of local cities explain the importance of the median voter theorem.
Intense competition among local governments may prevent gender from influencing policy outcomes, as it prevents political parties from implementing divergent policies. Also, the types of policies relevant to local government could play a role in mitigating potential policy changes that come from electing a female leader.
Economic responsibilities such as local taxation and the provision of basic services are the province of city government, while social issues such as abortion and gun control are not.
The authors also investigate whether having a woman attain the top executive position in a local government leads to greater participation in future races, both for mayor and for congress. Somewhat surprisingly (given the received wisdom), having a woman win the mayor's office seems to have virtually no positive impact on the probability of other females winning political office. Almost all of the future increase in female success is due to the woman who won in the first place.
Overall, their estimates indicate that women perform better in the ultimate political test once they assume office - namely, whether they will get re-elected. This result is consistent with the general perception of female participation in local elections.