Woman suffrage led to one of the greatest enfranchisements in history. Yet, women neither won the right to vote by force, nor did men grant it under the imminent threat of female unrest. These facts are difficult to reconcile with leading political economy theories of suffrage extensions. In this paper, we study suffrage extensions at the level of US states and territories in the late 19th and early 20th centuries to learn about the factors that accelerated, respectively delayed, a jurisdiction's transition to woman suffrage. Our results show that the general scarcity of women in the American West, or a high sex ratio, was the single most important factor behind the region's lead in the enfranchisement of women in the US. High ratios of grantors (men) to grantees (women) of the franchise appear to have promoted earlier suffrage extensions, as these imbalances reduced the political costs and risks for male legislators and electorates. Our finding may provide a more general insight into the economics of voluntary power sharing. All else equal, smaller groups should find it much easier to acquire rights or to get admitted to economic and political clubs.