Progress toward gender equality is thwarted by the underrepresentation of women in political leadership, even as most Americans report they would vote for women candidates. Here, we hypothesize that women candidates are often disadvantaged by pragmatic bias, a tendency to withhold support for members of groups for whom success is perceived to be difficult or impossible to achieve. Across six studies (N = 7,895), we test whether pragmatic bias impedes women's access to a highly significant political leadership position--the US presidency. In two surveys, 2020 Democratic primary voters perceived women candidates to be less electable, and these beliefs were correlated with lower intentions to vote for women candidates (Studies 1 and 2). Voters identified many reasons women would be less electable than men, including others' unwillingness to vote for women, biased media coverage, and higher requirements to prove themselves. We next tested interventions to reduce pragmatic bias. Merely correcting misperceptions of Americans' reported readiness for a woman president did not increase intentions to vote for a woman (Study 3). However, across three experiments (including one preregistered on a nationally representative sample), presenting evidence that women earn as much support as men in US general elections increased Democratic primary voters' intentions to vote for women presidential candidates, an effect driven by heightened perceptions of these candidates' electability (Studies 4 to 6). These findings highlight that social change efforts can be thwarted by people's sense of what is possible, but this may be overcome by credibly signaling others' willingness to act collectively. [ABSTRACT FROM AUTHOR]