The debate over political gender quotas is unduly confined to a supposed trade‐off between diversity and competence. We characterize the effects of a political gender quota in a citizen‐candidate model, to find that quotas do increase the overall quality of those elected whenever the rewards from public office are high, or the skill premium or political gender discrimination are sufficiently low. In such cases, high‐skill women candidates run for office in sufficiently high numbers, driving off low‐skill male and female candidates. Our model compares quotas with other policies in terms of their impact on the number and quality of those elected.