The money manager said it would vote against boards if a company failed to take steps to increase its number of members who are women. State Street plans to send a letter to 3,500 companies on Tuesday asking the companies to act. . . The money manager has cited gender diversity as a way to improve company performance and increase shareholder value. The lack of women on boards has long been a problem. Beyond pipeline issues, some boards see no reason to increase their gender diversity, data shows.