Optimal innovation occurs when there is an equal mix of men and women using a systematic process. Research in this area may have some suggestions why. Lynne Millward and Helen Freeman tested several hypothesis and reported the results in their article, "Role Expectations as Constraints to Innovation: The Case of Female Managers." The essence of the research is that, while men and women are equally innovative, their gender role within the context of an organization can affect how they are perceived and how they behave when innovating and sharing ideas. Men are perceived as more innovative and risk-taking, and women are perceived as more adaptive and risk-adverse. "Thus, gender roles may interact with the role of the manager to inhibit (in the case of women) or facilitate (in the case of men) the likelihood of innovative behavior."
They tested several hypothesis. People perceive innovative solutions to be more likely to come from a male manager, and they perceive adaptive solutions to be more likely to come from a female manager. They also found that innovative solutions were perceived to be more likely to be implemented if they were suggested by a male manager.
Innovation carries with it different levels of risk for men than for women. Men are expected to take more risks when innovating and sharing ideas. Failure is less damaging to men because that's what's expected of them. Women are expected to be less risky, and this appears to limit or constrain both their degree of innovation and their willingness to share it. Failure is more damaging for women so they behave more adaptively in innovation exercises.
For practitioners, there is both a negative and a positive aspect to this. On the one hand, innovation workshops need a process to assure that women feel they can innovate "bigger" and share those ideas with the group. If, as the research suggests, women are more likely to hold back, then the facilitation approach has to break through it. Otherwise, you lose the inherent value of the (equal) innovation talent they bring to the table.
On the positive side, these differences can be beneficial. The more adaptive behavior in women and more risk-taking behavior in men provides a certain balance or harmony during innovation. Togeher, they give a complementary effect that seems to yield better results. Each partner holds the other accountable for ideas that are, at the same time, novel but adoptable. Working in pairs, men and women also do a better job of expressing jointly-developed new ideas that may help overcome risks that women may be feeling. Workshop processes that pair men and women up to take advantage of this are going to be more fruitful.