Arguments for public involvement in science and technology are often based on ideas of developing a more capable public and the assumed effects this may have for science. However, such a relationship is yet to be sufficiently explored and recent work indicates that a more involved public may have counterintuitive effects. Using nationally representative survey data for the UK and Northern Ireland, the effects of the public's own beliefs about involvement are explored. Developing the concept of "belief in public efficacy," findings suggest those who believe that the public might be able to affect the course of decision making have less approving attitudes towards future applications of genetic science; however, an individual's political efficacy does not significantly influence these attitudes. Furthermore, political efficacy and belief in public efficacy have some distinct and opposing relationships with the principles of governance people prefer. Overall, findings provide support for suggestions that it is simplistic to consider increasing public involvement as a way of increasing the approval of risky new technologies.