I haven't done any specific studies on the subject, but when you look at all the data and make a comparison between states with laws defending the “right to work” and those with more automatic unionization procedures and dues, you find that the former have a much lower unionization rate than states with laws that offer better protection for unions. Unionization is especially low in the private sectors that need it most, i.e., those where competition is strong and wages and working conditions are low. So they are depriving the workers who need protection the most of a collective tool.