Cervical cancer is linked to infection with Human Papilloma Viruses 16 and 18. HPV infection commonly manifests as warts (genital or otherwise) and although there is some controversy, a growing body of evidence (example article) shows that there is a link between lack of circumcision and increased risk for HPV in men.
It can be surmised that decreased HPV rates in men (especially promiscous men) could lower the HPV rate in sexually-active women (thus leading to a decrease in cervical cancers due to HPV).
I am not a medical student by any means, I've only ready a few articles about and heard conversations from well-educated friends. I would assume that hygiene plays a large role in the matter.
m2c..