I think that the death rate of these diseases actually ends up being somewhere around 4000 per year in the US. "In 2006, an estimated 10,000 women in the United States will be diagnosed with this type of cancer and nearly 4,000 will die from it." http://en.wikipedia.org/wiki/Cervical_cancer The year in question could be an outlier but without better information it is what we can go with. Now, the vaccine will not stop all of those deaths from necessarily occurring so the deaths prevented from vaccinations across the US would be less than 4000. The cost for the vaccine is about 300 something dollars. Now that 300 dollars is in essence a payment to prevent something very unlikely to happen to an individual and the action has very little positive externality as the only way you can get this disease is taking an action where you choose to take this chance. Therefore making this vaccine mandatory is just forcing people to waste their money.
Yeah, I did finally do my research on this.