I seriously dont think this would work, why would Jagex store important customer account information in their own internet caches, this means they would have no records back at HQ whos voted and who hasnt, and would evidently lead to bug abuse.
Plus, if this information was stored in your internet cache, normal players would accidentally exploit it who happen to have more than one computer, or use multipler browsers, play Runescape at their friends etc, the system would constantly think you havent voted.