some kind of voting system based on the number of bitcoins a person owns?
This sort of system would inadvertently profile all the Bitcoin users that voted on the site. Many large holders don't want the world to know they are large holders.
You transfer one satoshi from every wallet you own and the API checks the balance and for each bitcoin you own you are allowed a single vote. (also transfer it back not looking to make money)
No need for this (Remember you'll never get the tx fee back anyway)
Instead just have users sign a message to prove ownership of address.
Also this is impractical, as a large bitcoin owner has their wealth spread over thousands of addresses.
(Also is easy to game, as the bitcoin user can resend coins to a new address after signing his proof and do it again and again, thus gaming your voting system)
Good luck!
