Choice voting, Preferential voting or Preference voting
Cumulative voting (also accumulation voting, weighted voting or multi-voting)
Perhaps STV and Cumulative voting can be combined. Actually there is no need because all your voting power would go to your first preference if it was needed to elect them. If there was a portion left over then it would be used as needed until it was used up.
-- ClifCox - 2011-10-21