There's actually a proposition here in BC to enact this kind of voting for provincial elections; as far as I could tell, it's exactly as we do it, but they call it the "Single Transferable Vote method" or something like that.
STV is different from what we have and is a form of PR.
Oh, how does it work? Maybe I didn't read the proposition carefully regarding what it does.
It is used in multi-member constituencies.
It requires that all those elected receive a majority of the vote in the constituency.
The "Droop Quota" is used to determine the number of votes necessary:
Q = (total votes cast/number of seats + 1) +1
E.g.
In a 5 member constituency with 360,000 electors, the required number of votes is 60,001.
In the first phase of the count anybody with 60,001 votes or more is elected (Usually at least one candidate is elected here) The votes that were for them are now transferred to their second preferences which can lead to the election of another candidate. From here in they eliminate from the bottom upwards until all the vacancies are filled.