Do I understand this correctly? The losers choose who they will give their votes to until there is only one left? Or am I confusing some other weird voting system?
No. Each voter makes a choice at the outset.
The Virginia GOP just used this method for their primary.
Let’s say that there are 7 Candidates in the race.
A, B, C, D, E, F and G.
Each voter will rank their preferences. Example:
1. G
2. A
3. B
4. F
5. C
6. D
7. E
If no candidate gets 50%+ of the vote, then the lowest ranked candidate is eliminated, and the 2nd choice ON THOSE ballots is distributed.
In our Hypothetical, lets say that the first round vote share was as follows:
1. G - 30%
2. A - 20%
3. B - 15%
4. F - 11%
5. C - 10%
6. D - 9%
7. E - 5%
E would be eliminated. On those 5% of the ballots, their 2nd Choice votes get redistributed.
The next round might look like this:
1. G - 30%
2. A - 23%
3. B - 15%
4. F - 12%
5. C - 10%
6. D - 10%
The process repeats until one candidate gets 50%+ of the vote.