Voting Theory: Instant Runoff

Instant run-off voting, also called the plurality with elimination, is a modification of the plurality method. This method removes the candidate with the least first-place votes, and the votes for the now-eliminated candidate are redistributed to the voter groups’ next choice. It continues until a candidate gets the majority (> 50%).

# Voters412513263015
1st ChoiceLLFFCC
2nd ChoiceFCLCFL
3rd ChoiceCFCLLF

Look at the previous example: L (for library) wins after getting 66 out of the possible 150 votes. For a majority, a candidate must get 76 votes.
L: 66
F: 39
C: 45
IRV method eliminated the last one, F. The table now looks like the following.

# Voters412513263015
1st ChoiceLLCC
2nd ChoiceCLCL
3rd ChoiceCCLL

The two empty entries against the 1st choice now go to the ones below – 13 to L and 26 to C. The updated votes are:
L: 79
C: 71

L now becomes the winner of the Instant run-off voting method.