Last Updated on 28. April 2023 by Martin Schuster

With the instant runoff-method, we can find a winner. It is similar to the Coombs Method.

• Step 1: Voters assign their preferences to all candidates.
• Step 2: The candidate who has more than 50% of all first preferences wins. The tallying is over.
• Step 3: If there is no candidate with an absolute majority, the candidate with the least first preferences gets canceled.
• Step 4: Remaining candidates move up. The process continues with step 2.

Example

Preference	A	A	B	B	C	C
Preference	B	C	A	C	A	B
Preference	C	B	C	A	B	A
Number of persons with this preference order	6	0	5	2	5	3

No candidate has the absolute majority. Hence, eliminating all candidates with the least first preferences. In our case, this is candidate A.

B and C move up.

Preference	B	C	B	B	C	C
Preference	C	B	C	A	B	B
Preference	–	–	–	–	–	–
Number of persons with this preference order	6	0	5	2	5	3

Now, B has the most first preferences (13) and wins the election.

The problem with this method is that a voter can harm a candidate by giving it a good vote.

Example

Preference	A	B	C
Preference	B	A	B
Preference	C	C	A
Number of persons with this preference order	10	6	5

C gets eliminated

Preference	A	B	B
Preference	B	A	A
Preference
Number of persons with this preference order	10	6	5

B wins.

If three voters have the preferences (A>B>C) voting differently (C>A>B) according to the following table, they can make A win the election.

Preference	A	B	C	C
Preference	B	A	B	A
Preference	C	C	A	B
Number of persons with this preference order	7	6	5	3

B gets eliminated.

Preference	A	A	C	C
Preference	C	C	A	A
Preference
Number of persons with this preference order	7	6	5	3

A wins instead of B, like in the first example.