Instant Runoff

Published by Mario Oettler on

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

PreferenceAABBCC
PreferenceBCACAB
PreferenceCBCABA
Number of persons with this preference order605253

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.

PreferenceBCBBCC
PreferenceCBCABB
Preference
Number of persons with this preference order605253

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

PreferenceABC
PreferenceBAB
PreferenceCCA
Number of persons with this preference order1065

C gets eliminated

PreferenceABB
PreferenceBAA
Preference   
Number of persons with this preference order1065

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.

PreferenceABCC
PreferenceBABA
PreferenceCCAB
Number of persons with this preference order7653

B gets eliminated.

PreferenceAACC
PreferenceCCAA
Preference    
Number of persons with this preference order7653

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

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