Coombs' method

The Coombs - election is an election process by which a single winner is determined. Just like instant runoff voting, each voter created according to its preferences, a ranking of the candidates.

The Coombs - election follows as well as the instant - runoff voting the principle that as long as candidates are eliminated and their votes are redistributed according to the rankings on the ballots to the remaining candidates until one candidate achieves an absolute majority. In contrast to the instant - runoff voting, however, differs in the Coombs - election of the remaining candidates are not those with the fewest Erstpräferenzen from, but the one who was most frequently chosen on the last rank.

Description of the selection method

If no candidate achieves an absolute majority among the Erstpräferenzen, it is the candidate who was most frequently chosen on the last rank or not marked with a rank, taken out of the race. The canceled on him votes are distributed to the second preferences. Similarly, the last rank of each ballot is passed on to the penultimate preference.

Has hereafter continue no candidate achieved an absolute majority, in turn, the remaining candidate is taken with the most votes from the last race and the canceled on him votes distributed to the second preferences; is the second preference was eliminated the third preference is used, etc. This procedure is continued until a candidate has achieved an absolute majority.

Example

Consider an election with four candidates A, B, C and D and the following voter preferences:

The first votes and last votes of the candidates would be:

Since no candidate has an absolute majority, the candidate with the most votes last, namely, candidate A is eliminated and his votes redistributed:

Still no candidate has an absolute majority, thus again, the candidate shall be deleted with the most ultimate placements, in this case is a candidate as

Finally, candidate C has an absolute majority and is therefore the winner of the election with Coombs' method.

Shortcomings

Like the instant runoff voting does not meet the selection Coombs the Condorcet criterion. This can be easily understood if one considers again the above example:

The Condorcet winner would be A, because this candidate is preferred by 58 % compared to the candidate B, of 60 % compared to candidate C and 51% of the votes over candidate D. Since candidate A with 49% Erstpräferenzen but will not achieve absolute majority and most often is in last place, Candidate A is using the Coombs choice eliminated first, although it would be a Condorcet winner.