Recursive Rankings

Recursive Rankings are based on another simple idea (although carrying out the procedure takes longer than for Extended Rankings).

Regardless of the particular voting method, the idea behind Recursive Rankings is the same:

  1. Run the election using a particular voting method; give first place to the winner.

  2. Remove the winner and re-run the election (using the same voting method); give second place to the winner.

  3. Continue re-running the election and assigning places to the winner until all candidates have been ranked.

For instance, in a Pairwise Comparisons election, Recursive Rankings would give first place to the candidate who won the most head-to-head matchups. This candidate would be eliminated and the election would be re-run. Second place would go to the candidate who won the most head-to-head matchups in this second election. This process of removing winners and re-running elections would continue until all of the original candidates had been ranked.

Applying this Recursive Ranking procedure to each of the five voting methods covered here, we have:

Recursive Plurality
Run a Plurality election. First place goes to the candidate with the most first place votes.
This candidate is eliminated and the election is re-run.
The winner of this second election (the remaining candidate with the most first place votes) gets second place.
Repeat this process (eliminating candidates and re-running elections) until all of the candidates are ranked.

Recursive Plurality with Elimination
Run a Plurality with Elimination election. (Remember that a Plurality with Elimination election consists of rounds in which the candidate with the fewest first place votes is eliminated--the winner is the last candidate remaining.) First place goes to the lone remaining candidate.
This winning candidate is eliminated and the election is re-run.
The winner of this second election (the lone remaining candidate after the elimination process) gets second place.
Repeat this process (eliminating candidates and re-running elections) until all of the candidates are ranked.
WARNING! Plurality with Elimination is a recursive process; that is, the winner is determined by repeating a series of elections (or rounds). Recursive Plurality with Elimination, then, adds another layer of 'recursion'; in other words, it is a repetitive process embedded within another repetitive process. So, be careful!

Recursive Borda Count
Run a Borda Count election. First place goes to the candidate with the largest Borda Count total.
This candidate is eliminated and the election is re-run.
The winner of this second election (the remaining candidate with the largest Borda Count total) gets second place.
Repeat this process (eliminating candidates and re-running elections) until all of the candidates are ranked.

Recursive Pairwise Comparisons
Run a Paiwise Comparisons election. First place goes to the candidate that wins the most head-to-head matchups (1 point for each head-to-head win; half of a point for each head-to-head tie).
This candidate is eliminated and the election is re-run.
The winner of this second election (the remaining candidate that wins the most head-to-head matchups) gets second place.
Repeat this process (eliminating candidates and re-running elections) until all of the candidates are ranked.

Recursive Approval Voting
Run an Approval Voting election. First place goes to the candidate with the most Approval Votes.
This candidate is eliminated and the election is re-run.
The winner of this second election (the remaining candidate with the most Approval Votes) gets second place.
Repeat this process (eliminating candidates and re-running elections) until all of the candidates are ranked.


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