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:
Run the election using a particular voting
method; give first place to the winner.
Remove the winner and re-run the election
(using the same voting method); give second place to the winner.
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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