A look around the various methods of Condorcet
Introduction
These methods are modern mathematical algorithms, sometimes heavy, to extend and complement the original methods of the Marquis de Condorcet, without ever results do contradict.
Specifically, these methods can overcome shortages such as the Condorcet paradox. A special case where no winner or loser can not normally be determined.
These methods are also used to represent a complete ranking of the election.
Each has its biases, its advantages and disadvantages, and may require more computing power or less. Meet certain anti-manipulation advanced criteria like "independence of clone", "Smith criterion" or "local independence".
If you do not have specific needs, we recommend the use of Schulze Winning method.
Specifications
Above all, a small table summarizing the characteristics of the main methods of advanced votes, that they meet or fail the Condorcet criterions.
Supported method on Condorcet-Vote.org
- Schulze method also know as: Schwartz Sequential Dropping (SSD), Cloneproof Schwartz Sequential Dropping (CSSD), the Beatpath Method...
- Ranked Pairs (exprimental implementation at this date)
- Kemeny-Young method also know as: Kemeny rule, VoteFair popularity ranking, maximum likelihood method and the median relation.
(Cause of performance consideration, works only for election with less than 7 candidates)
- Copeland method
- MiniMax Family methods also know as: Simpson-Kramer method, Successive reversal method
- MiniMax Winning
- MiniMax Margin
- MiniMax Opposition This is not a Condorcet method, because it fails occasionally its criteria!
- And of course, naturals winner & loser from original Marquis de Condorcet method if there s not paradox of Condorcet
Condorcet Methods Overview
Schulze
Resume
If for a pairwise contest X either beats or ties Y, then we say that X has a path to Y, with a strength equal to the number of voters ranking X over Y.
If X has a path to Y of strength m, and Y has a path to Z of strength n, then we say that X has a path to Z equal to the minimum of m and n.
Of all the paths from X to Y, a maximum path strength can be found. If the maximum path strength from X to Y is greater than the maximum path strength from Y to X, then Y cannot win. The winner is the candidate that does not lose any such maximum path strength comparisons.
The Schulze method is undoubtedly the most popular advanced Condorcet method. It is commonly used in organizations to collaborative vocation as Wikipedia, Debian, KDE, Pirate Party, Free Software Foundation Europe, OpenStack...
Documentation by Martin Schulze himself :
Variants
- Schulze Winning (Recommanded by M.Schulze)
- Schulze Margin
- Schulze Ratio
Note
Our implementation is simple and safe. It does not include the complex and heavy possible supplements (STV. ..) for advanced tie-breaking. Schulze meet the criterion of resolvability, the possibility of a draw as then already very low and increasingly unlikely when the number of voters exceeds the number of candidates.
Ranked Pairs
Resume
Ranked Pairs finds a complete ranking. pairwise victories are processed starting from the greatest margin, and working down. These victories are locked, which means that the final ranking will agree with this pairwise decision. If a victory is processed that is incompatible with the previously locked victories, it is skipped. Once all victories are processed, a complete ranking is left.
Documentation
Note
Our own implementation of this method is actually strange and experimental.
The results look good, but do not take care of contingencies equalities, yet frequent votes on small, sharp then these disputes arbitrarily.
Paradoxically, our implementation is more reliable on large elections as small.
Kemeny-Young
Resume
Each possible complete ranking of the candidates is given a "distance" score. For each pair of candidates, find the number of ballots that order them the the opposite way as the given ranking. The distance is the sum across all such pairs. The ranking with the least distance wins.
Note
This method, particularly heavy, simply involves a series of calculations for each final classification possible. It is therefore dependent on the number of candidates in the presence (and not specifically the number of voters). Thus, if five candidates are 120 possibilities to calculate, six are 720 and ten are 3 628 800 possible solutions to compute and store!
For this reason, the results of this method will here provides for election comprising at most 5 candidates.
Also, this method although excellent, tends not to reach a solution in the case of a very small number of voters (less than the number of candidates). This will be indicated in bold, and an arbitrary classification (but realistic) is provided for reference only.
Copeland
Resume
Each alternative's Copeland score is calculated by subtracting the number of alternatives that pairwise beat it from the number that it beats. The alternatives with the highest Copeland score win.
Copeland method is very fast and simple. But this method failed to the criterion of resolvability, so there is often tie on result. Of its ease of understanding, this method has been proposed and is still some local elections by universal suffrage around the world.
MiniMax
Resume
Minimax selects as the winner the candidate whose greatest pairwise defeat is smaller than the greatest pairwise defeat of any other candidate.
Variants
When it is permitted to rank candidates equally, or to not rank all the candidates, three interpretations of the rule are possible. When voters must rank all the candidates, all three variants are equivalent.
- MiniMax Winning
- MiniMax Margin
- MiniMax Opposition This is not a Condorcet method, because it fails occasionally its criteria!