An election calculator for the major Condorcet proposals using winning votes (WV): Schulze, Ranked Pairs, River, MinMax, and Smith-limited MinMax.
Equal ranking is supported, and resolution details are provided for the curious.
Methods
Schulze: Markus Schulze's method in which one elects the candidate whose strongest beatpath to each other candidate is at least as strong as each respective path back.
An alternative procedure exists where one alternates between recalculating the Schwartz set and dropping the weakest remaining defeat.
Ranked Pairs: A form of Nicolaus Tideman's proposal. Proceeding from strongest defeats to weakest defeats, gradually "lock" a final ranking of all the candidates, ignoring any defeats that would introduce a cycle.
River: Jobst Heitzig's method which resembles Ranked Pairs except that defeats against candidates already defeated are not counted. This offers a simpler way to resolve the election as well, since it is no longer necessary to track the structure within each partial ranking: It's enough to know which candidate sits at the top of any partial ranking so far computed.
MinMax: A simple but technically somewhat inferior method in which one elects the candidate whose worst pairwise defeat is the mildest. It can violate the Condorcet Loser and Mutual Majority criteria.
Smith//MinMax: A simple improvement of MinMax, where one removes all candidates outside the Smith set before assessing the worst defeats.
All of these except for plain MinMax elect from the Smith set. Schulze also guarantees that the winner is in the Schwartz set. (A difference is possible only when there are pairwise ties.)
Ranked Pairs: A form of Nicolaus Tideman's proposal. Proceeding from strongest defeats to weakest defeats, gradually "lock" a final ranking of all the candidates, ignoring any defeats that would introduce a cycle.
River: Jobst Heitzig's method which resembles Ranked Pairs except that defeats against candidates already defeated are not counted. This offers a simpler way to resolve the election as well, since it is no longer necessary to track the structure within each partial ranking: It's enough to know which candidate sits at the top of any partial ranking so far computed.
MinMax: A simple but technically somewhat inferior method in which one elects the candidate whose worst pairwise defeat is the mildest. It can violate the Condorcet Loser and Mutual Majority criteria.
Smith//MinMax: A simple improvement of MinMax, where one removes all candidates outside the Smith set before assessing the worst defeats.
All of these except for plain MinMax elect from the Smith set. Schulze also guarantees that the winner is in the Schwartz set. (A difference is possible only when there are pairwise ties.)
Instructions
Enter your ballots like this, one per line:
456: Alice>Bob=Carl>Debra
The number represents the size of the voting bloc. Decimals are OK. The size can also be left off and it will then be randomized.
Candidate names can contain spaces. Each candidate in the list should be separated by > or =. Pipes (i.e. |) and any series of > will be interpreted as single >s. Not every candidate needs to be listed; candidates present on the ballots but missing from one faction's ranking will be interpreted as ranked tied for last, below any explicitly ranked candidates.
Click submit to generate an analysis.
456: Alice>Bob=Carl>Debra
The number represents the size of the voting bloc. Decimals are OK. The size can also be left off and it will then be randomized.
Candidate names can contain spaces. Each candidate in the list should be separated by > or =. Pipes (i.e. |) and any series of > will be interpreted as single >s. Not every candidate needs to be listed; candidates present on the ballots but missing from one faction's ranking will be interpreted as ranked tied for last, below any explicitly ranked candidates.
Click submit to generate an analysis.
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Enter the ballots for an election:
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