List of Ranked Preference Voting Methods

Row #	Title	Image	Description
1	Instant Runoff		Instant runoff was developed by William Robert Ware around 1870, although similar methods had been developed earlier. Instant runoff has the following steps: 1. Count the number of first choice votes each candidate gets. 2. If no candidate has more than half of the first choice votes, eliminate the candidate with the lowest number of first choice votes. 3. The voters who ranked that candidate first, have their ranked preferences brought forward i.e. their second choice becomes their first; their third choice becomes their second etc. 4. If no candidate has more than half of the first choice votes, return to step 1, but consider only the remaining candidates. Assuming there isn't a tie, eventually there would be one remaining candidate with more than half of the first choice votes. That candidate is the winner.
2	Condorcet Voting		Condorcet voting was outlined in a paper written in 1785 by the mathematician, philosopher and politician, Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet. A similar method was divised by Ramon Llull in 1299. Each voter's ranked preference is converted into a Condorcet matrix (also called a victory matrix or beat matrix). For example, if a voter ranks the candidates A (first) then C then B, they would have the following Condorcet matrix: Each cell in the matrix represents a single pair wise comparison between candidates. Reading from left to right, starting at the top left hand corner, the matrix can be interpreted as follows: - 'Candidate A beats A' is false (0) - 'Candidate A beats B' is true (1) - 'Candidate A beats C' is true (1) - 'Candidate B beats A' is false (0) - and so on If candidate row beats candidate column then a 1 is assigned. If not, then a 0 is assigned. Once a Condorcet matrix been calculated for each voter, the matrices are then summed. For example, let's say there are three voters with the following individual level Condorcet matrices: Those three matrices are then added together: The Condorcet election winner is determined by the pairwise comparisons. If a candidate is preferred to all other candidates, they are the winner. If no such candidate exists, then there is a cyclical ambiguity and a resolution method must be used to determine the winner. Several resolution methods have been suggested, ranging from the simple Copeland method, to the advanced Schulze method.
3	Borda Count		Borda count voting was developed by Jean-Charles de Borda in 1770. With Borda count, each vote would be converted into a set of Borda scores. Borda's proposed scoring method was that if there were k candidates, the candidate ranked first by the voter would receive a score of (k-1), the second (k-2) etc. If a voter's preferences are strictly transitive for all candidates, their least preferred candidate would receive a score of zero. Once the Borda score set is determined for each voter, the Borda scores are added up for each candidate. The candidate with the highest Borda score is the winner.

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