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Ranked pairs (or RP), sometimes called the Tideman method, is a tournamentstyle system of rankedchoice voting first proposed by Nicolaus Tideman in 1987.^{[1]}^{[2]}
Ranked pairs begins with a roundrobin tournament, where the oneonone margins of victory for each candidate are compared to find a majority winner. If there is a Condorcet cycle (a rockpaperscissors sequence A > B > C > A), the cycle is broken by dropping nearlytied elections, i.e. the closest elections in the cycle.^{[3]}
The ranked pairs procedure is as follows:
At the end of this procedure, all cycles will be eliminated, leaving a unique winner who wins every oneonone matchup (that has not been crossed out). The lack of cycles means that candidates can be ranked linearly based on the matchups that have been left behind.
The River variant crosses out redundant (duplicate) defeats as well as cyclical ones. In other words, it does not "doublecount" multiple defeats for the same candidate. The River method allows for faster computation of winners.^{[note 2]} It also makes the election method less vulnerable to strategic nominations, by preventing weak candidates from creating several cycles to manipulate the outcome.
Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:
The preferences of each region's voters are:
42% of voters FarWest 
26% of voters Center 
15% of voters CenterEast 
17% of voters FarEast 





The results are tabulated as follows:
A B

Memphis  Nashville  Chattanooga  Knoxville 
Memphis  [A] 58%
[B] 42% 
[A] 58%
[B] 42% 
[A] 58%
[B] 42%  
Nashville  [A] 42%
[B] 58% 
[A] 32%
[B] 68% 
[A] 32%
[B] 68%  
Chattanooga  [A] 42%
[B] 58% 
[A] 68%
[B] 32% 
[A] 17%
[B] 83%  
Knoxville  [A] 42%
[B] 58% 
[A] 68%
[B] 32% 
[A] 83%
[B] 17% 
First, list every pair, and determine the winner:
Pair  Winner 

Memphis (42%) vs. Nashville (58%)  Nashville 58% 
Memphis (42%) vs. Chattanooga (58%)  Chattanooga 58% 
Memphis (42%) vs. Knoxville (58%)  Knoxville 58% 
Nashville (68%) vs. Chattanooga (32%)  Nashville 68% 
Nashville (68%) vs. Knoxville (32%)  Nashville 68% 
Chattanooga (83%) vs. Knoxville (17%)  Chattanooga: 83% 
The votes are then sorted. The largest majority is "Chattanooga over Knoxville"; 83% of the voters prefer Chattanooga. Thus, the pairs from above would be sorted this way:
Pair  Winner 

Chattanooga (83%) vs. Knoxville (17%)  Chattanooga 83% 
Nashville (68%) vs. Knoxville (32%)  Nashville 68% 
Nashville (68%) vs. Chattanooga (32%)  Nashville 68% 
Memphis (42%) vs. Nashville (58%)  Nashville 58% 
Memphis (42%) vs. Chattanooga (58%)  Chattanooga 58% 
Memphis (42%) vs. Knoxville (58%)  Knoxville 58% 
The pairs are then locked in order, skipping any pairs that would create a cycle:
In this case, no cycles are created by any of the pairs, so every single one is locked in.
Every "lock in" would add another arrow to the graph showing the relationship between the candidates. Here is the final graph (where arrows point away from the winner).
In this example, Nashville is the winner using the rankedpairs procedure. Nashville is followed by Chattanooga, Knoxville, and Memphis in second, third, and fourth places respectively.
In the example election, the winner is Nashville. This would be true for any Condorcet method.
Under firstpastthepost and some other systems, Memphis would have won the election by having the most people, even though Nashville won every simulated pairwise election outright. Using instantrunoff voting in this example would result in Knoxville winning even though more people preferred Nashville over Knoxville.
Of the formal voting criteria, the ranked pairs method passes the majority criterion, the monotonicity criterion, the Smith criterion (which implies the Condorcet criterion), the Condorcet loser criterion, and the independence of clones criterion. Ranked pairs fails the consistency criterion and the participation criterion. While ranked pairs is not fully independent of irrelevant alternatives, it still satisfies local independence of irrelevant alternatives and independence of Smithdominated alternatives, meaning it is likely to roughly satisfy IIA "in practice."
Ranked pairs fails independence of irrelevant alternatives, like all other ranked voting systems. However, the method adheres to a less strict property, sometimes called independence of Smithdominated alternatives (ISDA). It says that if one candidate (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the Smith set. ISDA implies the Condorcet criterion.
The River variant satisfies an additional criterion, independence of Paretodominated alternatives, which says that if any candidate would lose some election unanimously, they must not affect the outcome.
The following table compares ranked pairs with other preferential singlewinner election methods:
Criterion:  Majority  Majority loser criterion  Mutual majority criterion  Condorcet winner  Condorcet loser  Smith  ISDA  LIIA  Cloneproof  Monotone  Participation  Reversal  Laternoharm  Laternohelp  Polynomial time  Resolvability 

Schulze  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  Yes  No  Yes  No  No  Yes  Yes 
Ranked pairs  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  No  No  Yes  Yes 
Tideman alternative  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  No  No  No  No  No  Yes  Yes 
Kemeny–Young  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  No  Yes  No  No  No  Yes 
Ranked robin  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  No  Yes  No  Yes  No  No  Yes  No 
Nanson  Yes  Yes  Yes  Yes  Yes  Yes  No  No  No  No  No  Yes  No  No  Yes  Yes 
Black  Yes  Yes  No  Yes  Yes  No  No  No  No  Yes  No  Yes  No  No  Yes  Yes 
Instantrunoff voting  Yes  Yes  Yes  No  Yes  No  No  No  Yes  No  No  No  Yes  Yes  Yes  Yes 
Smith//IRV  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  No  No  No  No  No  Yes  Yes 
Borda count  No  Yes  No  No  Yes  No  No  No  No  Yes  Yes  Yes  No  Yes  Yes  Yes 
Baldwin  Yes  Yes  Yes  Yes  Yes  Yes  No  No  No  No  No  No  No  No  Yes  Yes 
Bucklin  Yes  Yes  Yes  No  No  No  No  No  No  Yes  No  No  No  Yes  Yes  Yes 
Plurality  Yes  No  No  No  No  No  No  No  No  Yes  Yes  No  Yes  Yes  Yes  Yes 
Coombs  Yes  Yes  Yes  No  Yes  No  No  No  No  No  No  No  No  No  Yes  Yes 
Minimax  Yes  No  No  Yes  No  No  No  No  No  Yes  No  No  No  No  Yes  Yes 
Antiplurality  No  Yes  No  No  No  No  No  No  No  Yes  Yes  No  No  No  Yes  Yes 
Dodgson  Yes  No  No  Yes  No  No  No  No  No  No  No  No  No  No  No  Yes 