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Ranked Pairs (RP) 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 majoritypreferred candidate; if such a candidate exists, they are immediately elected. Otherwise, if there is a Condorcet cycle—a rockpaperscissorslike sequence A > B > C > A—the cycle is broken by dropping the "weakest" elections in the cycle, i.e. the ones that are closest to being tied.^{[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 directly based on the matchups that have been left behind.
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^{[broken anchor]} 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 following table compares ranked pairs with other singlewinner election methods:
Criterion Method 
Majority  Majority loser  Mutual majority  Condorcet winner 
Condorcet loser  Smith 
SmithIIA 
IIA/LIIA 
Cloneproof  Monotone  Participation  Laternoharm 
Laternohelp 
No favorite betrayal 
Ballot type  

Antiplurality  No  Yes  No  No  No  No  No  No  No  Yes  Yes  No  No  Yes  Single mark  
Approval  Yes  No  No  No  No  No  No  Yes 
Yes  Yes  Yes  No  Yes  Yes  Approvals  
Baldwin  Yes  Yes  Yes  Yes  Yes  Yes  No  No  No  No  No  No  No  No  Ranking  
Black  Yes  Yes  No  Yes  Yes  No  No  No  No  Yes  No  No  No  No  Ranking  
Borda  No  Yes  No  No  Yes  No  No  No  No  Yes  Yes  No  Yes  No  Ranking  
Bucklin  Yes  Yes  Yes  No  No  No  No  No  No  Yes  No  No  Yes  No  Ranking  
Coombs  Yes  Yes  Yes  No  Yes  No  No  No  No  No  No  No  No  Yes  Ranking  
Copeland  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  No  Yes  No  No  No  No  Ranking  
Dodgson  Yes  No  No  Yes  No  No  No  No  No  No  No  No  No  No  Ranking  
Highest median  Yes  Yes 
No 
No  No  No  No  Yes 
Yes  Yes  No 
No  Yes  Yes  Scores  
Instantrunoff  Yes  Yes  Yes  No  Yes  No  No  No  Yes  No  No  Yes  Yes  No  Ranking  
Kemeny–Young  Yes  Yes  Yes  Yes  Yes  Yes  Yes  LIAA Only  No  Yes  No  No  No  No  Ranking  
Minimax  Yes  No  No  Yes 
No  No  No  No  No  Yes  No  No 
No  No  Ranking  
Nanson  Yes  Yes  Yes  Yes  Yes  Yes  No  No  No  No  No  No  No  No  Ranking  
Plurality  Yes  No  No  No  No  No  No  No  No  Yes  Yes  Yes  Yes  No  Single mark  
Random ballot 
No  No  No  No  No  No  No  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Single mark  
Ranked pairs  Yes  Yes  Yes  Yes  Yes  Yes  Yes  LIAA Only  Yes  Yes  No 
No  No  No  Ranking  
Runoff  Yes  Yes  No  No  Yes  No  No  No  No  No  No  Yes  Yes  No  Single mark  
Schulze  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  Yes  No 
No  No  No  Ranking  
Score  No  No  No  No  No  No  No  Yes 
Yes  Yes  Yes  No  Yes  Yes  Scores  
Sortition 
No  No  No  No  No  No  No  Yes  No  Yes  Yes  Yes  Yes  Yes  None  
STAR  No  Yes  No  No  Yes  No  No  No  No  Yes  No  No  No  No  Scores  
Tideman alternative  Yes  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes  No  No  No  No  No  Ranking  
Table Notes 
