Editing Condorcet method (section)

===Ranked pairs===
{{Main|Ranked pairs}}
{{Unreferenced section|date=March 2021}}

The order of finish is constructed a piece at a time by considering the (pairwise) majorities one at a time, from largest majority to smallest majority. For each majority, their higher-ranked candidate is placed ahead of their lower-ranked candidate in the (partially constructed) order of finish, except when their lower-ranked candidate has already been placed ahead of their higher-ranked candidate.

For example, suppose the voters' orders of preference are such that 75% rank B over C, 65% rank A over B, and 60% rank C over A. (The three majorities are a [[rock paper scissors]] cycle.) Ranked pairs begins with the largest majority, who rank B over C, and places B ahead of C in the order of finish. Then it considers the second largest majority, who rank A over B, and places A ahead of B in the order of finish. At this point, it has been established that A finishes ahead of B and B finishes ahead of C, which implies A also finishes ahead of C. So when ranked pairs considers the third largest majority, who rank C over A, their lower-ranked candidate A has already been placed ahead of their higher-ranked candidate C, so C is not placed ahead of A. The order of finish is "A, B, C" and A is the winner.

An equivalent definition is to find the order of finish that minimizes the size of the largest reversed majority. (In the 'lexicographical order' sense. If the largest majority reversed in two orders of finish is the same, the two orders of finish are compared by their second largest reversed majorities, etc. See [[Lexicographical order|the discussion of MinMax, MinLexMax and Ranked Pairs in the 'Motivation and uses' section of the Lexicographical Order article]]). (In the example, the order of finish "A, B, C" reverses the 60% who rank C over A. Any other order of finish would reverse a larger majority.) This definition is useful for simplifying some of the proofs of Ranked Pairs' properties, but the "constructive" definition executes much faster (small polynomial time).