# Pairwise Sorted Methods

From Electowiki

Pairwise Sorted Methods all share these properties:

- The list of candidates is first sorted top to bottom according to some metric. This can be considered to be a seed for the next sorting stage.
- Starting at the top of the list, each pair of candidates is processed in some way in accordance with their pairwise (one-to-one) contest.
- The winner is the candidate that ends up at the top of the list.

Almost all methods of this type satisfy the Condorcet Criterion because a candidate that pairwise defeats every other candidate will eventually be bubble-sorted to the top of the list.

In other fields, the pairwise sorting stage is known as Local Kemenization. See, for example, Rank Aggregation Methods for the Web.

One nice by-product of local Kemenization is that the initial seed order is acyclic --- any pairwise cycles that might exist are precluded from the final result.

Among pairwise sorted methods that have been suggested on the election-methods mailing list are

- Pairwise Sorted Approval: Use total Approval score in descending order for initial seed.
- Pairwise Sorted Bordal: Use total Borda score in descending order for initial seed.
- Approval Sorted Margins. Use total Approval score in descending order for initial seed. For subsequent pairwise sort, repeat until all pairs are ordered pairwise:
- Search through list for pairs that are out of order pairwise.
- Reverse the pair with the least difference in approval.