# [EM] IRV / RCv advances

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Jul 13 13:32:55 PDT 2018

```On 2018-07-13 20:56, Richard Lung wrote:

> I took ranked pairs to mean Condorcet pairing. No?

Not quite. Perhaps the terms can be a bit confusing.

The Condorcet criterion is a voting method criterion that says "if there
exists a candidate who would win a two candidate runoff against any
other candidate, based on the ballot preferences, then that candidate
must win". In other words, if there exists a candidate A, so that for
any other candidate B, more voters prefer A to B than B to A, then A
must win.

A Condorcet method is a method that satisfies that criterion. These can
use pairwise matrices (what I called c and d in my description of Ranked
Pairs), but they don't need to. For instance, the Borda analog of IRV
(where you repeatedly eliminate the candidate with the lowest Borda
score) is a Condorcet method although no pairwise matrices are needed to
calculate who wins.

A pairwise method could be the same as a Condorcet method, or could be a
Condorcet method that explicitly uses a pairwise matrix.

Ranked Pairs is a Condorcet method that uses an election's associated
pairwise matrix to determine the winner of that election. Schulze is
another (as is Minmax, Copeland, River, etc...)

So Ranked Pairs is not a class of methods, but a particular method - or
two methods if you consider the version proposed by Nicolaus Tideman
(with margins definition of d) as a different method than the version
proposed by Steve Eppley (with wv definition of d).

I called d the pairwise matrix in my description of Ranked Pairs, but
it's probably more accurate to call c the pairwise matrix (or Condorcet
matrix). When doing precinct counts, the election authority would get
different c matrices from each precinct, sum them up element-wise, and
then convert to d when running Ranked Pairs (or Schulze, Minmax,
Copeland, River, or what method it might use).
```