This is a different way to think about the Schulze Method, which might convince people who don't like the "beatpath" construction.

I wrote about the Schulze method in the previous post, giving a justification that is based on the standard presentation of the method using beatpaths.

This is a different look at the same method, implemented a different way.

Suppose you first looked for a Condorcet winner: so you look at all the pairwise matchups, and find out who is preferred to who. You make a matrix of pairwise preferences, and maybe for convenience subtract the number of voters who preferred Y to X from the number who preferred X to Y to get the margin of pairwise preferences. (These matrices are in the example in the Wikipedia link to the Schulze method above -- if I were more detail-oriented, I'd put an example here.)

Any row that's all positive means that candidate beats all others head-to-head: that's a Condorcet winner!

But suppose there isn't a row that's all positive. What do we do? Well, first, we can eliminate any Condorcet *loser*: a candidate that is not preferred in **any** head-to-head matchup. (We'll spot a Condorcet loser in the matrix because it's got a row of margins that's all negative, or equivalently a column that's all positive.)[see footnote]

Then, since we want the closest thing to a Condorcet winner, let's "grade on a curve", and do one of the following (these are equivalent):

- add something to all the margins: add 5 (for example) to all the margins of pairwise preferences (add more if you haven't changed anything from negative to zero/positive, add less if you've changed too many elements) OR
- find the negative margin that's closest to zero (-3 is closer than -10) and set it to zero.

*and*C, eliminate both of them - clearly the winner should be A, B, or C.) But in terms of justification, this is a technical point; the idea is that you're looking for the "closest to Condorcet" winner.