In terms accessible to someone new to electoral systems, what does the Schulze system do in case of no condorcet winner?

Question

The title pretty much summarizes it. I am new to the idea of different electoral systems. Schulze is one that I find very interesting, but I find it difficult to understand what it does in case of no condorcet winner. Some help would be much appreciated.

Answer 1

There are several algorithms for calculating the Schulze winner that give the same result. Here’s one with a particularly simple explanation (source):

For every pair of candidates A and B, draw an arrow A → B if its supporting voters (preferring A over B) outnumber its opposing voters (preferring B over A). Call a candidate “competitive” if they have a forward path along one or more arrows to each other candidate. There’s guaranteed to be at least one competitive candidate.

Now, some arrows A → B are stronger than others because they have more supporting voters, or the same number of supporting voters but fewer opposing voters. Go through the arrows in order from weakest to strongest, erasing any arrows that can be erased such that there’s still at least one competitive candidate. The last remaining competitive candidate wins.