Visual explanation of the Condorcet method

Under a spatial model of voters, a Condorcet method partitions the ideological space into two for each pair of candidates. If a Condorcet winner exists, they are on the majority side of each partition.

In this animation voters are small dots, candidates are big black or blue dots, and the Condorcet winner is a big red dot. The big blue dot is the current candidate being pairwise compared to the Condorcet winner. The thin line joining the two is a visual aid to highlight the comparison being made.

Each pairwise comparison defines a cut (thick blue line across the image) and creates a "dominant region" (in light blue background) on the majority side. The Condorcet winner is always on this dominant region.

Over all possible partitions, the Condorcet winner will "carve" itself a "Condorcet region" of the ideological space (yellow background), and ever voter in that region (red dots) is in the "Condorcet winner's faction", as defined by this current distribution of candidates and voters. (A different distribution of candidates, even with the same voters, would create different factions.)

This "Condorcet faction" is the group of voters that are more closely represented by the Condorcet winner, and the election. The consensus of the voters within this faction is shown as the small black cross, and the population's overall consensus is the origin over the entire space, as denoted by the axes.

The distance between the two positions is the ideological deviation of a Condorcet method. Despite this deviation, note that the yellow "Condorcet region" always contains the overall consensus.

This illustrates how Condorcet methods find the "faction which is closest to the consensus".