The math behind Polis groups you together with people who tend to vote in agreement with you.
This is similar to the product or movie recommendations you see on Amazon or Netflix. These services use statistics to group you with people who buy and watch similar things as you, then surface other things those people bought or watched.
Similarly, once Polis has grouped you with the users you tend to agree with, it finds the comments in the conversation which your group tends to agree with (but other groups tend to disagree with). It also shows you the comments in the conversation your group tends to disagree with (but other groups tend to agree with). We call these representative comments, because they are representative of how your group voted differently from other groups.
Polis goes even further by also showing you the representative comments for other groups. This lets you explore how other groups in the conversation relate to yours. You click on a group to see what separates it from others.
Finally, Polis is also interested not only in how groups differ from each other, but also in where there tends to be consensus. What comments do people from all groups tend to agree or disagree with? For this, you can click the "Majority Opinion" button underneath the visualization.