I'm not too big of a fan of this site but it is nice. One thing I wanted to point out is the spoiler effect. Often we talk about it but similarly we generally only talk about a weak spoiler. So I wanted to show an example of a strong spoiler[0]. In this example Hexagon splits Triangles votes just by a little, but the sum of Triangle and Hex are larger than Square. But here IRV has Square winning but Approval has Hex winning.
This is one big issue for me with IRV vs Cardinal systems. Both handle _weak_ spoilers but IRV doesn't handle ''strong,, spoilers. Understanding that these are two different types of spoilers is really important. It is "Bernie vs Hillary" and "Cruz vs Trump." Even with IRV we'd still see the parties trying to prevent strong primary candidates from running independently because they could spoil the election. With cardinal methods (approval, score, star) this is far less of a concern and thus I think more democratic of an election. I honestly think we should be much more concerned with strong spoilers than weak spoilers (weak spoilers don't affect elections much anyways).