I'm glad there's plenty of people here mentioning the Condorcet Winner. Because that's the one and only voting property that I can't compromise on. If there is a Condorcet Winner, a voting system that doesn't choose it is useless. But it's not like IRV has to be entirely thrown out. As some have suggested, it would be just fine to use a hybrid system like "pick Condorcet Winner if it exists, use [IRV/STAR/etc] otherwise".

I'd like more people to talk about Ranked Pairs / Tideman. It satisfies a ridiculous number of voting criteria, even more than Schulze, but with the huge advantage that it's explainable to a layperson. https://en.wikipedia.org/wiki/Ranked_pairs