Maybe IRV got an early start as a poster child of alternative voting systems, thus it's popularity. In any case, I would argue along with other commenters that IRV's run-offs would probably be far easier to understand for the general electorate than other, more complex vote-processing systems. I would very much disagree with your (xvedejas's) characterization of ranked pairs as being simpler than IRV, though range voting would indeed seem easier to explain and implement than IRV. A math major (or at least a minor) seems like a requirement for someone to understand the ranked pair system.

I was unfamiliar with the ranked pairs system, and will study it more to understand it better. It looks promising as far as technical excellence, though I'm afraid it'd still be too hard to understand for the general populace in most (or all) countries.

One thing I suspect about range voting is that it seems to require strategic voting. A voter would still need to give a very favorable score to a majority party that's kind of aligned with their views, as opposed to giving them a lower score than a minority/third party he or she would prefer. One of the strongest appeals to me from IRV is the opportunity it provides for a minority party to unseat majority parties, which is appealing given the political stagnation experienced by many countries. I had also thought that it allowed voters to avoid strategic voting and express their true, individual voting preferences.

After reading IRV's description in http://zesty.ca/voting/sim/ , I realized that I had misunderstood one important detail. I had thought that the least popular candidates were eliminated first until only the top two candidates remained, and the one with most votes among them remained. I dislike that the "real" IRV (not the one that was in my head) first checks for a 50%-plus-one majority before eliminating the bottom candidates. That feels too much like the first-past-the-post system for my liking. I wonder if having successive rounds where the least-favorite first place candidate is eliminated would make most people's favorite candidates "bubble up" to the top, producing a final match between two highly-favored candidates. I wonder if such a system is closer to a Condorcet method than the real IRV...