That would basically be instant runoff voting. The main issue with that is that in a polarized election you can have a moderate compromise option eliminated ea

That would basically be instant runoff voting. The main issue with that is that in a polarized election you can have a moderate compromise option eliminated early. For example, suppose the election is between a far-left, moderate, and far-right candidate. 40% prefer the far-left candidate, 20% prefer the moderate candidate, and 40% prefer the far-right candidate. In this case 60% of the population prefers the moderate candidate to the far-right candidate, and 60% prefer the moderate candidate to the far-left candidate and so the moderate candidate should win the election. But in an IRV-type system, the moderate candidate gets eliminated immediately and the election is then between the extreme candidates.