This problem can be solved by a system called ranked-choice voting, aka instant-runoff voting
First off, there are multiple voting systems based on ranking your choices. The system you're describing is just one example, and it's a pretty bad one, so it's frustrating that people refer to it as "ranked-choice voting", as if it's the only ranked system.
This system is more specifically referred to as "Instant-Runoff Voting". (Though taken literally, there are other systems that use instant runoff rounds, but "IRV" always means this particular system.)
Second, it has a number of problems:
IRV has a spoiler effect
It eliminates the concern that third party candidates act as spoilers.
It doesn't, though. It actually leads to two-party domination in every country it's adopted in.
It's true that voting honestly for a fringe candidate (Yellow) is safe, since they'll be eliminated immediately and your second choice will go to a mainstream candidate (Green). So IRV is better than plurality in this case (where Red would win even though a majority opposes Red):
However, when the third party candidate becomes more competitive (which is the whole point of adopting an alternative voting system), voting honestly for them takes away votes from your second choice, who will get eliminated first, and then your most-disliked candidate will win in the following round. If the third party hadn't run, your more-preferred candidate would have won, so the third party is acting as a spoiler, and in fact the effect is worse than in plurality (red bar extends further to the right):
Video illustration of this effect:
Favorite Betrayal in Plurality and Instant Runoff Voting
These effects have been modeled graphically on 1-dimensional and 2-dimensional political spaces, and produce bizarre win regions where the population moving toward a candidate causes them to lose, and vice versa. In this example, if the population's opinions shifted to the right, reducing support for Red and increasing support for Yellow, it would cause Red to win instead of Green!:
In 2 dimensions, we can see IRV giving the election to Green even when the population is centered exactly on the Yellow candidate. There's also a bizarre Yellow island that's nowhere near the Yellow candidate, and not present in any of the other voting systems pictured.
Approval voting or Condorcet ranking both have results that make sense, with the candidate nearest to the population center winning:
Animated 2D comparison of different systems:
Yee Animations 0.8
IRV excludes moderates
Similar to above, if there are two more-extreme partisan candidates and a moderate/compromise candidate in the middle, the compromise candidate is eliminated early (for not being anyone's first choice), even though they are the best representative of the population as a whole, and a more partisan candidate is elected instead. This is called the "center-squeeze effect".
This is essentially what happened in Burlington Vermont's 2009 election, which led to IRV being repealed. Montroll was "centrist" relative to the other major candidates, but was eliminated in the 4th round, and a more extreme candidate won, even though Montroll had a higher approval rating than the winner.
Here are the ideal win regions for 14 candidates, with each winning if the population center is nearest to them:
Here's what happens in IRV. All the candidates near the center are eliminated, and only the more extreme fringe candidates can win:
These two effects lead to political polarization and two-party domination. You can see how IRV skews Australia's House in favor of the two main parties even though 1/4 to 1/3 of the population would prefer third parties (while STV leads to a more proportional Senate):
IRV is not a Condorcet system
In the Burlington election, Montroll was also the Condorcet winner, meaning he would have won against every other candidate in head-to-head elections. The overall preferences of the population were unambiguous: Montroll > Kiss > Wright > Smith > Simpson. But IRV is not a Condorcet system; it eliminated Montroll and elected the population's second favorite Kiss instead.
If your system doesn't elect the most-liked candidate (the "Utilitarian Winner"), it should at least elect the most-preferred candidate (the "Condorcet Winner"). IRV guarantees neither.
IRV enables tyranny of the majority
Here's a (contrived) example:
- Candidate A is loved by 55% of the population, and hated by 45% of the population (55% overall approval rating)
- Candidate B is liked by everyone (85% overall approval rating)
Under IRV, the polarizing Candidate A would win, because they are preferred by a majority, even though the population as a whole would be much happier with Candidate B winning the election.
"Utilitarian" voting systems like Score/Approval choose the candidate with the higher approval rating, which is considered a better outcome by advocates of these systems.
Another way of viewing this is that Candidate A is a great representative of half of the population, while Candidate B is a good representative of the entire population.
Majoritarian voting systems are not as inclusive, leading to adversarial politics, inefficiency, and even civil wars.
And if the Republican primaries had used ranked-choice voting, Trump wouldn't have won the nomination, since a majority of the electorate was against him, it's just that the anti-Trump vote was split.
There's not much good data about this, but it's likely that IRV would still have elected Trump:
Score or Condorcet voting would likely have elected Sanders or Kasich, as they had the highest approval ratings: