In America, most elections are based on first-past-the-post voting, where whoever gets a plurality of the votes wins. For instance if candidate A gets 40% of the vote and each of candidates B and C get 30% of the vote, then candidate A wins, even if 60% of the electorate are steadfastly opposed to candidate A.
This problem can be solved by a system called ranked-choice voting, aka instant-runoff voting, where voters rank candidates from best to worst. Suppose there are six candidates. Then each voter ranks the candidates from 1 to 6. Then the voters's first-choice votes are all tallied up, and whichever candidate gets in 6th place is eliminated, and his voters are reallocated to whoever was their second choice. Once this reallocation is done, the 5th place candidate is eliminated, and this process is repeated until only one candidate is left. (And there are some rules on handling ties, just as there are in the first-past-the-post system.) For more information see here.
Ranked-choice voting has many advantages. It eliminates the concern that third party candidates act as spoilers. 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.
But my question is, what arguments have been made against ranked-choice voting. It seems like an obviously superior system to me. The only downsides I can think of is that it may be too hard to understand for some voters, and there may be implementation costs. But it's been implemented in San Francisco and several other jurisdictions, and it doesn't seem to have caused any catastrophic problems.
EDIT: My question is not about the difficulties of switching to ranked-choice voting, but about what disadvantages (if any) there are of the system itself.
