Earlier this week in the Minnesota Supreme Court, a case questioning the contitutionality of instant runoff voting was heard. There hasn't been a ruling yet, but the suspicion is that the judges will find that IRV is constitutional, and the plaintiffs are already preparing an appeal to the U.S. Supreme Court.
This may be surprising, but I agree with the judges (supposed) decision. Just because IRV is a bad system (and I think it is) that shouldn't make it unconstitutional. Plurality is a bad system too, and we've been using it since before the constitution was even ratified. Part of the argument was that IRV violates the principle of "one person, one vote", since you can indicate more than one candidate for a position on your ballot; this is also one of the major arguments used against approval voting. But it's a spurious argument. A "vote" isn't necessarily one candidate's name, but rather it is the expression of one voter's will via their ballot. The principle of "one person, one vote" is meant to be taken as no voter should have a greater (or lesser) impact upon the outcome of the election than another; if I could submit two ballots in a plurality election, that would be as bad as if could submit two ballots in an IRV (or approval or score) election. But as long as everyone's ballot is treated identically, and everyone can only submit one ballot, than the "one person, one vote" principle is still followed. Counting a voter's choice toward their second choice after their first is eliminated isn't "changing their vote", it's following their will; as the defense attorney said "You have cast that second choice ballot."
There is additional complaint over multi-winner elections (such as for the school board), which I assume are using some variation of Single Transferable Vote (STV). STV is the grandfather of IRV, and can involve moving around fractions of a vote (if the quota to be named a winner is, for example, 300 votes, and a candidate, let's call them "A", gets 310, then 10 of those votes are re-distributed in proportion to all 310 "A" voter's second choices; so if 180 of them had candidate "B" as their second choice and the rest had some other candidate(s), then B gets 10*(180/310) = 5 and 25/31 votes); apparently, some people feel that these fractional votes mean their vote is carrying less weight (and thereby violating "one person, one vote"), but that's not the case either; those fractional votes will always have come from voters who have already had one of their earlier choices chosen as a winner; the alternative is to drop the extras, penalizing voters for picking a choice that was too popular by not allowing them any say in who the other winners should be in the election. And how would that not be disenfranchisement?
So yes, while I think approval and score are much better systems than instant runoff, I also think all of them are legal under the constitution (and that all of them perform better than plurality.)
(While I'm here though, I feel I should mention that there is a proportional score-voting-style system, called reweighted score voting, which could be used for the sort of multi-winner elections that STV is used for. But I'm not aware of much research into its benefits versus STV; my suspicion is that it will be better, but not so dramatically better than score and approval are as compared to instant runoff.)