First a point of terminology, Ranked Choice Voting (or Ranked Voting) refers to any of several systems in which votres rank several or all of the candidates in the order of their preference, and these rankings are used to determine the outcome. These systems include the Instant Runoff, Restricted Instant Runoff, the Single Transferable Vote, the Borda count, and some versions of the Condorcet method. See the linked Wikipedia article for details.
The question describes an Instant Runoff system, although most US jurisdictions employing this actually use a Restricted Instant Runoff system, in which voters can rank only a limited number of choices, often their first three preferences.
While this method has not yet been used to elect a member of the US Congress (such an election is now being challenged), it has been used in a number of local elections, and has been upheld as constitutional by several US courts, although there has been no Supreme Court ruling on the subject that I know of.
In Dudum vs Arntz (2011) the 9th Circuit Court of Appeals upheld the use of restricted IRV in elections for various offices in the city of San Francisco, Mayor, Sheriff, District Attorney, City Attorney, Treasurer, Assessor-Recorder, Public Defender, and members
of the Board of Supervisors.
The opinion in Dudum vs Arntz gives a through description of this system of voting, and of other related systems, and of their advantages and drawbacks compered with a more traditional "first past the post" system.
The opinion in Dudum vs Arntz considers challenges to this system on the grounds of claimed Equal Protection ("one person one vote") and Due Process violations. The opinion did not find any of these challenges to have merit. In particular the opinion considered the claim that some voters are allowed by this system to vote "more than once" while others are not. The opinion said:
In actuality, all voters participating in a restricted IRV election are afforded a single and equal opportunity to express their preferences for three candidates; voters can use all three
preferences, or fewer if they choose. Most notably, once the polls close and calculations begin, no new
votes are cast.
[The plaintiff's] contention that restricted IRV threatens to exclude some voters from voting is therefore incorrect. The contention sidesteps the basic fact that there is only one round of voting in restricted IRV.
In sum, the City’s restricted IRV system is not analogous to limitations on voting in successive elections, because in San Francisco’s system, no voter is denied an opportunity to cast a ballot at the same time and with the same degree of choice among candidates available to other voters.
The Plaintiff in Dudum argued that "exhausted" ballots are excluded from any effect in later rounds of tabulation, and so the voters who cast them are not allowed a vote. The opinion responded to this by saying:
In essence, a more complete explication of the tabulation process demonstrates that “exhausted” ballots are counted in the election,
they are simply counted as votes for losing candidates, just as if a voter had selected a losing candidate in a plurality or run-off election.
[E]ven though last-place candidates
could no longer mathematically win the election, and could not obtain further votes, one could clutter the tabulation process by showing their votes on the tabulation tables even after they had been proven incapable of prevailing. The winner could then be defined as the candidate who receives a plurality of the total votes cast
(including votes cast for candidates mathematically eliminated in prior stages), as long as he also
receives a majority of the votes cast for candidates who were not mathematically eliminated previously.
The opinion quotes McSweeney v. City of Cambridge , 422 Mass. 648 (1996), which upheld against a similar challenge a Single Transferable Vote system (a variant of ranked voting used when multiple officials, such as members of a council, board, or legislature, are to be elected from the same district). The quoted passage is:
“[exhausted ballots] too are read and counted; they just do not count toward the election of any of the nine successful candidates. Therefore it is no more accurate to say that these ballots are not counted than
to say that the ballots designating a losing candidate in a two-person, winner-take-all race are not counted.”
The Dudum Court went on to say that:
In short, Dudum’s contention that the City’s system discards votes is incorrect. Instead, the system “counts” all the ballots, but the final tabulation recognizes that some of the ballots ranked only losing candidates. Like his inaccurate
comparison of the algorithm used in restricted IRV to a series of elections, Dudum’s “counting” argument reveals an at most minimal—and perhaps nonexistent—burden on voters’ constitutional rights.
The plaintiff Dudum further argued that;
“some voters—those who vote for continuing candidates—only have one vote counted in ‘the election’; other voters, however, have votes counted for three different candidates.”
The court responded that:
In fact, the option to rank multiple
preferences is not the same as providing additional
votes, or more heavily-weighted votes, relative to other votes cast. Each ballot is counted as no more than one vote at each tabulation
step, whether representing the voters’ first-choice candidate or the voters’ second- or third-choice candidate, and each vote attributed to a candidate, whether a first-, second- or third-
rank choice, is afforded the same mathematical weight in the
election. The ability to rank multiple candidates simply provides a chance to have several preferences recorded and counted sequentially, not at once.
Every voter, the 9th Circuit court pointed out, has this same chance to express multiple preferences, and all voters are treated alike.
The court went on to say that:
The burdens Dudum
identifies, however, are largely ephemeral, disappearing upon examination. The restricted IRV scheme does
not provide disparate opportunities for any voter to cast additional ballots or votes. The appearance that some votes are not “counted” is just a product of how the algorithm operates for efficiency’s
sake; the result would be identical were the “exhaustion” feature eliminated, and the “exhausted” ballots recorded and counted throughout the process for what they are—votes for losing candidates. As the votes from “exhausted” ballots are
taken into account in the election, as much as “wasted” votes ever are, the practical burden on voters is no different than in other election systems. Finally, Dudum’s vote dilution argument fails as well, because the ability to rank preferences sequentially does not affect the ultimate weight accorded any vote cast in the election.
The "one person, one vote cases", particularly
Anderson vs Celebrezze, 460 U.S. 780, 787 (1983) and Reynolds v. Sims, 377 U.S. 533 (1964), were lagely concerned with making sure that each person's vote was weighted equally. The Renolds case held that legislative districts must be of nearly equal size, with Chief justice Warren saying that:
Legislators represent people, not trees or acres. Legislators are elected by voters, not farms or cities or economic interests.
These decisions did not deal with voting systems or methods, as long as each person's vote has the same weight, and is treated in the same way, as each other person's vote.