The US constitution was written in 1787 and ratified along with the Bill of Rights in 1791. It nowhere says that a "vote" has to consist of "the name of exactly one candidate, then shut up." In fact it nowhere defines "vote," although it mentions votes about 20 times.
The constitution is rife with such ambiguities and that was usually intentional. We at the Center for Range Voting believe that it was also intentional in this case: the authors of the constitution intentionally wanted to allow other kinds of voting than just plurality voting; they knew there were other kinds of voting and intentionally chose not to forbid them; and they intentionally remained agnostic on the question of what kind of voting system to use.
Why do we say that? Because we know that Thomas Jefferson, Edmund Randolph, and James Madison all owned copies of Condorcet's book, describing and advocating a voting system in which your vote is a rank-ordering of all the candidates. (At that time, range voting was little-known. These French and American people were struggling to develop the concepts of democracy from scratch.) In fact Jefferson bought copies of everything by Condorcet he could lay his hands on, and in at least one case, he annotated his copy, and he was so enthusiastic that he sent copies to Randolph and Madison. This all happened before ratification of the Constitution plus Bill of Rights in 1791. And we know that Benjamin Franklin apparently knew Condorcet personally (both were high in the French Academy of Sciences) and indeed Condorcet gave a warm elogy for Franklin upon the latter's death.
And we know Jefferson knew Borda (who in a 1781 paper introduced and advocated a different voting system in which your vote is a full rank-ordering of all candidates; this was the subject of a famous acrimonious dispute between Borda and Condorcet) too, since he mentioned him in a manner connoting familiarity in a letter he wrote. And "Between 1778 and 1789 both Adams and Jefferson met Condorcet on a number of occasions. Franklin, who already knew Condorcet well through the Academy of Science, first introduced Adams and presumably Jefferson to him. Adams made no comment at the time except to describe Condorcet's 'paper-white complexion.' But later he showed himself to be a fierce enemy of Condorcet's thought." Jefferson is known to have translated some Condorcet's writings into English (some fragments survive).
This quote and information is from Iain McLean: The Political Economy of the French and American Enlightenments: Jefferson in Paris 1785-9. Jefferson was Ambassador to Paris following Franklin.
So while perhaps Jefferson et al did not fully follow Condorcet's mathematically intricate arguments, it is absolutely inconceivable that they did not grasp his fundamental starting point that rank-ordering-type votes were to be used in his (and Borda's) voting systems. And it also is absolutely inconceivable that they did not realize that there was an acrimonious conflict between Condorcet and Borda over whose voting system was better, i.e. they realized the question of which voting system was best, was not a trivial one and the answer was not clear.
And other voting systems besides plurality have already been used for US congressional, and state governor, positions at various times and places throughout US history. The cumulative system was used throughout Illinois between 1870 and 1982 to elect representatives; it involved votes which were integer vectors summing to a constant (so your vote could express opinions about more than one candidate in this system, e.g. you could give a score of 3 to one candidate and 2 to another). The Bucklin system was used in various primaries to elect some state governors in the early 1900s. It involved rank-ordering (Borda-style) votes. We don't recommend those two systems, but they make it clear there is plenty of precedent in US history for other kinds of votes!
"Each Elector should give two votes, one naming his first choice, the other naming his next choice. If there be a majority for the first, he to be elected; if not, and a majority for the next, [then] he is to be elected: If there be not a majority for either, then the names having the two highest number of votes on the two lists taken together, to be referred to a joint ballot of the Legislature." – James Madison, proposing a ranked ballot method (apparently an abridged and somewhat confused version of what later was called "Bucklin voting") for the Electoral College in 1824
We also note that Jefferson's top rival/enemy among the Founding Fathers, John Q. Adams, also was aware that other kinds of voting system existed and were used, e.g. see this quote from Adams' 1787 book describing Venice's voting system which is approval- or score-based.
Finally, the Constitution's initial system for electing US presidents was, essentially, approval voting.
No. The "one man, one vote" ideal really is that no voter should have more power than any other. That is just as true for Range Voting as it is for any other fair system.
"We hold that, construed in its historical context, the command of Article I, Section 2 [of the Constitution] that Representatives be chosen 'by the People of the several States' means that, as nearly as is practicable, one man's vote in a congressional election is to be worth as much as another's"
– U.S. Supreme Court, Wesberry v. Sanders, 1964. This quote constitutes the USA's legal definition of what above was colloquially called the "one man one vote principle."
And look at it this way. Suppose candidates A and B are tied. Great! You can break that tie and have an impact on the world, with your vote. In both range voting and in the present plurality system, election-ties (or situations extremely near-to-being-ties) are the only situations in which your vote can change the election result. Well, with range voting, you are exactly as capable of that as any other voter.
And further, Range Voting actually gives more equal power to voters than plurality or IRV, since under plurality you cannot break the tie between A and B if you unfortunately voted for C, making you less powerful than a voter who votes A or B. (Supporters of third parties are "zeroed out" and their votes never have an effect. Fair? I don't think so.) And under IRV voting, your vote, even though it does express a preference A>B (say) still can have zero impact on a crucial A-B tie if your top-rank vote was for somebody else at the moment the IRV process decides whether to eliminate A.
That causes a voter's A-versus-B expressed preference, under the IRV system, to be either ignored, or used, and which happens depends upon the voter and the election situation in a peculiar and whimsical-seeming way. This can happen in a highly highly biased way, for example if the "prefers A" voters are always ignored while the "prefer B" voters are never ignored. See Burlington 2009 for one example of an IRV election in which such highly-biased-ignoring happened, yielding an election winner who would have lost by majority to another if all voter preferences had been counted.
So actually, the problem is not that range fails to satisfy one-man-one-vote. In fact, it satisfies it better than plurality and IRV.
I have already intimated to you the danger of parties in the State, with particular reference to the founding of them on geographical discriminations. Let me now take a more comprehensive view, and warn you in the most solemn manner against the baneful effects of the spirit of party generally.
This spirit, unfortunately, is inseparable from our nature, having its root in the strongest passions of the human mind. It exists under different shapes in all governments, more or less stifled, controlled, or repressed; but in those of the popular form it is seen in its greatest rankness and is truly their worst enemy....
It serves always to distract the public councils and enfeeble the public administration. It agitates the community with ill-founded jealousies and false alarms; kindles the animosity of one part against another; foments occasionally riot and insurrection. It opens the door to foreign influence and corruption, which finds a facilitated access to the government itself through the channels of party passion. Thus the policy and the will of one country are subjected to the policy and will of another.
There is an opinion that parties in free countries are useful checks upon the administration of the government, and serve to keep alive the spirit of liberty. This within certain limits is probably true; and in governments of a monarchical cast patriotism may look with indulgence, if not with favor, upon the spirit of party. But in those of the popular character, in governments purely elective, it is a spirit not to be encouraged. From their natural tendency it is certain there will always be enough of that spirit for every salutary purpose; and there being constant danger of excess, the effort ought to be by force of public opinion to mitigate and assuage it. A fire not to be quenched, it demands a uniform vigilance to prevent its bursting into a flame, lest, instead of warming, it should consume.
Moral: Washington thought political parties and political party dominance was a very bad idea. He wanted it to be about the best candidate winning. Not about 2 parties taking over and preventing all other parties – no matter how good their candidates – from having a chance. Makes you wonder whether Washington is spinning in his grave.
With Range Voting 2-party dominance should be lessened, consonant with the top expressed wish of George Washington.