Not only does the Constitution make no mention of the term "popular vote," but such an idea is meaningless within the context of America's founding document. The designation "popular vote” evolved over time as a sort of shorthand to describe the votes cast for presidential electors who had publicly committed to vote in the Electoral College for a particular qualified presidential candidate.
No presidential electors in any state were chosen by voters until 1824. The Constitution says nothing about how presidential electors are chosen by states except that each state legislature shall determine the method of choosing those electors. Gradually, states on their own began to provide that these electors would themselves be chosen by popular vote. So in 1824, Andrew Jackson “won” the popular vote but lost the presidential election. In 1820, there was no "popular vote" at all.
Actually, as stated implied earlier, the term "popular vote" for president is a misnomer: Not one single vote was cast or could have been cast for Jackson or any other presidential candidate — votes were cast for the presidential electors. Presidential electors gradually came to be chosen in every state by popular vote; however, state legislatures, rather than the people, chose presidential electors as late as the 1876 presidential election, when, for instance, the state legislature of Colorado chose its presidential electors.
So the very term “popular vote” is meaningless. Unless the Constitution itself is amended through the Article V process, every presidential elector is chosen by a method defined by the legislature of the state from which he comes. The purpose of giving state legislatures, rather than the people, the right to determine how presidential electors are chosen was to provide a check on the rise of a national democracy instead of a limited republic of sovereign states. The allocation of electors — one for each member of Congress in a state (both in the House and the Senate) — was also consciously intended to grant small states the same disproportionate strength that these states had in the Senate. So, for instance, Wyoming has at least three electoral votes, even if that translates into proportionately greater demographic representation in the Electoral College than the state of New York.
The term “popular vote” has another problem: Each presidential elector — each of the three from Wyoming and the 55 from California, for instance — once chosen, may vote for whomever they wish, regardless of any previous promises. These officials are no more “bound” to vote based upon professions before their election than Senators or Congressmen are bound by their campaign promises. No state or federal law can change that: It is part of Article II and the constitutional election process.
State legislatures were given the power to decide how presidential electors were chosen because the Founding Fathers deemed it important to grant great residual powers to state legislatures. These bodies — until the 17th Amendment, born out of the “progressive” era — also chose the membership of the U.S. Senate. The Founders understood that giving state legislatures real muscle — the ability to choose the President and the Senate — would as a practical matter insure that the federal government would not become a bully. Moreover, in the doctrine of states’ rights, each small state had the same incentive in preserving the sovereignty of other small states.
So, although Vermont and Wyoming might have very different ideas about good governance, each had an interest in preserving the rights of the other, so that the Vermont and the Wyoming legislatures could each enact policies which their state legislators thought best. One great fear of the Founding Fathers was that large states would come to dominate the federal government, ignoring the prerogatives of state sovereign power, or that certain regions of the country would seek to impose their will on other regions. The dispersal of electoral votes in such a way as to enhance the power of small states — creating a system through which state legislatures alone might choose their manner of selecting presidential electors — was intended to preserve what Benjamin Franklin told a woman in Philadelphia was the government he and the other Founders had created: “A republic, if you can keep it.”