The theory has recently been put forth by talking heads and political pundits that if a party convention were to nominate a candidate other than one who received a plurality (but not a majority) of primary votes, that candidate would suffer from a lack of "legitimacy".
This theory reflects a fundamental misunderstanding of the role parties play in the election process set forth in the constitution. In fact, political parties are not even mentioned in the constitution, reflecting that a large number of founding fathers didn't even contemplate the future existence of political parties, and if they did, certainly not along the lines of those which evolved in the parliamentary system of the mother country from which they declared independence. George Washington belonged to no established political party, but political parties soon began to coalesce around those who had different visions of federalism.
The two party system that ultimately evolved is virtually unique among the world's democracies. Even in Great Britain, a three party system requires the creation of fragile and often unstable coalitions in order to govern, and in multi-party presidential systems such as exist in France, voters are often faced with contentious "run-offs" that often present voters with a stark choice between two candidates who, though only winning only a small percentage of the votes in the first round, nevertheless make the final round --despite being opposed by an overwhelming majority of voters-- only because their thin pluralities were slightly greater than a multitude of other party candidates.
There is, of course, nothing in the Constitution that forbids the creation of political parties, and in fact the First Amendment rights of association gives parties the right to make their own rules for how it selects a nominee. While over the past decades the two major political parties have sought to provide their convention delegates with advice and guidance from voters in the form of primaries and caucuses, no party has yet seen the need to provide a national "run-off" system when there are multiple candidates for the nomination. But of course, that is the purpose of a convention. If the theory that a party should be bound to nominate a candidate who won only a plurality of primary votes but less than a majority had any validity, there would of course not be any reason for holding a convention at all. As a practical matter then, conventions perform the sole function of providing a "run-off", and a candidate who may have won a plurality of primary votes, but is opposed by two-thirds of the elected delegates, is not likely to fare well in such a runoff. The notion that such a runoff is somehow "undemocratic" is not only a novel one, but one which if implemented would eviscerate any party's rational goal of nominating a candidate who has the best chance of winning the general election.
Consider the unlikely but not impossible scenario in which twenty candidates seeks a party's nomination. (Perhaps not so unlikely, considering that there were fourteen original candidates seeking the Republican party nomination). Assume further that after all primaries and caucuses are conducted, each candidate has won five percent of the votes, except one who received four percent, and another who received six percent. Would any rational political scientist suggest that only the candidate who received the six percent plurality would be a "legitimate" nominee?
Until the Constitution is amended to incorporate the two dominant political parties into the presidential election system, with some sort of national "run-off" system of the kind employed in France, Russia, and many South American countries like Venezuela, the right and indeed moral imperatives of party conventions should be respected, including the right and legitimacy of choosing the candidate favored by the majority of duly elected delegates.