In the New York Times, Eric Maskin and Amartya Sen explain Condorcet’s

system for electing candidates who truly command majority support. In this system, a voter has the opportunity to rank candidates.

Maskin and Sen’s fictitious example of the American primaries illustrates the difference between a plurality system (as used in the primaries) and a majority system a la Condorcet (where the winner is the one who defeats any other candidate in pairwise comparison). They also point out that

Kenneth Arrow’s famous “impossibility theorem” demonstrates that there is no perfect voting system, and majority rule is no exception. Specifically, as Condorcet himself noted, a majority winner might fail to exist … Such an outcome is quite unlikely in practice, but if it were to arise, a tiebreaking procedure would be needed.