That is the Republican problem today. Do a little thought experiment: Suppose the standard for election were not a mere plurality but a real majority of more than 50 percent, and suppose there were a way of counting all voters’ second and third choices. Would Trump have been the winner? Probably not, because we know that he has intense minority support but great opposition among voters who cast ballots for other candidates.

There is an electoral system that surfaces second and third (and lower-order) preferences that has been used successfully in Australia for a century. It is called the Alternative Vote. It uses a ballot that asks voters to mark first, second, third, etc., preferences. Then, if there are more than two candidates, the one with the fewest first preferences is dropped out, and his or her voters’ second preferences are reallocated as if they were first preferences. The process is repeated until one candidate receives a majority. (There are several ways of doing the actual counting, but in each case the aim is to find a winner with real majority support among all the voters.)

Generally, the leader in first preferences wins even when all preferences have been counted, so alternative voting is not a radical departure from first-past-the-post, but it can produce a different result when most voters strongly prefer someone other than the first-preference leader or find that leader unacceptable.