…of the greatest event in human history.

…of the greatest event in human history.

As you probably know, the usual voting system in the United States is called “first past the post”: whoever gets the most votes wins, even if the vote is split ten ways and the winner gets 11% of the votes. Worse, if more than one person runs whom a lot of voters like, they can split the vote and the most-disliked candidate can win! For example, in 2000, Al Gore and Ralph Nader split the progressive vote in Florida, and George Bush won the state with fewer votes than Gore+Nader, so a majority of the voters got the candidate they least wanted. (I’m assuming that all Gore voters would have preferred Nader over Bush and vice versa, which seems pretty likely.)
My preference among alternate voting systems is Instant Runoff Voting (IRV), also known as Ranked Choice. You rank the candidates #1 for your favorite, #2 for your next favorite, etc. If only two candidates are running, this works exactly the same as first-past-the-post. If more than two candidates run, but one gets more than 50% of the #1 votes, that candidate immediately wins. Otherwise the last-place finisher loses and the #2 votes on their ballots are recounted as though they were #1 votes. Just like holding a runoff but without the delay or expense.
For reference, science fiction fans use IRV to pick their most popular SF novel, short story, movie etc of the year (the Hugo Awards). They’re a ridiculously nitpicky and pedantic group… but this is their preferred voting system.
Nicky Case created an interactive guide to various voting systems. You can drag the voters or the candidates around to see how the systems work.