When the Academy of Motion Picture Arts and Sciences began allowing more than five films to be nominated for best picture, in 2009, it also changed the way the votes were counted. The system is called instant-runoff voting, and it’s designed so that the film preferred by the widest consensus of Academy voters wins.

Voters aren’t asked to pick their favorite film when they fill in their ballots; instead they’re asked to rank the films up for best picture from most preferred to least preferred.

When PricewaterhouseCoopers counts up those votes, its tabulators first sort the best picture ballots into piles based on first choice. If one film accumulates more than 50 percent of the vote, that film is the winner. If not, the film that received the lowest number of first-choice votes is removed from contention, and all its ballots are redistributed to their second choices. This process is repeated until a film has more than 50 percent of the vote, at which point a winner is declared.

To show how this works, I asked SurveyMonkey Audience to run a survey of moviegoers — people who have seen at least one movie in the past six months — to rank the best picture nominees the same way the Academy voters do. I then cut the ballots down to people who had seen one or more of the nominated films. I was left with 514 — not a mighty group, but the Academy itself is only 6,000 people, so this sample will do for demonstrative purposes.

It shouldn’t come as too much of a shock that the films the most people watched — in this sample Wes Anderson’s “The Grand Budapest Hotel,” followed by Clint Eastwood’s “American Sniper,” then Richard Linklater’s “Boyhood” — were the films that did the best. So think of this less as an Oscar prediction and more as a people’s choice award.

(It also shows why sending out free screeners to voters is such an important part of the Academy Awards campaigning process, particularly for films that didn’t get a ton of play in theaters.)

So what happens when I run the SurveyMonkey ballots through the instant-runoff algorithm?

In the initial sample, American Sniper had a plurality, but not a majority. Under a first-past-the-post system, it would be our best picture. But then we start reallocating votes. “Whiplash” is first to be eliminated, followed by “The Theory of Everything” and “Birdman.” Notice that most of those films’ initial 19 percent of the vote was redistributed to films that weren’t “American Sniper” — this means that most of the people who put those movies first didn’t have “American Sniper” very high up on their lists. Next we knock off “Selma,” then “Boyhood,” neither of which is able to push a leader over the 50 percent threshold.

Now that we’re down to only three films, the next elimination shows us the major advantage of instant-runoff voting. “American Sniper” has 40 percent of the vote, “The Grand Budapest Hotel” has 30 percent and “The Imitation Game” has 29 percent.

When we redistribute the votes for “The Imitation Game,” though, “The Grand Budapest Hotel” is pushed past 50 percent. That’s because a little less than three-quarters of “The Imitation Game” supporters preferred Anderson’s film to Eastwood’s.

So despite winning a plurality of the initial votes, “American Sniper” (barely) misses having enough widespread support to take home the prize.

What does this mean in reality? The film that wins Sunday night might not have been everyone’s first choice, but it will have had the most fans across the Academy.

The rest of the award categories — each of which has five nominees — are all decided by conventional means, so whoever gets the most votes wins. In our survey (again for the subset of people who have seen at least one best picture nominee), the people chose Bradley Cooper for best actor, Robert Duvall for best supporting actor, Julianne Moore for best actress and Patricia Arquette for best supporting actress. Linklater takes home the prize for best director. Based on our own Oscar-prediction model, the crowd has the right idea for the actress and director categories but is probably a little off the mark for the actors.

Also, the people like “How To Train Your Dragon 2” to win best animated feature. I’m pulling for “Big Hero 6,” but I realize the film could be confusing for those who never saw the first five.