They Shoot Oscar Prognosticators, Don't They?
A Primer on Preferential Voting
By J Don Birnam
February 19, 2014
BoxOfficeProphets.com
Instead of selecting one pick for Best Picture in any given year, Academy voters are now asked to rank the Best Picture nominees from their favorite (“1”) to least favorite (“9”). Under the rules, a movie needs half plus one #1 votes to win Best Picture. For purposes of this exercise, assume there are 1,000 voters and that each ranks all nine contenders. In that scenario a movie needs 501 first place votes to win. The PricewaterhouseCoopers accountants in charge of tabulating Oscar voting results start their task by making nine piles, one for each of the Best Picture nominees, and in each pile placing the respective ballots that voted for that particular film as their #1 choice. What happens if no movie gets the needed 501 #1 votes? It is a safe bet that in most years, simply given the large number of nominees, no movie is going to get as many as half the votes outright. That is where redistribution kicks in - the part where it gets confusing for some people.
Redistribution works as follows. If no movie has crossed the half plus one threshold, the accountants go to the pile of the movie with the fewest number #1 votes and look at what each voter put as their #2. Suppose, for example, that of our 1,000 voters, only 30 of them picked Nebraska as their favorite of the year, the fewest of any of the nine nominees. The accountants will then take those 30 ballots and redistribute them to the piles of the movies selected as #2 in each of those 30 ballots. Effectively, the ballots are split up into one of the remaining eight piles as if they had originally selected a movie other than Nebraska as their #1 pick. That was probably the hardest part to understand, so if you are still with me you are in good shape.
At that point, there are eight remaining contenders, and each (in theory) has seen their respective vote totals increase by however many votes they got allocated from the movie that was first eliminated - again, the movie with the fewest number one votes. If any movie has crossed the threshold needed to win, the process is over and we have a winner. So, in our example, if 499 people selected Gravity as their #1 movie, but two people who selected Nebraska as their #1 selected Gravity as #2, Gravity will win when those two Nebraska ballots are redistributed to it in the first round of redistribution.
If this does not happen, the process of eliminating movies and redistributing ballots continues until one movie hits or crosses the 501 mark. So, to be abundantly clear, the next step is to go to the pile of the movie with the fewest votes after the first redistribution occurred and redistribute that movie’s ballots. Note that after the initial count a movie may have been in, say, eight place, but the redistribution of the ninth place movie’s ballots could theoretically bump that movie up enough so that it becomes the seventh or higher place movie, allowing it to survive at least another round.
What happens if, in redistributing the ballots of the movie in eighth place, the accountants run into a voter who picked as his or her #2 pick Nebraska, the movie that was eliminated in the first round? In that situation, the accountants go on to the voter’s #3 slot to determine where to place the ballot. Eventually, if the voter ranked all nine nominees, the ballot will go to someone still in the race (if not, the ballot may be discarded and the magic number needed to win adjusted accordingly). In subsequent rounds, it could happen that a voter’s #4 or #5 pick becomes relevant and provides a vote to a movie still in the race. Indeed, in a close year with no clear Best Picture consensus, one can expect the redistribution process to go on for several rounds, making voters’ selections beyond simply the #1 pick incredibly relevant and important.
Hopefully the process is a bit less intimidating now. Understanding it can provide helpful clues to who is going to win this year’s Best Picture race and in subsequent races. If you run the preferential ballot redistribution system in your mind a few times, several truths quickly emerge. First, it is clear that you need a lot of early #1 votes to stay in the race. If you lack those, it does not matter that you may have a lot of #2 votes sitting in piles waiting to be redistributed, because you will likely be eliminated from contention before it can get to that. Remember, the movie with the lowest number of #1 votes gets eliminated first. So, for example, a movie that many people love (say, Nebraska or Philomena) but that does not engender #1 type votes, will be quickly eliminated.
The second thing that becomes clear is that the preferential ballot system many times produces results similar to straight up voting. What it boils down to is still this: what movies do most people like? Eventually, a movie with the right combination of #1 votes to start and high numbers across the other ballots that do not pick it #1 will eventually float up to the top. It sounds simple to the point of stupid to say that all that matters is what movies are most popular, but to see it play out in terms of the preferential ballot process really demystifies the procedure to a great degree.
But here is a corollary and how preferential voting most differs from regular voting: a controversial or divisive movie has no chance to win under preferential voting. Under regular voting, it was theoretically possible for a movie that a lot of people hate to win if it got, say, 250 out of the hypothetical 1,000 votes, if the remaining movies split the field up evenly. In that scenario, a full three-quarters of the Academy may hate a movie and that movie could win anyway. Under preferential voting, that movie needs to climb up to 501, and if it is hated by the three-quarters that did not select it as #1, it will obviously not rank high enough in their ballots to win. Thus, under preferential voting, consensus candidates win - choices that are at least “OK” to at least half the people voting.
The third truth that emerges is a refinement of the previous rule. What matters is not only what movie people like the most, but how people feel about the main contenders as compared to the other contenders. So, for example, it likely does not matter if every single 12 Years a Slave voter ranks Gravity as their #2 pick. As we will see shortly, 12 Years a Slave is likely to be one of the last two films standing in the redistribution process. Unless it gets eliminated in an early round, an unlikely scenario, 12 Years’ ballots will never be redistributed and will never help out Gravity. Similarly, it does not matter whether a Gravity voter prefers American Hustle over 12 Years a Slave. Again, if we believe Gravity is going to make it into the last round of redistribution, then its ballots will never be used to help another movie. What does matter, however, is how voters rank the top-three contenders with respect to each other. If a Nebraska voter ranks Slave as #2 and Gravity as #3, it will not help Gravity to have placed that high up on the ballot, as the ballot will likely go to 12 Years’ pile and never be redistributed from there.
So what does this all mean for this year’s race? My short answer is that, for the first time, I can see Gravity actually pulling off a Best Picture stunner. Whether you believe me or not will depend on how much you trust the assumptions I will have to make as I construct the argument.
To start, let us assume two relatively uncontroversial propositions about this year’s Best Picture race. First, assume that it is a close contest at the top - i.e., no movie is going to receive over half of the Academy’s “#1” votes outright and win without needing to resort to redistribution. Second, let’s assume that the close race is between three movies and that those three are American Hustle, 12 Years a Slave, and Gravity. This is important because it means that none of the three will be very close to the 50% mark after the first round. If you run simulated preferential ballots you will see that if one movie is way ahead of the competition after just the first round, it is essentially impossible to catch it because the redistribution of ballots will push it over the top quickly. But this year, if we assume the race is close, we may believe that, for example, each of those movies is pulling about 25% of the #1 votes in the first round, with the other six pulling in the remaining 25%. This means that the eventual winner will need a lot of help to get to 50%. People’s #2 and #3 votes will matter a lot, and redistribution may go on for several rounds.
What happens next? Well, you can play infinite scenarios in your head but, as I said, what it boils down to is what movie is higher on the ballots not voting first for the top three contenders. So, essentially, all the number one votes for Her and Philomena and Nebraska eventually get knocked out. Of the top three contenders, which movie are those Her and Philomena and Nebraska voters likely to rank highest?
Enter more assumptions. I propose that the answer to the question is not American Hustle. Many people love it, but a lot of people also cannot see what all the fuss is about and think it is average. Stated differently, few people dislike Gravity or 12 Years a Slave, but some people actually do not like Hustle, so it is fair to assume it will be lower on most of those redistribution ballots than the other two.
You might ask, “What about Argo?” A lot of people liked it last year but many thought it was average and it still won. Yeah, but Argo did not live in this three-way split world - it barely had one clear competitor, let alone two, so I presume that after the first round it was already so near the 50% mark that all it took was for a handful more votes from other piles to carry it through. In other words, Argo literally could not be mathematically stopped.
Okay, so we are down to two movies. The million dollar question then becomes: of Gravity and 12 Years a Slave, what movie is likely to rank higher on the ballots that chose American Hustle first? In other words, where will the American Hustle ballots be redistributed? The shocking truth emerges: the people who pick American Hustle as their #1 movie may well control the outcome of the entire thing.
Enter the final, crucial assumption of the whole exercise: an American Hustle voter is ever so slightly more likely to pick Gravity as its next favorite than 12 Years a Slave. The basis for this theory is that, like American Hustle, Gravity can be enjoyed as a simple popcorn movie (although it is undoubtedly much more than that) and leaves viewers pretty satisfied after the credits roll. 12 Years a Slave, in marked contrast, is a much more difficult movie to stomach or even sit through, and the type of person who loves American Hustle is unlikely to think highly of 12 Years a Slave. Thus, in the final round, Gravity may even be sitting in second place, but if it is close enough to Slave, it may pull off a surprise victory.
Oh, you can fiddle with these assumptions and quickly reach a different result. You can say that an American Hustle voter will vote for a simple movie with his or her #1 pick and will get serious when it gets to #2. You can argue that 12 Years a Slave will be knocked out first and its ballots will determine the winner between the remaining two.
This whole exercise was meant to exemplify that the traditional theories used to predict a Best Picture race can be easily incorporated into the preferential ballot system. In a way, it does not matter that the Academy uses this system, because the old theories still determine how movies get ranked. In another way, preferential balloting can be of the utmost important in a close year like this one, when I believe it is entirely plausible and likely that voters may be unwilling to give a certain movie #1 votes because it is not “serious” enough, but will rank it highly anyway because it is so well-respected. The perhaps unintentional result of ranking Gravity high without giving it #1 votes is that it may still win anyway as long as it has a solid base of #1 votes.
We will never know, of course, how the actual voting shakes down, but it still makes for a rather interesting (if somewhat nerdy) conversation.
Here’s my final argument for why these theories as to why Gravity may actually win make sense. Gravity has lost the Best Picture race every time it has been up against 12 Years a Slave in a straight-up voting system. It lost the Globe, the BAFTA, and the Critics’ Choice, despite winning Best Director in all three of those contests. But all of those bodies use regular voting. Only one award precursor uses preferential voting to determine their winner. Which one? Why, the Producers Guild Award, of course. And who won that race? Well, surprise, surprise: Gravity and 12 Years a Slave tied. So, at the absolute least, the preferential ballot appears to have helped Gravity, and will likely make the Best Picture race much closer in Gravity’s favor than the repeated Best Picture losses in other contents otherwise suggest.