Also from The Envelope and LA Times:
Here's how Oscar voting works: the actual ballot process
Believe it or not, it's done by hand. Accountants sort the nomination ballots into stacks based upon what contenders get ranked first. Let's say that 5,200 people out of the academy's 5,800 members vote for best picture. We'll use that number and category as an example of how the process works, but keep in mind that most other categories are determined by peer group. Thus the acting nominees are decided only by the 1,260 members in that academy branch.
In order to be nominated, a film needs one-sixth of the votes plus one — that's about 868 out of 5,200 votes. As soon as accountants figure that, say, "Sweeney Todd" reaps that tally, they stop counting and set those ballots aside, decreeing "Sweeney" a best pic nominee. The remaining ballots with "Sweeney" on top get distributed to other stacks based upon their second-ranked choices.
If no other movie has enough number-one votes or those number twos once the stray "Sweeney" ballots are re-distributed, then accountants turn to the movies with the fewest votes and redistribute those ballots based upon number-two votes.
Over and over they repeat the process, working from the smallest stacks to the largest, until a film has the magic 868 votes. Then counting for that film stops, the stack is set aside and the remaining ballots in that stack get re-distributed, too, based on the film with the highest next ranking. Over all, about a dozen rounds of redistribution occur before the five nominees are settled.
This voting process benefits films with a passionate following. It doesn't matter if a movie is absent from the vast majority of ballots. If it nabs one-sixth of the votes plus one, it's in. That's how movies like "Little Miss Sunshine" and "The Full Monty" got nominated in the past. Those highly commercial, feel-good films were probably snubbed by most academy members, who tend to be snobs, and they probably wouldn't have been nominated if the Oscars used a weighted ballot, but they had enough rabid devotees to survive preferential voting.