While the Best Picture nominees will be determined with a new counting method, contenders in the other top categories will be selected under the preferental system that has been in place for years. To illustrate how that system works, let's look at the 2012 Best Actress race.
Between our Experts, Editors and Users, 1,375 ballots were cast for Best Actress. As per the preferential system, we sorted these ballots by the first choice and only those women listed at the top of at least one ballot continued on in the process.
There are five nominees for Best Actress. In our scenario, the initial threshold for a nomination was set at 230 votes (i.e., 1,375 divided by 6 and rounded up). If each of five women reaches this cut-off, they will account for 1,150 votes, making it mathematically impossible for a sixth actress to get more than 225 votes.
With the magic number set at 230 (16.73% of ballots), the first place votes are counted. Meryl Streep ("The Iron Lady") has 770 votes and Viola Davis ("The Help") has 357 and both will reap a bid. Usually, these ballots would be set to one side at this point. However, each of these newly minted nominees was so popular that they reaped at least 20% more first place votes than needed to be nominated -- in our scenario that is 276 votes -- and triggered the surplus rule.
When this happens, the ballots for this nominee are apportioned as follows: a share goes to the nominee such that they reach the magic number and the remaining share goes to the actress below her on the ballot who is still in the running and not yet nominated.
Streep made the grade with 56% of our voters. She only needed 230 first place votes to reach the initial threshold so each of her 770 votes is apportioned with .30 of the vote going to her and .70 to the actress listed in second place, assuming she got at least one first place vote from someone to remain eligible and is not already deemed to be a nominee. Those fractional votes are the equivalent of 540 ballots in all. Likewise, with Davis, .64 of each of her votes will be counted in her column while .36 will go to someone further down the ballot.
Because Streep and Davis are already deemed to be nominees, neither needs the fractional votes they would be entitled to under the surplus rule. Therefore, any ballot that listed Streep and Davis in the top two slots, in either order, would see part of their vote going to the actress in the third position (assuming she got at least one first place vote from someone to remain eligible.)
Perhaps Michelle Williams ("My Week with Marilyn"), who had 102 votes, picked up enough fractional votes to now reach the threshold of 230. If so, those ballots would be set aside as well.
And so ends round one with three of the five slots filled.
Before beginning round two, a new magic number needs to be calculated based on the ballots still in the process. We started with 1,375 ballots and have removed 1,229 [770 (Streep), 357 (Davis), 102 (Williams)] leaving 146. There are two spots left so we divide 146 by three and round up giving us a new magic number of 49. If two actress each got this many votes they would account for 98 votes, leaving only 48 in play. Glenn Close ("Albert Nobbs") exceeds this magic number with her own first place votes, so she is the fourth nominee.
Before beginning round three, a new magic number is calculated. We removed Close's 83 ballots leaving 63. With one spot left, we divide 63 by two and round up for a new magic number of 32. If one actress achieves this, there will only be 31 votes in play.
At this point, the accountants redistribute the ballots of the actress with the fewest number one votes to the next actress further down on the ballot who is still in search of a nomination. Ellen Barkin ("Another Happy Day"), Olivia Colman ("Tyrannosaur"), Mia Wasikowska ("Jane Eyre") and Rachel Weisz ("The Whistleblower") have one vote apiece. The accountants would look on each of these ballots for the next highest ranked actress still in the running (i.e., not Streep, Davis, Williams or Close). This will be done with the ballots of each actress who has the least number one votes until someone reaches the magic number of 31.
In our scenario, Rooney Mara ("The Girl With the Dragon Tattoo") and Tilda Swinton ("We Need to Talk About Kevin") came into this round with 25 first place votes. They may also have picked up fractional votes in the surplus run-off so would be tantalizing close to the 31 needed.
While the Best Picture winner is determined by a version of the preferential system, the winners of the other races are those that top the popular vote -- i.e, a voter picks just one of the nominees and the Oscar goes to the that nominee with the most votes.