Oscar nominations: How many votes do you need?

Every December, the academy updates its branch totals in anticipation of voting for the nominations, which kicks off on Wednesday (December 30) and runs until January 8. Nominations will be announced on January 14 and the Oscars are on February 28.

This year, 6,261 members can take part in the voting process; that is up from 6,124 last year and 5,856 three years ago. This uptick in membership is the result of the decision by the academy to do away with the cap that allowed only for replacement of those members who had died or declined to renew. 

We know the introduction of online voting has increased participation to record levels. Assuming all members take part in the process, we can calculate the "Initial Magic Number" of votes needed for a nomination in the various categories.

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Seven categories — Animated Feature, Foreign-Language Feature, Makeup & Hairstyling, Visual Effects, and the three Shorts (Animated, Documentary, Live-Action) — require attendance at special screenings and those various methods of nomination are detailed at the bottom of this post. 

For all other categories except Best Picture (which can have up to 10 nominees and uses a different method of counting), this "Initial Magic Number" is calculated by dividing the number of ballots cast by six and adding one (i.e., if five contenders each get this number of first-place votes, it is mathematically impossible for a sixth to do so — click here for a detailed description of this method of counting). 

BEST PICTURE
All 6,261 members can cast ballots for Best Picture 
"Initial Magic Number": 570
(Click here for a detailed description of the method of counting.)

Five branches vote only in this race (and can take part in the selection process for Animated Feature and Foreign-Language Feature if they so choose):

Casting Directors Branch: 86 members (up from 76)
Executive Branch: 458 members (up from 457)
Members-At-Large: 216 members (up from 210)
Producers Branch: 483 members (down from 485)
Public Relations Branch: 388 members (up from 378)

These branches total 1,631 members and mean that 26% of the academy roster have no Oscar category to call their own. 

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BEST ACTOR, BEST ACTRESS, BEST SUPPORTING ACTOR, BEST SUPPORTING ACTRESS
Actors Branch: 1,138 members (down from 1,150)
"Initial Magic Number": 190 
 

BEST SOUND EDITING, BEST SOUND MIXING
Sound Branch: 437 members (up from 428)
"Initial Magic Number": 73 
 

BEST DIRECTOR
Directors Branch: 394 members (up from 382)
"Initial Magic Number": 66 
 

BEST ADAPTED SCREENPLAY, BEST ORIGINAL SCREENPLAY
Writers Branch: 392 members (up from 386)
"Initial Magic Number": 66 
 

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BEST PRODUCTION DESIGN
Designers Branch: 278 members (up from 269)
"Initial Magic Number": 47
 

BEST SCORE, BEST SONG
Music Branch: 257 members (up from 244)
"Initial Magic Number": 43
A reminder list of the 112 eligible scores and a DVD with excerpts of the 74 eligible songs is sent to the branch members. 
 

BEST FILM EDITING
Film Editors Branch: 254 members (up from 236)
"Initial Magic Number": 43 
 

BEST CINEMATOGRAPHY 
Cinematographers Branch: 227 members (up from 266)
"Initial Magic Number": 38 
 

BEST DOCUMENTARY FEATURE 
Documentary Branch: 237 members (up from 222)
"Initial Magic Number": 40 
Each branch member receives DVD screeners of the 124 entries and is assigned to watch one-fifth of these but encouraged to view as many as they can. Members list their top 15 picks on a preferential ballot and those results are compiled and produce a shortlist of 15 contenders. All members are encouraged to watch the films on this list that they have not yet seen and cast preferential ballots with their top five choices.
 

BEST COSTUME DESIGN
Costume Designers Branch: 115 members (up from 113)
"Initial Magic Number": 20 

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How nomination ballots (except for Best Picture) are counted

Seven categories have special rules as detailed below:

BEST ANIMATED FEATURE
Voting on this award is restricted to academy members from any branch who volunteer to be on the screening committee and see at least two-thirds of the 16 eligible films (i.e, at least 11). Members score each film from 6 (poor) to 10 (excellent) and only those films with an average rating of at least 7.5 remain as contenders. If only one film merits such a score, it will receive a special award; otherwise, the five highest ranked above 7.5 will be the nominees. 
 

BEST ANIMATED SHORTBEST LIVE-ACTION SHORT
Short Films and Feature Animation Branch: 401 members (up from 387)
Voting on these two awards is done in two stages. First, branch members who volunteer to be on the screening committees watch the 60 animated and 144 live-action shorts submitted. Members score each film from 6 (poor) to 10 (excellent) and the 10 highest ranked above 7.5 go on to the second stage. All members of the branch are invited to screenings of these 10 semi-finalists and those five with the highest scores above 7.5 are the nominees. 
 

BEST DOCUMENTARY SHORT
Documentary Branch: 237 members (up from 222)
Voting on this award is done in two stages. First, branch members who volunteer to be on the screening committee watch the 74 documentary shorts submitted. Members score each film from 6 (poor) to 10 (excellent) and the 10 highest ranked above 7.5 go on to the second stage. All members of the branch are invited to screenings of these 10 semi-finalists and those five with the highest scores above 7.5 are the nominees. 

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BEST FOREIGN-LANGUAGE FEATURE
Voting on this award is restricted to academy members from any branch who volunteer to be on the screening committee. They were divided into groups and required to watch at least 16 of the 80 submissions for Foreign Language Film over a two-month period. They scored them from 6 to 10 and their top six vote getters made it to the next round, as did three films added by the 20 members of the executive committee. 

The nine semi-finalists will be screened three per day beginning in early January by select committee members in both Gotham and Hollywood who will then vote for the final five nominees. The entire academy membership will get screeners of the five nominated films and can vote for the winner.
 

BEST MAKEUP & HAIRSTYLING
Makeup & Hairstyling Branch: 141 members (up from 135)
Nominations are determined in two stages. First, upwards of 15 members of the branch who attend special screenings cast preferential ballots with the top seven vote-getters moving on to the second stage. Those members from the first stage and any other members who attend screenings of excerpts from these seven semi-finalists cast preferential ballots and the top three films are nominated. 
 

BEST VISUAL EFFECTS
Visual Effects Branch: 359 members (up from 340)
The executive committee of the branch determines the 10 semi-finalists. All members of the branch are invited to a screening of excerpts from these 10 films at which potential nominees may discuss their work. Ballots are counted using a system of reweighted range voting to determine the five nominees. 

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