Grokking E Pluribus Hugo 
[Aug. 28th, 201604:29 pm]
KarlJohan

Right now I see a bit of pushback against the newly ratified E Pluribus Hugo rules (see eg Jed Hartman and Rachael Acks). In part this is because the test runs on prior Hugo nominations didn't yield as good results as some may have hoped for, another might be that many fans do not feel they can exactly understand how EPH works. FPTP may be unfair, but it's simple to understand.
At its core, E Pluribus Hugo isn't about selecting the works with the most "support". It's more about selecting the set of works that generates the most voter happiness, where happiness is defined as "getting a work onto the final ballot". I think this framing has gone missing from the discussion.
But in order to help with understanding, no, grokking how EPH works, here is my manually run example. To show how this is done, here is my (hardly random) example set of ballots, with 15 ballots, each with four nominations, and the goal is to reduce the 26 nominees to four finalists. Four of the ballots are also showing very similar taste (due to being on a slate or for some other reason).
I recommend keeping a set of the WSFS agenda from Midamericon 2 at hand, since I'm going to refer to the rules there.
Here are the ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 
D 
0,25 
2 
A 
B 
C 
D 
0,25 
3 
A 
B 
C 
D 
0,25 
4 
A 
B 
C 
E 
0,25 
5 
A 
F 
G 
H 
0,25 
6 
F 
G 
I 
J 
0,25 
7 
F 
I 
J 
K 
0,25 
8 
G 
I 
J 
L 
0,25 
9 
J 
K 
L 
M 
0,25 
10 
M 
N 
O 
P 
0,25 
11 
Q 
R 
S 
T 
0,25 
12 
U 
V 
X 
Y 
0,25 
13 
K 
O 
T 
Z 
0,25 
14 
L 
P 
R 
V 
0,25 
15 
N 
M 
Q 
U 
0,25 
Ballot is the ballot ID; Works is the set of works that the ballot nominates (FIELD35 can be ignored); and Points is the number of points that the ballot generates per work, per the calculation phase 3.A.1(1).
This yields the following table, sorted by work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,25 
1, 2, 3, 4, 5 
B 
4 
1 
1, 2, 3, 4 
C 
4 
1 
1, 2, 3, 4 
D 
3 
0,75 
1, 2, 3 
E 
1 
0,25 
4 
F 
3 
0,75 
5, 6, 7 
G 
3 
0,75 
5, 6, 8 
H 
1 
0,25 
5 
I 
3 
0,75 
6, 7, 8 
J 
4 
1 
6, 7, 8, 9 
K 
3 
0,75 
7, 9, 13 
L 
3 
0,75 
8, 9, 14 
M 
3 
0,75 
9, 10, 15 
N 
2 
0,5 
10, 15 
O 
2 
0,5 
10, 13 
P 
2 
0,5 
10, 14 
Q 
2 
0,5 
11, 15 
R 
2 
0,5 
11, 14 
S 
1 
0,25 
11 
T 
2 
0,5 
11, 13 
U 
2 
0,5 
12, 15 
V 
2 
0,5 
12, 14 
X 
1 
0,25 
12 
Y 
1 
0,25 
12 
Z 
1 
0,25 
13 
Work is the ID of the work; Nominations is the raw number of ballots with the work on it; Points is the number of points from ballots as used in the selection phase; and Ballots is simply a list with the ballots which list the work, I found it useful for bookkeeping purposes.
Per the old FPTP rules for Hugo nomination, A, B, C, and J would be the nominees. Lets see what happens when we start using EPH.
First comes the selection phase. All of the works with the least points total are selected as possible targets for elimination. E, H, S, X, Y, and Z all have 0.25 points, and are selected. Since they all have the same number of nominations (ie 1), they are tied. Per 3.A.3(4) of the WSFS rules, that means all of them are eliminated.
Round 2 has the following set of adjusted ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 
D 
0,25 
2 
A 
B 
C 
D 
0,25 
3 
A 
B 
C 
D 
0,25 
4 
A 
B 
C 

0,333333333333333 
5 
A 
F 
G 

0,333333333333333 
6 
F 
G 
I 
J 
0,25 
7 
F 
I 
J 
K 
0,25 
8 
G 
I 
J 
L 
0,25 
9 
J 
K 
L 
M 
0,25 
10 
M 
N 
O 
P 
0,25 
11 
Q 
R 

T 
0,333333333333333 
12 
U 
V 


0,5 
13 
K 
O 
T 

0,333333333333333 
14 
L 
P 
R 
V 
0,25 
15 
N 
M 
Q 
U 
0,25 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,41666666666667 
1, 2, 3, 4, 5 
B 
4 
1,08333333333333 
1, 2, 3, 4 
C 
4 
1,08333333333333 
1, 2, 3, 4 
D 
3 
0,75 
1, 2, 3 
F 
3 
0,833333333333333 
5, 6, 7 
G 
3 
0,833333333333333 
5, 6, 8 
I 
3 
0,75 
6, 7, 8 
J 
4 
1 
6, 7, 8, 9 
K 
3 
0,833333333333333 
7, 9, 13 
L 
3 
0,75 
8, 9, 14 
M 
3 
0,75 
9, 10, 15 
N 
2 
0,5 
10, 15 
O 
2 
0,583333333333333 
10, 13 
P 
2 
0,5 
10, 14 
Q 
2 
0,583333333333333 
11, 15 
R 
2 
0,583333333333333 
11, 14 
T 
2 
0,666666666666667 
11, 13 
U 
2 
0,75 
12, 15 
V 
2 
0,75 
12, 14 
Note that the points from most of the "slate" ballots (ballots 13) are unchanged, while the points to each work from other ballots have increased noticably.
N and P are selected in round 2. Since they each have the same number of nominations and points, both are eliminated.
Round 3 has the following adjusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 
D 
0,25 
2 
A 
B 
C 
D 
0,25 
3 
A 
B 
C 
D 
0,25 
4 
A 
B 
C 

0,333333333333333 
5 
A 
F 
G 

0,333333333333333 
6 
F 
G 
I 
J 
0,25 
7 
F 
I 
J 
K 
0,25 
8 
G 
I 
J 
L 
0,25 
9 
J 
K 
L 
M 
0,25 
10 
M 

O 

0,5 
11 
Q 
R 

T 
0,333333333333333 
12 
U 
V 


0,5 
13 
K 
O 
T 

0,333333333333333 
14 
L 

R 
V 
0,333333333333333 
15 

M 
Q 
U 
0,333333333333333 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,41666666666667 
1, 2, 3, 4, 5 
B 
4 
1,08333333333333 
1, 2, 3, 4 
C 
4 
1,08333333333333 
1, 2, 3, 4 
D 
3 
0,75 
1, 2, 3 
F 
3 
0,833333333333333 
5, 6, 7 
G 
3 
0,833333333333333 
5, 6, 8 
I 
3 
0,75 
6, 7, 8 
J 
4 
1 
6, 7, 8, 9 
K 
3 
0,833333333333333 
7, 9, 13 
L 
3 
0,833333333333333 
8, 9, 14 
M 
3 
1,08333333333333 
9, 10, 15 
O 
2 
0,833333333333333 
10, 13 
Q 
2 
0,666666666666667 
11, 15 
R 
2 
0,666666666666667 
11, 14 
T 
2 
0,666666666666667 
11, 13 
U 
2 
0,833333333333333 
12, 15 
V 
2 
0,833333333333333 
12, 14 
Q, R, and T are selected in round 3. Since they each have the same number of nominations and points, all are eliminated. (This also makes ballot 11 a sad puppy, since none of the works from that ballot will make it onto the final ballot.)
Round 4 has the following adjusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 
D 
0,25 
2 
A 
B 
C 
D 
0,25 
3 
A 
B 
C 
D 
0,25 
4 
A 
B 
C 

0,333333333333333 
5 
A 
F 
G 

0,333333333333333 
6 
F 
G 
I 
J 
0,25 
7 
F 
I 
J 
K 
0,25 
8 
G 
I 
J 
L 
0,25 
9 
J 
K 
L 
M 
0,25 
10 
M 

O 

0,5 
12 
U 
V 


0,5 
13 
K 
O 


0,5 
14 
L 


V 
0,5 
15 

M 

U 
0,5 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,41666666666667 
1, 2, 3, 4, 5 
B 
4 
1,08333333333333 
1, 2, 3, 4 
C 
4 
1,08333333333333 
1, 2, 3, 4 
D 
3 
0,75 
1, 2, 3 
F 
3 
0,833333333333333 
5, 6, 7 
G 
3 
0,833333333333333 
5, 6, 8 
I 
3 
0,75 
6, 7, 8 
J 
4 
1 
6, 7, 8, 9 
K 
3 
1 
7, 9, 13 
L 
3 
1 
8, 9, 14 
M 
3 
1,25 
9, 10, 15 
O 
2 
1 
10, 13 
U 
2 
1 
12, 15 
V 
2 
1 
12, 14 
So far, EPH has only eliminated works with few nominees. However, this changes now. Since ballots 10, 12, 13, 14, and 15 only have two works left on them, they give more points to them. Instead, the two works with the least amount of points in round 4 are D and I, each with three nominations. Since they each have the same number of nominations and points, both are eliminated.
This is the key feature of EPH. Ballots with few works remaining on them will gain in strength and make it less likely that the remaining works will have to face elimination.
Round 5 has the following ajusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 

0,333333333333333 
2 
A 
B 
C 

0,333333333333333 
3 
A 
B 
C 

0,333333333333333 
4 
A 
B 
C 

0,333333333333333 
5 
A 
F 
G 

0,333333333333333 
6 
F 
G 

J 
0,333333333333333 
7 
F 

J 
K 
0,333333333333333 
8 
G 

J 
L 
0,333333333333333 
9 
J 
K 
L 
M 
0,25 
10 
M 

O 

0,5 
12 
U 
V 


0,5 
13 
K 
O 


0,5 
14 
L 


V 
0,5 
15 

M 

U 
0,5 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,66666666666667 
1, 2, 3, 4, 5 
B 
4 
1,33333333333333 
1, 2, 3, 4 
C 
4 
1,33333333333333 
1, 2, 3, 4 
F 
3 
1 
5, 6, 7 
G 
3 
1 
5, 6, 8 
J 
4 
1,25 
6, 7, 8, 9 
K 
3 
1,08333333333333 
7, 9, 13 
L 
3 
1,08333333333333 
8, 9, 14 
M 
3 
1,25 
9, 10, 15 
O 
2 
1 
10, 13 
U 
2 
1 
12, 15 
V 
2 
1 
12, 14 
F, G, O, U, and V are all selected in round 5. F and G have three nominations each, while O, U, and V have two each. Per 3.A.1(3), works with the least number of nominations are eliminated, so O, U, and V are eliminated (making ballot 12 a sad puppy).
Round 6 has the following adjusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 

0,333333333333333 
2 
A 
B 
C 

0,333333333333333 
3 
A 
B 
C 

0,333333333333333 
4 
A 
B 
C 

0,333333333333333 
5 
A 
F 
G 

0,333333333333333 
6 
F 
G 

J 
0,333333333333333 
7 
F 

J 
K 
0,333333333333333 
8 
G 

J 
L 
0,333333333333333 
9 
J 
K 
L 
M 
0,25 
10 
M 



1 
13 
K 



1 
14 
L 



1 
15 

M 


1 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
1,66666666666667 
1, 2, 3, 4, 5 
B 
4 
1,33333333333333 
1, 2, 3, 4 
C 
4 
1,33333333333333 
1, 2, 3, 4 
F 
3 
1 
5, 6, 7 
G 
3 
1 
5, 6, 8 
J 
4 
1,25 
6, 7, 8, 9 
K 
3 
1,58333333333333 
7, 9, 13 
L 
3 
1,58333333333333 
8, 9, 14 
M 
3 
2,25 
9, 10, 15 
F and G are selected in round 6. Since they both have the same number of points and nominations, both are eliminated.
Round 7 has the following adjusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 
B 
C 

0,333333333333333 
2 
A 
B 
C 

0,333333333333333 
3 
A 
B 
C 

0,333333333333333 
4 
A 
B 
C 

0,333333333333333 
5 
A 



1 
6 



J 
1 
7 


J 
K 
0,5 
8 


J 
L 
0,5 
9 
J 
K 
L 
M 
0,25 
10 
M 



1 
13 
K 



1 
14 
L 



1 
15 

M 


1 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
2,33333333333333 
1, 2, 3, 4, 5 
B 
4 
1,33333333333333 
1, 2, 3, 4 
C 
4 
1,33333333333333 
1, 2, 3, 4 
J 
4 
2,25 
6, 7, 8, 9 
K 
3 
1,75 
7, 9, 13 
L 
3 
1,75 
8, 9, 14 
M 
3 
2,25 
9, 10, 15 
B and C are selected in round 7. Since they both have the same number of points and nominations, both are eliminated. Note that the entire slate but work A has been eliminated now.
Round 8 has the following adjusted set of ballots:
Ballot 
Works 
FIELD3 
FIELD4 
FIELD5 
Points 
1 
A 



1 
2 
A 



1 
3 
A 



1 
4 
A 



1 
5 
A 



1 
6 



J 
1 
7 


J 
K 
0,5 
8 


J 
L 
0,5 
9 
J 
K 
L 
M 
0,25 
10 
M 



1 
13 
K 



1 
14 
L 



1 
15 

M 


1 
Also an adjusted table sorted per work.
Work 
Nominations 
Points 
Ballots 
A 
5 
5 
1, 2, 3, 4, 5 
J 
4 
2,25 
6, 7, 8, 9 
K 
3 
1,75 
7, 9, 13 
L 
3 
1,75 
8, 9, 14 
M 
3 
2,25 
9, 10, 15 
K and L are selected in round 8. Since they have the same number of points and nominations, both should be eliminated, but since that would leave the final ballot at three nominees, 3.A.2 comes into effect.
The final ballot from running EPH would thus be:
A, J, K, L, and M
All the nominators but poor 11 and 12 (or 13%) will have at least one of their nominated works on the ballot, and the slate (numbering 4 out of 15, or about 27%) have one work on the final ballot.
We can compare this with the FPTP system, which would have yielded the following ballot:
A, B, C, J
Here ballots 10, 11, 12, 13, 14, and 15 (40%!) would have had no impact at all on the final ballot.
The calculations of points were done with the help of Numbers for Mac OS, but all selections and adjustments of the eliminated works were made by hand.
My set of CSV files (note: uses ; as separator and , as decimal marker) for import into spreadsheets.


