I'm tremendously grateful to Paul Evans for providing me with the 1984 data he described here. Having spent a couple of evenings crunching figures, I now feel huge sympathy and admiration for the Hugo administrators trying to make sense of the variant titles and spelling submitted by voters. Administering what are essentially thousands of write-in ballots is not exactly straightforward, and I am not sure that I would have the patience to do so in an RL setting myself. Not surprisingly, my tallies vary a bit from Paul's. He has taken more time over it, so his numbers are probably right.
I've picked three different ballot categories from 1984 to analyse mainly because they were relatively easy to process, with less name and category confusion than some of the other options would have presented.
First, Best Fan Writer - in some ways the easiest, because fewest nominations were submitted in this category (481 nominations of 174 candidates by 181 voters). My figures differ from Paul Evans' totals - he found a couple more votes for some of the candidates than I did - but it doesn't make a lot of difference to the story. This is a case where EPH clearly works, and a slate candidate with bullet votes would have had to get enough support to win under the old system as well.
The top seven candidates by nominations were:
56 Mike Glyer
36 Richard Geis
33 Dave Langford
28 Arthur D. Hlavaty
18 Teresa Nielsen Hayden
12 Ted White
10 Claire Anderson
A nice big gap between the fifth and sixth placed candidates, and indeed between the fourth and fifth. Under EPH, the points for each candidate on the final ballot would have been:
Mike Glyer (56 nominations): 28 + 21/2 + 4/3 + 3/4 = 40.583
Richard Geis (36 nominations): 16 + 13/2 + 4/3 + 3/4 = 24.583
Arthur D. Hlavaty (28 nominations): 14 + 7/2 + 4/3 + 3/4 = 19.583
Dave Langford (33 nominations): 6 + 20/2 + 4/3 + 3/ = 18.083
Teresa Nielsen Hayden (18 nominations): 7 + 9/2 + 2/3 = 12.167
To knock Teresa Nielsen Hayden off the ballot, a single slate candidate would have needed to also have 18 nominations which were bullet votes (or at least shared less with other candidates than hers), which would have beaten her 12.167 EPH points. I must say I'm not completely content with this; precisely because TNH had more voters who also supported other popular candidates, she is in a disadvantage in a head-to-head against a more sectarian candidate. But I think any variation of a single divisible vote system delivers this result, and what it basically means is that the last place may go to a representative of a small minority. The question is, how small?
I looked at Best Non-Fiction next because there was a more even spread of candidates at the lower end. 206 voters made nominated 86 different works here. The top 9 were:
45 Dream Makers, volume ii
43 The High Kings
29 The Fantastic Art of Rowena
26 Staying Alive: A Writer's Guide
19 The Encyclopedia of Science Fiction and Fantasy, vol iii
16 Worlds Beyond: the Art of Chesley Bonestell
11 Amber Dreams
11 The SF Book of Lists
11 Uranian Worlds
If we apply the EPH system, it doesn't change much in ranking:
Dream Makers, volume ii (45 nominations): 18 + 13/2 + 9/3 + 4/4 + 1/5 = 28.7 points
The High Kings (43 nominations): 17 + 14/2 + 8/3 + 3/4 + 1/5 = 27.617 points
The Fantastic Art of Rowena (29 nominations): 12 + 8/2 + 4/3 + 4/4 + 1/5 = 18.533 points
Staying Alive: A Writer's Guide (26 nominations): 9 + 6/2 + 8/3 + 2/4 + 1/5 = 15.367 points
The Encyclopedia of Science Fiction and Fantasy, vol iii (19 nominations): 4 + 7/2 + 4/3 + 3/4 + 1/5 = 9.783 points
But because the successful candidates shared a relatively large number of supporters, a single slated candidate with 16 bullet votes would have got onto the ballot, and would have knocked off the actual winner, vol 3 of The Encyclopedia of Science Fiction and Fantasy.
41 slate voters, ie fewer than voted for either of the two front-runners in the category, who voted for two candidates, and only those two, could have knocked out Staying Alive out as well.
The most striking results I've found are for the 1984 John W. Campbell Award, which had a very lopsided vote distribution - one front runner far ahead of the field, and a number of candidates jostling around the edge of the ballot. 247 voters made 519 nominations here. The top 15 candidates, with their total nominations, were:
121 R.A. MacAvoy
19 Joseph H. Delaney
19 Joel Rosenberg
18 Sheri S. Tepper
17 Lisa Goldstein
17 Warren Norwood
15 Barbara Hambly
12 Robin Wayne Bailey
12 Dan Simmons
10 P.C. Hodgell
10 Kim Stanley Robinson
10 Lucius Shepard
9 David Brin
9 John De Chancie
Some of these were not exactly new writers in 1984. Timothy Zahn had first published in 1980 and I guess was excluded from the final ballot for that reason. That brought in both Lisa Goldstein and Warren Norwood, tied on 17 nominations.
If we apply the EPH points system, the final six (Zahn having been excluded) end up in the following slightly different ranking:
R.A. MacAvoy (121 nominations): 89 + 23/2 + 9/3 = 103.5 points
Joel Rosenberg (19 nominations): 19 points
Warren Norwood (17 nominations): 9 + 7/3 + 1/4 = 11.583 points
Lisa Goldstein (17 nominations): 7 + 3/2 + 6/3 + 1/4 = 10.75 points
Joseph H. Delaney (19 nominations): 5 + 6/2 + 7/3 + 1/4 = 10.583 points
Sheri S. Tepper (18 nominations): 2 + 14/2 + 1/3 + 1/4 = 9.583 points
Sherri S Tepper would have been eliminated at this stage, although she had more nominations than two other surviving candidates (Warren Norwood and Lisa Goldstein). 165 of the original 247 nominating ballots are still in play. (Wow, MacAvoy made a pretty big splash, didn't she!)
After Sherri S Tepper's votes are redistributed, the point scores for what would have been the final ballot under EPH are as follows:
R.A. Macavoy (121 nominations): 103 + 10/2 + 8/3 = 110.667 points
Joel Rosenberg (19 nominations): 19 points
Warren Norwood (17 nominations): 9 + 1/2 + 7/3 = 11.833 points
Lisa Goldstein (17 nominations): 7 + 3/2 + 7/3 = 10.833 points
Joseph H. Delaney (19 nominations): 5 + 6/2 + 8/3 = 10.667 points
163 of the original 247 ballot papers would have remained in play.
A slate candidate with 11 nominators, none of whom supported any of the other surviving candidates, would have been ahead of Goldstein and Delany on points and would have made it to the final ballot (Goldstein would have lost due to having fewer nominations than Delaney). Such a candidate would have had fewer nominations than five excluded candidates - Lisa Goldstein, Sherri S Tepper, Barbara Hambly, Robin Wayne Bailey and Dan Simmons. These seems to me very unsatisfactory.
It's not irrelevant to note that Joel Rosenberg had 19 bullet votes at this stage (a few of whom had voted for other less popular candidates as well), and that these included ten voters with consecutive membership numbers who cast nominating votes identically for him in this category and for a novel called The Sleeping Dragon and a short story called "The Emigrant". You'll never guess who those works were by.
25 slate voters would have been able to get two works onto the shortlist here (if you eliminate Delaney, Norwood ends up with 12.5 points in third place). Again, that seems to me to be, simply, too low.
Conclusion and recommendation
I hope it's fairly clear that while EPH does, as advertised, make it very difficult for a small set of voters to dominate entire ballot categories, as has happened this year, it also actually lowers the barrier to a small detached group getting their first candidate onto the list. Of course, minorities should not have insurmountable barriers placed in front of them, but for my taste, EPH as presently constructed goes too far the other way. A slate candidate which had fewer nominations than ten more popular candidates could still have got onto the John W Campbell Award ballot. A slate candidate could have knocked the eventual RL winner off the Best Non-Fiction Work ballot despite getting fewer nominations. I don't think that's quite right.
My modest proposal is that the divisor for calculating points should not be the number of candidates supported by a voter, but the square root of that number. Square roots have a venerable place in political calculus, particularly in the apportionment of seats, both in the U.S. Congress and for enlightened commentators on the European Union. Basically, instead of weighting your vote by 0.5 if you still have two candidates left in the race, 0.333 if you have three, and 0.25 if you have four, your vote gets weighted instead as 0.707, 0.577 and 0.5. Looking at my test cases above, the new weighted points would be:
Best Fan Writer:
|Arthur D. Hlavaty||33||18.083||23.952|
|Teresa Nielsen Hayden||18||12.167||14.519|
A slate candidate would still need 18 bullet votes to displace Teresa Nielsen Hayden from the ballot; no change.
Best Related Work:
|Dream Makers, v2||45||28.7||34.836|
|The High Kings||43||27.617||33.466|
|The Fantastic Art of Rowena||29||18.533||22.413|
|The Encyclopedia of Science Fiction and Fantasy, v3||19||9.783||13.206|
A slate candidate would now need 19 bullet votes, rather than 16, to displace the Encyclopedia. That seems to me an improvement.
John W. Campbell Award:
Before we get to considering the slate, there's that matter of the fifth and sixth places to resolve. The top six now look like this:
|Joseph H. Delaney||19||10.583||13.784|
|Sheri S. Tepper||18||9.583||12.977|
Lisa Goldstein would drop off due to having fewer nominations than Sheri S. Tepper, and the final ballot would look like this:
|Joseph H. Delaney||19||11.333||14.380|
|Sheri S. Tepper||18||9.667||13.054|
A slate candidate would now need 15 bullet votes, rather than a mere 11, to get on the ballot. That would be the same number of votes as the candidate who just missed in 1984, Barbara Hambly. For me, that's a more equitable outcome.
So, basically, EPH can be improved by using square roots as divisors. That is all.