A.1 Computing the Finalists and Sweeps Charts

To compute the numbers for the charts, we needed the organic vote totals (that is, excluding the slate votes) for ranks 1-6 in each category for each year. We also needed the "EPH Deflator" for each rank 1-6 in each category. The EPH Deflator is just the ratio of the total votes to the total points--it's a measure of how much EPH has "deflated" the votes. The challenge is that not all of this infomation is directly available.

A.1.1 Vote Totals

A.1.2 EPH Deflator



For the new Best Series category, we used the deflator from Best Novel. To get EPH deflator for each category, we again used the numbers from the 2014 2015 , and 2016 Hugo Nominations Organic Estimates . For 2017, where that data won't be available until August, we used the median deflator for each category across the previous three years and applied it to all ranks.For the new Best Series category, we used the deflator from Best Novel.

A.2 Slate Impact on Finalists

A.2.1 Some Terminology

A few definitions will make this discussion a lot easier to follow.





A voter is anyone who nominated anything for a Hugo in a particular category. A slate voter is someone who voted a slate of candidates mindlessly. That is, he/she voted for the whole slate and nothing but the slate. An organic voter is any voter who isn't a slate voter.





An organic nominee is one that didn't come from a slate, versus a slate nominee, which is one that did.





The list of finalists is the top-6 nominees as chosen by any particular voting method. The organic finalist list the the list we would have had in the absence of any slates.





An organic finalist is an organic nominee that would have ended up in the top-6 list if there had been zero slate nominees. The #6 organic finalist refers the the 6th-ranked organic finalist. Ideally, the list of finalists would all be organic.





The slate refers to the list of six nominees that the slate organizer wanted to win in a particular category. (Or the 15 candidates, in the case of 3SV.)



A subslate is a list of 5 slate nominees taken from a slate and given to a particular slate voter. Slaters need to use subslates to get optimal results because a ballot is limited to five nominees. Slate organizers can assign voters to subslates by means such as telling them to look at the last digit(s) of their telephone numbers. (E.g. for a 6-way subslate, find the last digit that's in the range 1-6 and that's your subslate.)



A ballot is what a member submits to WorldCon to make nominations for the Hugo.





Because subslates are smaller than slates, the number of slate votes that a slate nominee receives will be less than the total number of slate voters.





EPH points are computed from votes as a way to penalize slates. Just looking at the list of finalists (so not thinking about the intermediate process), any voter who had N of the finalists on his/her ballot contributed 1/N EPH points to each such finalist. A voter with only one finalist on his/he ballot gave one point and one vote to that finalist. A voter with five finalists on his/her ballot gave each one one vote but only 1/5 of a point. (With EPH+ it would be 1/9 of an EPH+ point.)

A.2.2 Traditional Method

To get an idea of how the general algorithm works, let's start with the old voting method, where every voter nominated up to 5 candidates, and the finalist list contained the 5 nominees with the most votes. We didn't compute that here, but understanding it will help a lot.

Imagine that we are making a slate and we start with zero slate voters. Obviously we don't get anywhere. Start increasing the number of slate voters, one by one. At what point do we get our first finalist?

Look at all the #5 organic finalists across all categories. Find the one with the fewest organic votes. As soon as we have that many slate voters, we'll tie that finalist and get a slate nominee into the finalist list.

In general, just take the number of votes received by all finalists in all categories and sort them all into a single big list. That gives you the "jump points." When the number of slate voters reaches a jump point, the number of slate finalists increases by one. Fairly simple.



To compute stats for sweeps, do the same thing, but only use the #1 finalists rather than all finalists. This works because when the number of slate voters exceeds the number of organic votes that a #1 finalist received, that category will only have finalists from the slate; there will be no organic finalists.

That's all there is to it. All the other voting schemes are attempts to require more slate voters before giving up spots on the finalist list. Our task is to compute how many that is for each organic finalist across all categories. (That is, for each organic finalist in each category, we're computing how many total slate voters would be required to knock that finalist out of the list.)

Summary : For the traditional case, to knock a particular organic finalist out of the list requires slate voters > organic votes for that finalist. (Remember that, by definition, every slate nominee in every category gets the same number of votes.)



Clean and simple. It's also why slates were able to sweep so many categories; slate votes go up linearly with the number of slate voters, but organic votes only increase as the square root of the number of organic voters.

A.2.3 Standard 5 of 6

If the slate organizer only makes a single slate of 5, it will be impossible to sweep any categories, so the optimal strategy to attack the plain 5/6 system (that is, without EPH or 3SV) is for the organizer to make a slate of 6 nominees and then create 6 "subslates" of 5 by deleting one of the nominees from each. He/she then sends each slate voter one of the six subslates, evenly distributed.



This has the effect of diluting the slate votes for each nominee by a factor of 5/6. In order for a slate nominee to knock out any particular organic finalist, there must be 20% more slate voters (6/5) than there were organic votes for that finalist.



If the organizer knows in in advance that there are certain categories he/she can't easily sweep, then it would make sense to offer slates of just 5 candidates for those categories. Our numbers here do not reflect that strategy.





Summary : To eliminate any given organic finalist requries number of slate voters > organic votes for that finalist times 6/5

A.2.4 E Pluribus Hugo

As with 5/6, the optimum strategy to attack EPH is to create 6 subslates of 5 nominees each. Otherwise sweeping a category is impossible for the same reasons as above. As we will see, unlike 5/6, there is no advantage to the organizer creating a 5-nominee slate for categories that can't be swept, unless the organizer believes the slate will struggle to get even a single finalist in that category.





There are two cases here: beating the #6 organic finalist and beating any other organic finalist.









The way EPH works, taking the #6 spot means beating the #6 organic finalist in terms of votes, not EPH points. Since the subslates dilute the number of slate votes, this will require 20% more slate voters (6/5) than the finalist's tally of organic votes. In other words, the situation for the #6 finalists is exactly the same as for the case of 5/6 (above). If the slate organizer thinks it will be hard to get even one finalist, then he/she should give everyone a list of 5. (It never makes sense to send a list of just 1.)





Beating the #R Organic Finalist for R < 6





In order for a slate to beat the Rth-ranked organic finalist, its nominees have to have more EPH points than the organic finalist does. This is because the way EPH works, in each successive round of the algorithm, the number of points any nominee has never decreases. It either stays the same or goes up. (Or the nominee gets eliminated, but we're only talking about the ones that survived to become finalists.) If a slate nominee starts off with more EPH points than any organic finalist above #6, it will never be subject to an elimination test. That is, it will never be at the bottom of the list, so it never has to survive the comparison.





The organic finalist will also have a number of points that's less than the number of organic votes, but the deflator will be around 1.5 or less--virtually never as big as 2. We have estimated values for the organic deflators for all finalists in all but two categories for 2014-2016. Our article Slate Voting Analysis Using EPH Data: 2014-2016 explains in detail how this was calculated.





So all we need to do is compute how many slate voters it would take before every slate nominee in the finalist list would have more points than any particular organic finalist.





EPH hands out points based on how many ballots each nominee appeared on. If we want to capture spots 5 and 6, that means we'll have two nominees from the master slate in the finalist list, so you'd think EPH would give each one half as many points as it had votes. Then we'd need double the slate voters (plus we've still got that factor of 6/5 to apply).





But because of the overlapping subslates, that's not quite right. The slate item we want to put into slot #5 appears on only 5 out of 6 ballots. The one for slot #6 also appears on only 5/6 ballots. They appear together on only 4/6 ballots. So the slate nominee for position #5 gets 1/6 as many points as there are slate voters from the ballots that it is on alone and it gets 2/6 as many from ballots it shares with whatever ends up in slot #6 for a total of 1/2. The factor of 5/6 disappears.





In fact, at all positions except for #6, it turns out that we need 7 - R times as many slate voters as there are organic points for the organic finalist at that level. This is exactly what would happen if members were allowed to put six nominees on each ballot.





N = 7 - R slated nominees in the finalist list, then all N of them appeared on (6-N)/6 of the ballots and N - 1 of them were on (N-1)/6 of the ballots--and there are no other combinations. The number of points will then be





To see this, satisfy yourself from the combinatorics of the problem that if there are= 7 -slated nominees in the finalist list, then allof them appeared on (6-)/6 of the ballots and- 1 of them were on (-1)/6 of the ballots--and there are no other combinations. The number of points will then be

Summary: To knock organic finalist #6 off the list requires number of slate voters > organic votes times 6/5.





To knock organic finalist #R (R < 6) off the list requires number of slate voters > organic votes times (7 - N) divided by that finalist's organic EPH deflator.





Note: It is barely possible for the number of slate voters required to take spot #5 to be less than what's required to take spot #6. This has no effect on the graphs above.

A.2.5 EPH Plus

EPH+ is like the original EPH algorithm, except instead of dividing by N you divide by 2N-1. That is, instead of 1, 2, 3, 4, 5 the sequence is 1, 3, 5, 7, 9. Otherwise the calculations are the same as for EPH, with the caveat that the result isn't as elegant. Also, MidAmeriCon II didn't give data for EPH+, so we'll have to estimate the organic deflators as well.









Assuming that the EPH deflator is a combination of ballots with one finalist and ballots with two then





For some a between 0 and 1. We know D for any given organic finalist, so we can compute a





We can define the EPH+ deflator in terms of a as well.





So substituting the value for a above, we can estimate the EPH+ deflator from the EPH deflator.





This will work so far as our assumption is correct--that nearly all organic ballots have either 1 or 2 organic finalists on them.



Slate Deflators



To estimate the organic deflators for EPH+, we look at the organic estimate again . Notice that these are fairly small numbers--between 1.2 and 1.5 for the most part. This suggests that most voters' ballots were down to a single candidate by the end of the EPH process, and that most others were down to just two. Making that assumption, we can estimate the EPH+ deflator from the EPH deflator as follows:Assuming that the EPH deflator is a combination of ballots with one finalist and ballots with two thenFor somebetween 0 and 1. We knowfor any given organic finalist, so we can computeWe can define the EPH+ deflator in terms ofas well.So substituting the value forabove, we can estimate the EPH+ deflator from the EPH deflator.This will work so far as our assumption is correct--that nearly all organic ballots have either 1 or 2 organic finalists on them.

Using the same logic we used for EPH, the case for a single slate finalist is the same: it needs 1.2 times as many slate voters as organic votes for organic finalist #6.

For the case where R < 6, as above there are N = 7 - R slate finalists and so the number of slate points as a fraction of total slate votes will be

We need this in terms of R = 7 - N and we need the reciprocal, which is:

Summary: To knock organic finalist #R off the list requires number of slate voters > the finalist's organic votes times 6(13 - 2R)(11-2R)/(67 - 12R) further divided by that finalist's organic EPH deflator.

This messy formula hides an interesting result. Where subslates hurt the slates against 5/6, and they are neutral against EPH (except for position #6), they actually help the slates (slightly) against EPH+. Making smaller subslates (with fewer than 5 nominees) helps further at the higher levels (that is, helps in managing a sweep) but at the expense of making it harder to get 1, 2, or 3 finalists.

As above, we'll assume slate organizers can't predict the future, so we'll figure 6 subslates of 5 nominees as the optimal strategy against 5/6, EPH, and EPH+ all three.

A.2.6 Three-Stage Voting (3SV)

In this system, there is a middle stage of voting after nominating but before the final vote. This allows members to preemptively disqualify bad nominees. This is meant to allow people to remove things like pornographic nominees submitted in order to embarrass the awards. The first stage of voting is the same as always--people nominate 5 candidates. In the 3SV stage, however, everyone gets to see the top-15 (but not the number of votes--just the names) and can delete any or all of them. If enough members vote to delete an item, it cannot become a finalist.





For the optimal attack on 3SV, the slate organizer prepares a slate of 15, divides it into three, non-overlapping subslates of 5, and distributes those evenly to all slate voters.





This now operates the same as in the standard 5 of 6 model, except that votes get multiplied by 3, not 6/5. At the point where there are enough slate voters (divided by three) to overwhelm the organic finalist in spot #6, they will have taken over all the spots from #7 to #15. This strategy defeats 3SG by forcing the members to make a list of finalists with fewer than 6 nominees--possibly zero.

Summary : To kick any given organic finalist out of the list requires number of slate voters > the finalist's organic votes times 3.



This assumes the slate organizer doesn't really care which of his/her 15 slate nominees ends up in the finalist list, just as long as 6 of them do.

A.2.7 EPH/3SV

When EPH is used to calculate the 3SV list, the slaters need 9 items in the list before they can get one into the top 6. That 10th item will be one of 4 submitted by his/her subslate. This means the slate has to beat the number of points (not votes) for nominee #6 and the slate EPH deflator will be 4. It will be 4 for nominees 5 and 4, and will be 5 for nominees 3, 2, and 1.



Summary : To kick an organic finalist out of position #4, 5, or 6 requires number of slate voters > the finalist's organic votes times 12 divided by the finalist's EPH deflator.



To kick an organic finalist out of position #1, 2, or 3, requires number of slate voters > the finalist's organic votes times 15 divided by the finalist's EPH+ deflator.

A.2.8 EPH+/3SV

We use the same method as for EPH/3SV but with the EPH+ organic deflator and the EPH+ slate deflators.





Summary : To kick an organic finalist out of position #4, 5, or 6 requires number of slate voters > the finalist's organic votes times 21 divided by the finalist's EPH deflator.



To kick an organic finalist out of position #1, 2, or 3, requires number of slate voters > the finalist's organic votes times 27 divided by the finalist's EPH+ deflator.

A.3 Slate Impact on Sweeps



A.4 Raw Data We've shared the Excel spreadsheet used to construct the graphs . The meanings of the columns should be obvious, given the explanations above, but, if not, feel free to post a question in the comments below.

A slate sweeps an entire category if and only if it manages to beat the #1 nominee in that category. To compute this, simply use the same method as described above for finalists, but only take the #1 nominee from each category.

For those who want to know exactly how we came up with these numbers, read on.