[EM] Guardian 100 Best Novels

[Kristofer Munsterhjelm]

On 2026-05-18 18:50, Ross Hyman via Election-Methods wrote:
> The Guardian's 100 Best Novels
> https://www.theguardian.com/books/ng-interactive/2026/may/12/the-100-best-novels-of-all-time
> inlcudes 172 ballots ranking voters' 10 favorite novels.  I think it
> would be interesting to use different voting methods on this ballot
> set..
> 
> The method the Guardian used to determine their l00 novel list from
> the ballots is very mysterious to me.
> 
> They state "We scored the titles according to how often they were
> voted for, and then added a weighting based on individual rankings to
> produce the overall list of 100 greatest books."
> 
> I played around and could not find anything that fit this vague
> description and would produce the presented list.
> 
> For example, My Antonia in 100th place is ranked on 4 ballots while
> 99, The Go-Between is ranked on 3. So rankings are not just being used
> to break approval ties.
> 
> Then look at 89 The Left Hand of Darkness, also ranked on 4 ballots.
> But Antonia at 100 is higher ranked on its four ballots than Darkness
> is on its four.
> 
> What is their formula?

Interesting. The raw data is defined in this large minified JS script:

https://interactive.guim.co.uk/atoms/2026/03/2026-best-100-books-testing/best-100-books/v/1778864974/app.js

I've pulled the data into JSON files[1][2], which can be parsed with a 
simple Python script[3]. After cleaning up the names, Quadelect gives 
the following top 20 with Schulze:

  1. Middlemarch
  2. Beloved
  3. Ulyssses
  4. To the Lighthouse
  5. Anna Karenina
  6. In Search of Lost Time
  7. War and Peace
  8. Jane Eyre
  9. Bleak House
10. Pride and Prejudice
     Madame Bovary
12. The Great Gatsby
13. Nineteen Eighty-Four
     Moby Dick
     Emma
16. One Hundred Years of Solitude
17. Mrs Dalloway
18. Persuasion
19. The Portrait of a Lady
20. Wuthering Heights

and with Smith,Ext-Minmax (which is quite decisive, but not clone 
independent or ISDA):

  1. Middlemarch
  2. Beloved
  3. Ulysses
  4. To the Lighthouse
  5. Anna Karenina
  6. In Search of Lost Time
  7. War and Peace
  8. Madame Bovary
  9. Emma
10. Pride and Prejudice
11. Mrs Dalloway
12. One Hundred Years of Solitude
13. Moby Dick
14. Bleak House
15. The Great Gatsby
16. Wuthering Heights
17. Nineteen Eighty-Four
18. Persuasion
19. The Portrait of a Lady
20. Jane Eyre

The description does make it sound like they're using Approval and 
Borda, so I took a guess that their Borda doesn't eliminate the 
non-contenders first, hence that a candidate's Borda penalty (negative 
score) is just the sum of the ranks they're listed in.

By linear programming, I found the following weighting that *almost* works:
	score = 30 * approvals - borda penalty

where the approvals and borda penalties are calculated like this:

	from collections import defaultdict

	approvals = defaultdict(int)
	borda_penalties = defaultdict(int)

	for voter in voting_info:
		for vote in voter["topTen"]:
			approvals[vote["name"]] += 1
			borda_penalties[vote["name"]] += vote["position"]

	scores = []
	best_fit_scores = []

	for candidate in approvals.keys():
		scores.append((approvals[candidate], -borda_penalties[candidate], 
candidate))
		best_fit_scores.append((30 * approvals[candidate] - 
borda_penalties[candidate], candidate))

with a tweak taking into account that "The Life and Opinions of Tristram 
Shandy" has two different names in the input data.

This is accurate up to position 53. The first mismatch is "Orlando" and 
"The Transit of Venus". Exact ties (both Borda and Approval scores 
identical) seem to be broken in ascending alphabetical order.

(It should be possible to determine the weights more accurately, but I 
couldn't be bothered to manually input 100 Approval/Borda score pairs 
into my solver.)

So if I were forced to guess at the method, I would say it's a weighted 
Approval/Borda score. It is a very good fit, at least.

I suppose that's a reasonable method in this case, since presumably the 
voters were honest men (to echo Borda) and there's little reason to 
suspect strategic nomination either.

-km

[1] https://munsterhjelm.no/km/elections/guardian_best_100_2026/pb.json
[2] https://munsterhjelm.no/km/elections/guardian_best_100_2026/gb.json
[3] 
https://munsterhjelm.no/km/elections/guardian_best_100_2026/investigate_votes.py