I thought I saw you answer this question before but now I can't find it. Which seven questions would lead to the most accurate sorting (with no house's designated answer being disproportionately popular...if that makes any sense)?
The question sets I use for Most Accurate and 2nd-Most-Accurate Sortings are composites (in the sense that I'm trying to balance out the fairest question with which questions would produce the fairest Sorting, because technically the scent Q2, path Q5, and forest/river Q6 are all fairest for the individual questions, but together can produce a really heavy reliance on forest vs. water in terms of Gryff/Slyth - you really don't want log fire/woodsy path/forest on the same Sorting because then people who like forests are going to be heavily Gryff whether or not they actually value Gryffindor things, in the same way that someone getting sea or pool/merpeople/river often get Slytherin simply because they like water.)
Ignorant/cowardly/selfish/ordinary
Silvery potion/golden potion/plums and chocolate/inky potion*
Q1 - This is pretty clear-cut. There are only 4 Q1s, and the love/power/wisdom/glory one is worst on a number of levels (Love Potion confusion, power/glory being underpowered comparatively.) This one is excellent in terms of spread, having an appealing, specific answer for every House (ignorant in particular gets awards for drawing Ravenclaws in droves), and not featuring any particular answer that comes in #2 in all the other Houses (in other words, each House is picking what it's supposed to AND there's not any answer that they're all going for after that one.)
Q2: *as I've said, this is not quite as fair in numerical terms as the scent question but comes pretty close - the main issue is that slightly fewer people pick the inky potion and slightly more go for plums and chocolate - but if looking at an overall Sorting it's probably better than having 3 forest-y questions on the same quiz.
Q3/4: Not much to say; these are both best possible questions by far. Q3 features a slight disadvantage to Ravenclaw because Ravenclaw doesn't appear to have a primary weighting on any of the Q3s, but it's FAR better than trusted (which may well be the worst question on the entire quiz) and doesn't feature the everybody-picks-cure/book/records issue with the 2nd-best-Q3. The Q4 is the same way - all Q4s have one flaw or another, but this features the best spread of any of them.
Q5 - All Q5s are bad; most are awful. This one is least-bad. Gryffindor still has a slight overall edge and Slytherin a slight overall disadvantage, and that woodsy path is generally #2 in all the other Houses (that illustration is gorgeous!) but this is by far the best Q5 and one of the few where you don't have Houses swapping answers or 1-2 Houses stuck with an answer that nobody actually picks.
Q6 - forest/river is by far fairest, but Q6s tend to have issues compared to Q7.
Q7 - All Q7s are fairly good, but this one is best in terms of stats.
Second-best Sorting Questions:
The ____ (great/good/bold/wise)
Scent: parchment/sea/fire/home (actually statistically-fairest Q2, but note forest/water issue)
cure/book/record ordering
Muggle confrontation (ask/jinx/bluff/mental ward)
This Q1 is 2nd-best over memories after death because Slytherin and Gryffindor answers are relatively less-appealing on that one (Hufflepuff's is #1) and because occasionally I've found anecdotal evidence of religious beliefs skewing the issue. The Gryff/Puff answers are slightly less popular on The Bold/Good and there's a fair amount of crossover with Slyth picking Wise and Claws picking Great, but everybody still picks what they're supposed to.
Q2 - As stated before, scent is statistically fairest but not as good when placed in a larger context for the quiz. (Again, other Q2s tend to run into major fairness issues - for the garden, Gryffs actually pick the Claw answer as their #1 and the Gryff answer is a strong #2 in Ravenclaw; the instruments show Ravenclaw and Slytherin piano/violin being WAAAY more popular than Gryff and Puff drum/trumpet (even though everybody does pick what they're supposed to - drum is #1 in Gryff and trumpet #1 in Puff); the boxes are worst of all, with Ravenclaws picking the Slytherin box as their #1, nobody picking the Claw box, and the Puff and Claw boxes being relatively unpopular compared to Gryff and Slyth.)
The cure Q3 is MUCH fairer than the trusted Q3 even though both feature ALL of the Gryffindor answers at the very top of the popularity scale (and in the order that they give Gryff points - so that the #1 answer on each question gives the most points to Gryffindor!) But at least the top 4 answers have answers that give points to every House, and everybody mostly goes for the answers they should after picking the Gryffindor/Ravenclaw cure/book/records as #1 overall. (Trusted is by far worst for a TON of reasons I've already articulated - but one stat: 93% of Ravenclaws pick a non-Claw answer on that one, with about 50% going for trusted, 21% for praised, 21% for liked, 1% for feared. Trusted is #1 across the board by a large margin; trusted/praised are Gryff answers and are the #1/#2 answers overall - and trusted/praised are 1-2 overall in every House save Puff, where trusted-liked is 1-2.) Suffice it to say that the cure is flawed but not nearly as badly as the only other option.
Superpower - also flawed (Puffs get a bad selection, Slyths have an awesome one; change appearance is picked by 50% of Claws but gives more points to Slytherin while read minds gives more points to Claw than Slyth but divides evenly) but FAR better than the creature question (again terrible - Claws/Puffs/Gryffs don't pick what they should, Gryffs get points for the top 3 answers in the order that they're popular - e.g. ghosts is #1 overall and also throws most points to Gryff) while Slytherin lacks a creature in the top 3 and has 2/3 of the bottom 3 creatures) - so yeah, again, superpower MUCH better than the alternative.
Again, all Q5s bad, but at least everybody picks the answer they should. This one has the disadvantage of Slytherin having a relatively unpopular answer and Ravenclaw getting a slightly more popular answer (they tend to get the Slyth votes when Slyths don't pick the jinx), but here are the issues with all the other questions:
cheating classmate would be okay except that the Gryff answer is #2 in every House AND the Puffs pick Slyth's answer as their #1 while Slyths pick the Puff answer as their #1 (they flipped!)
noise-in-darkness has Puff answer as too popular (Ravenclaw is 2nd) - but worse, only about 5% of people and not even 15% of Slyths overall will pick the Slytherin answer. FIVE PERCENT. That is not close to being fair.
Troll confrontation is probably 3rd fairest but draw lots and volunteer to fight are not very popular, and draw lots in particular is not a good answer. Again, slight edge to Ravenclaw on this one.
Nightmare question is by far the worst: Claws pick the Gryff answer as their #1, Slyths pick the Claw answer as their #1, nobody picks the Slyth answer, and the Gryff one tends to be disproportionately popular overall.
(Overall, though, basically 3 Q5s have a very popular Gryff answer, 2 have a very popular Claw answer, 1 has a very popular Puff answer. Slyths tend to get screwed.)
Dawn/dusk features the "I'm not a morning person" problem but is FAR better than stars/moon, by far the worst either-or question (90% of Claws pick stars and stars is a Huffledor answer, while fewer than 50% of Gryffs pick stars.)
Heads/tails is marginally better than black/white, both in terms of splitting the numbers 50/50 and with symbolic issues. Heads/tails does have the problem of people using a coin flip to decide, while black/white has people picking differently depending on whether the chess piece is supposed to mean anything. Heads/tails is probably better overall based on numbers.
WORST (LEAST FAIREST QUESTIONS)
Love/power/glory/wisdom potions
Boxes (Merlin/pewter/ornate/tortoise)
Trusted/liked/praised/envied/feared/imitated
Centaurs/ghosts/merpeople/werewolves/goblins/trolls/vampire
no one knows you/eye at keyhole/up high/silly voice
(I'm super-Ravenclaw - about 70% of my Sortings go that way flat-out - but depending on my mood, this answer set might feature me giving absolutely zero Ravenclaw answers in terms of points - love/merlin/trusted/werewolves/eye at keyhole/stars/black is thoroughly Gryffindor with ZERO Ravenclaw. Even in a more Claw mood of wisdom/ornate/trusted/ghosts/eye/stars/black, I'd still come out Gryff with that - even though a majority of Ravenclaws pick Merlin's box, trusted, ghosts as their #1 and werewolves as #2, the eye at keyhole, and stars. Even though 50% of Claws pick trusted, 90% pick stars, etc., they don't get credit for any of those answers.)