A sorting algorithms is the wrong choice here. Use iterative Bradley-Terry and always choose the closest comparison (i.e. the two things that are ranked closest) that you haven't compared before.
This will give you good results fastest and it will robustly handle conflicting results (A beats B beats C beats A) that sorting algorithms wouldn't.
I've had very similar ideas many times, but never decided to make anything. Specifically, the A versus B idea. My ideas for such a system are always about a giant public databases of ratings and not about making tier lists.
I don't think such a system can create tier lists. Tier lists are about giving individual things a 5 to 0 rating: S, A, B, C, D or F, and then plotting them on a chart. You could have 1 S and 11 Fs! And that's a different list than if they're evenly distributed amongst the ranks. Or if all twelve things are a B.
Your binary approach can only produce a linear ranking of items: First place, second place, third place, fourth place, etc. You can't produce a tier list from that data.
That sounds really promising since the user input doesn't need to be "A vs B" but can can accept nuances (with a cursor of some sort). (https://lemmy.world/comment/18834907)
Well shit, I guess that changes everything. In some board game tournaments, they keep track of the point spread in each game and use it in rankings. Sometimes this spread can be so large that second place needs to beat first place like four times in a row to win, for example. You could look into a system like that. That's what Scrabble tournaments use. In the US, at least, I think.
Merge sort is easy to implement and looks cool when animated.
I think you may be wanting something like probabilistic programming. You aren't sorting. You are getting facts to infer something else with a high probability.
This is not unlike what LLMs/GPTs are doing. Inferring the next best word after asking billions of questions.
That sounds really promising since the user input doesn't need to be "A vs B" but can can accept nuances (with a cursor of some sort).
I'll look further into it
the problems are: my elements are not comparable without a user input (I added an example with fruits in an edit in my post), and even if I chose a good pivot, most of the first questions would be "Do you prefer Coconut or Apple? Do you prefer Coconut or Banana? Do you prefer Coconut or Durian?" (supposing Coconut is the pivot) which would be a bit boring
Maybe merge sort. Its O(nlogn) and fun, or at least less boring than manually bubble sorting.
And add some random caracters in the comparaison like emojis nulber, or one number is written in letter, or which side have more cat and you show emoji cat or picture with cats. Be creative on the number presentation to add some sillyness and fun
You can take the median of three random elements as your pivot, to get a good chance of it being near the middle without a lot of comparisons.
Merge sort is really promising since I can first break my list into pairs, sort every pair (if my list is randomized, those pairs are random, which is good for entertainment) and then alternate between the different merges so we don't focus on one half of the list
I already managed to break the code for my sorting algorithm to take an async lambda as a comparison function. Therefor I can choose my sorting algorithm on the fly.
As for magic, I thought the interface would show you pairs of elements that look randomly picked and after a while it gives you your sorted list. So, the "magical" thing would be that not-so-random selection of pairs
Fully random matchups, and Elo. Then define a curve for your tier list and study how Elo actually works so you can map the Elo to the tier.
QuickSort sounds good since it's, well... quick, but the whole pivot thing would compare the pivot to everything as a first step which would not be very entertaining if done manually.
n*log(n) algorithms are the way to go, though
I would break it into an interface that abstracts the sorting algorithm so that the sorting logic is decoupled from comparison logic or from the visuals. This would make it so that you can use different sorting algorithms and compare between them to see which one seems the most magical.
Magical might mean something different between us, so I don't want to assume and just give you an algo.
It might be something that is pretty different than what you are looking for, but for interactivity it might be funnier and less repetitive if you demonstrate some sort of bucket/radix sort to not have comparisons at all "choose which buket this number should go into"
Maybe also mergesort would be fun to simulate. You can split the array as usual and then ask the user to pick which number should go next from the two lists.
Among the classics, perhaps quick sort? Since it is unstable.