By dkl9, written 2024-280, revised 2024-280 (0 revisions)

If you ask for my "favourite", or whatever is "best", in any broad domain, I will refuse to answer, or else give an answer I know to be probably wrong.

Goodness-judgments are fuzzy, i.e. subjective and intuitive. Fuzzy values only compare one way or the other when values compared are far enough apart. The more items there are to compare in a set, the closer together their respective qualities will be, on average. Hence, as sets get larger, fuzzy comparisons among its members get less reliable.

Something confidently known to be best in its category is (definitionally) known to be strictly better than each other item in its category. So we can only be certain about the best item in a category if the category is small, or if we expend great effort to compare items.

More precisely, suppose you ask about a domain of `n` objects, with qualities (`x`_{1} thru `x`_{n}) sampled from a normal distribution.
In the average scenario, the normal CDF of `x`_{1} thru `x`_{n} is evenly-spaced by 1 / `n`.
To find the best item, we must (at worst) compare best to second-best.
That entails comparing inverse CDF values at (2`n` - 1) / 2`n` to those at (2`n` - 3) / 2`n`.

Comparing is difficult in inverse proportion to the difference.
As `n` increases, that difference in inverse CDF values approaches 1/2.

Questions about favourites have included foods, neighbours, and programming languages.
In each case, I'm familiar with dozens of options.
That large `n` prohibits finding a confidently, correctly-known best option in any convenient timescale.

"X" isn't [my favourite] word, but it's the first word that comes to mind.

— Chuck Palahniuk, approximately

What I can do instead is alter the question from "which is your favourite?" to "which is distinctly good?", picking an option which compares as either greater-than or ambiguous against each other option, and so is in the top few.