Picking favourites is hard

post by dkl9 · 2024-12-04T20:46:47.470Z · LW · GW · 3 comments

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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 ( thru ) sampled from a normal distribution. In the average scenario, the normal CDF of  thru  is evenly-spaced by . To find the best item, we must (at worst) compare best to second-best. That entails comparing inverse CDF values at  to those at .

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

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.

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comment by Dagon · 2024-12-05T17:32:54.474Z · LW(p) · GW(p)

As I've gotten older, I note more and more problems with the literal interpretation of topics like these.  This has made me change my default interpretation (and sometimes I mention it in my response) to a more charitable version, like "what are some of your enjoyable or recommended ...".   In addition to the problems you mention, there are a few other important factors that make the direct "exactly one winner, legibly better than all others" interpretation problematic:
 

  • Variable over time.  I explicitly value variety and change, and my ordering of things changes based on which attributes of that thing are more important in this instant, and how I estimate my reaction to those attributes in this instant.
  • Illegible preferences.  I have no idea why I'm drawn to some things.  I can make up reasons, but I have no expectation that I can actually discern all my true reasons, and I'm usually unwilling to try very hard.
  • High-dimensionality.  Most discussions and recommendation-requests of this form are about non-simple experiences.  Comparing any two requires a LOT of choice in how to weight various dimensions of comparison in order to get a ranking.  
comment by papetoast · 2024-12-05T13:13:14.087Z · LW(p) · GW(p)

There is also the issue of things only being partially orderable.

When I was recently celebrating something, I was asked to share my favorite memory. I realized I didn't have one. Then (since I have been studying Naive Set Theory a LOT), I got tetris-effected and as soon as I heard the words "I don't have a favorite" come out of my mouth, I realized that favorite memories (and in fact favorite lots of other things) are partially ordered sets. Some elements are strictly better than others but not all elements are comparable (in other words, the set of all memories ordered by favorite does not have a single maximal element). This gives me a nice framing to think about favorites in the future and shows that I'm generalizing what I'm learning by studying math which is also nice!

- Jacob G-W in his shortform [LW(p) · GW(p)]

comment by Richard_Kennaway · 2024-12-04T23:18:40.413Z · LW(p) · GW(p)

“I rather like bad wine; one gets so bored with good wine.”

— Disraeli