Interestingly uninteresting

Concept
This idea came about first while hiking: say you were leaving a place, and knew you'd come back in the future. You also have an object you want your future self to have, but you can't take it with you, so decide instead to leave it somewhere and pick it up on your return. Where would you leave it?

To add some constraints: (a) you're not sure exactly when you'll return. Maybe 5 years, maybe 50. Also, (b) you prefer populated areas to those with lower density (faster to pick it up when you return). In maths terms, you're trying to minimize #visits(place) / #visits(surrounding areas) - that is, the fewer times people visit where you leave it, the better (ideally 0) but it's also good if people visit the
places close by often.

I eventually settled on somewhere like under unkempt plants near an industrial zone of a stable business (unlikely to change, also near road/foot traffic going to the building), but realized that really want I wanted was a really uninteresting place, surrounded by interesting places.

Numbers
To continue this idea, we can go from places to numbers. What is the least interesting number? There's the joke/proof that there is no smallest uninteresting number as that fact would make it interesting (the interesting number paradox), but we avoid this by saying something like: it roughly corresponds to the number's frequency. e.g. for positive integers, interestingness(x) ~ 1/x, borrowing from Benford's law,

Thankfully, this concept is already covered on youtube much better than I could hope to do, so instead I'd recommend watching these videos about both the most favorite numbers and Sloane's Gap of interestingness (or if you like papers, there's one about number appearance online).

One quote from the first video that stands out, and moves well into the next section, is from one person saying why they chose j: "You don't want to pick what everyone else has gone for".

Humans
The next part is where it gets most interesting when considered in the context of my previous post on prediction - that is, how to predict what humans will find uninteresting. This may seem an academic exercise, but it's surprisingly common: think about people going fishing, or off-piste skiing: you want to go where others aren't, essentially you want to find an uninteresting place (albeit a 'fun' or 'fish-laden' one).

This even shows itself in exploration games like minecraft: if you're in a world with lots of people, often you want to be the first one to explore an area, which requires deciding taking a path others have found uninteresting. I'm curious to see how this will happen in the upcoming exploration game No Man's Sky, but really, it'd be awesome to write one where the entire point of the game is to be the first to go to certain places.

Note that the question: "Go where others will not have gone" is self-referential, and so it runs into the same problems as the famous two-thirds-of-the-average game. That is, there will be some 'level-0' people who will just pick somewhere; then there'll be 'level-1' people who pick where to go but then remove these options and pick somewhere else. Then 'level-3' who pick from the places 'level-2' do not go, etc... As with the original game, the question becomes "Now that you know about the level principle, given a random selection of people who may or may not know about it also, where do you go?"

Short side-note: I was thinking of hipsters at this point (if level-1 people try to be different by avoiding the same numbers, they'll end up being quite similar in their different-ness) and it turns out I wasn't the only one. This has already been dubbed the hipster effect.

Testing
Checking answers to this is in theory quite simple: Ask people to pick a number between 1 and 100, but tell them that if they pick a number no-one has picked yet, they win a prize (e.g. $20). Before reading my hypothesis, what would you pick?

My hypothesis would be that level-0 people (and to some extent, level-2 and others) will pick 'interesting' numbers, although there'll probably be a lot fewer of them than in the previous game. level-1 people (which I'm guessing will be quite a lot) would then pick the interesting uninteresting numbers - i.e. those that are considered to be identifiable uninteresting (like...17 maybe? Although apparently it's popular too). The numbers that will be picked last should then be the ones that none of the levels found interesting - the truly uninteresting ones.

In the absence of a spare $2000 and lots of free time / test subjects, the closest I could get was using Google consumer surveys - I recently received a $75 voucher to use it (something to do with thanksgiving promotion), so decided to run a survey to test this. Unfortunately the service is far from ideal for this purpose: it's roughly $1/answer so the sample size is small (only 94 responses, they had some extra responses), plus all respondents had to answer the same questions in the same order, and worst, the options were bucketed so exact responses are hidden, but the three questions I ended up asking were:

Q1: Pick any number, from 30 to 40
Q2: When people are asked to pick any number from 30 to 40, what do you think the most common answer will be?
Q3: Pick any number from 30 and 40, that you think the fewest number of people answering this question will pick.

**spoiler alert**: I'd suggest taking a moment to first think what you would answer, then check out the results below.


Note also that I picked 30-40 to have only a small range of answers, but also to avoid using a range that has already been studied and might be known (e.g. a lot of people know that 7 is a common answer for 1-10). Q2 ideally I wanted to ask some people what they thought the least common would be, but I didn't to ask both (most and least), so just stuck to the 'most' variant.
Q1 results
Q2 results
Q3 results
Keeping in mind the bucketing (i.e. '40' bucket only has one number, so values are halved-ish), and the large error bars, some things worth noting:
  • People seem to go for the middle when picking (there's a few things that support this, e.g. moderacy bias or the center-stage effect).
  • The Keynesian beauty contest Q2 seems promising, it seems people think that people will go for the middle.
  • Some people might just always pick 30 or 40 regardless of the question
But the thing I found most interesting: the sum for buckets of Q1 plus Q3 is (very roughly) flat - 43/35/37/28/31/28 after doubling the 40 bucket. Proper data would be needed, but here's one theory: when we pick a number, our brain proposes all of them with various strengths, and we sample from that. When asked Q3, the strengths are inverted (/converted to inhibitions) before sampling. I guess at least it suggests that people weren't mistaking it as "which number would be picked the least", as I'd expect that to be closer to the opposite of Q2 (i.e. 34-35 much lower). However a version with that variant for Q2 is needed to confirm this - perhaps if I get another coupon...


Also interesting would be to have added a question asking what the subjects answer for the two-thirds-the-mean problem, and correlate that to the answers in Q3, although I don't believe the google service has that feature either.

Conclusion
Predicting what is not interesting is very tricky...especially when humans are involved. And especially when the question is self-referential, and you're really predicting what others predict others predict others predict....etc...is uninteresting.

To extend this even further and bring it back to an earlier post - you can even get into problems when just revealing information related to what is uninteresting. For instance, if someone published findings that stated 38 was the least likely to get picked, it'd surely invalidate itself quite quickly...

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