[rbmktechik]

Parents algorithm always works, the one described has a massive failure mode - people slowly learn that they are likely to say 7 and self-censor by picking another number. Or maybe in a different culture the distribution changes (say China and the numbers 4, 8).

[bnegreve]

> the one described has a massive failure mode

Well, if you're really interested in generating random numbers using a group of people, then yes, this may be a problem.

But you should take this as an illustration of the more general problem of generating uniform random numbers from a distribution that is not.

If you think about it this way, author's solution can be applied in a number of practical scenarios. For example, if you want to generate a hash values for objects using properties that are not uniformly distributed. Or if you want to generate random numbers from a physical artifact that is not perfectly uniform.

[OscarCunningham]

I would guess that in China the probabilities of 4 and 8 goes down. Asking people to pick randomly drives them away from special numbers.

[Ill_ban_myself]

In the US 7 is a lucky # and a statistical outlier in that it was more frequently chosen in the article above.

[OscarCunningham]

You might be right, but my guess is that 7's reputation for luck isn't famous enough to make a difference, and in fact it's common because other numbers seem too "unrandom".

We could test by asking people to pick numbers less than 100. I bet people would focus on odd numbers, especially those greater than 50, not ending in 5 or not having both digits the same.

[sokoloff]

I decided to do that.

Data and light analysis is here: https://docs.google.com/spreadsheets/d/1Dh0wiTCRkBhckWGXtjZg...

I definitely overpaid on Mechanical Turk per response, given how lightning quickly the data came in. (I decided to pay $0.10/HIT for 50 responses and got 68 responses in 8m26s.) I suspect that offering a nickel would have gotten the survey filled in under half an hour still...

[Ill_ban_myself]

Maybe 7 cents?

[FabHK]

Excellent point. The algorithm in the article is predicated on a specific distribution and iid, GP algorithm is predicated only on iid.