[simonh]

Put everyone in a numbered sequence unknown to them. Add their chosen number to their sequence number, mod 10.

This re-maps everyone’s choices so they actually have no idea what number they are actually choosing and efficiently redistributes the bias in their choices without massively complicated functions. It is also robust to changes in the distribution pattern. However it would only work well if you had at least 10 people and the number of people is divisible by 10.

[bifel]

Wouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have?

[hanoz]

> Wouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have?

Yes. The above answer just obfuscates the issue. Consider ten people overwhelmingly biased towards 7. The suggested approach in all likelihood gets you 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then what? You're clearly not much closer to getting a single random number without a random way of picking one of them.

[simonh]

>You're clearly not much closer to getting a single random number without a random way of picking one of them.

That’s a characteristic of the original formulation of the question, not specifically in my solution. It’s implicit in the article that you can choose an arbitrary person in the room without bias.

[hanoz]

It's a shortcoming specifically introduced by your proposal. If you've got a random way of picking one of ten people, then you've already got a random number between one and ten. Your answer essentially reduces to: ask one person to think of a number then add an actual random number and mod 10.

[simonh]

From the article:

>The easy thing to do is to ask someone “Hey, pick a random number from 1 to 10!”. The person replies “7!”. Great! Now you have a number. However, you start to wonder, is the number uniformly random?

So the problem reduces to transforming one form of randomness (picking a person) to another form (a uniform numeric distribution. That's implicit in the whole rest of the article.

>If you've got a random way of picking one of ten people, then you've already got a random number between one and ten.

You've got a source of randomness, but you still need to turn that into a number. The article gives one method and I've given another. You could also assign the people numbers from a stack of shuffled numbered tiles, then pick a person although that requires you have the tiles which is not really part of the setup. The conceit is that you have to use people's ability to pick numbers pseudo-randomly. There are probably numerous ways.

[hk__2]

> Wouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have?

No, because that ordering can be chosen by someone not in the sequence.

[Fronzie]

Assuming you would put them in 10 buckets, that order wouldn't have to be random, as long as people have similar biases.

[simonh]

Actually the proposal in the article requires that the group's biases be stable and uniform, where mine doesn't.

[simonh]

The question assumes we have the normal faculties of humans. You can choose whatever non random criteria for ordering them you like as long as it doesn’t affect their number choice.

For example height, or age, or distance from the door to the room, or how much I like them, or where in the sequence I arbitrarily decide to put them in. As long as that does not a priori influence their number choice we’re good.