Imagine the following experiment: you wait say at a subway exit, and ask everyone passing "please tell me a number" (positive integer, of course). You do this day after day, until you reach say 1M people. 


* What is the distribution $\mu$ on the positive integers that you get?


This is a serious question, obviously some numbers are "nicer" than some other, say arithmetically speaking, so $\mu$ is probably a very interesting measure!


Of course, if you would do the poll with very small kids, $\mu$ would be more or less uniform on $2,3,4,5$ or so, perhaps with some mass at 1, and probably at $0$ too (coming from scientists's kids, proud of knowing what 0 is :) 


My question of course concerns adults, and results obtained via a real poll like the one suggested above: does anyone know, is anything written on this subject? 


(question inspired from [The human body's random number generator](https://mathoverflow.net/questions/117034/the-human-bodys-random-number-generator), I mean from the title of that question.)


[Edit Jan 2: thanks very much everyone, as a partial conclusion: (1) the measure $\mu$ certainly depends on the precise location of the poll, interesting would be for instance the results of an experiment - I mean, the picture/precise formula of $\mu$ - in a "random" place, say Times Square, (2) there are lots on interesting links signaled below (by MP, Joel, JSE..), papers by cognitive scientists, plus some interesting math interpretations/speculations (by quid, Alexander, Andreas, Yuichiro..) but I'm still afraid there's no picture of some particular $\mu$ emerging from all this, (3) will keep looking etc., and of course, if I ever get a huge grant, with some freeness in spending it :) think I'll conduct such a poll experiment myself - it's probably worth it.]



What is a random number? (poll experiment)
Cognitive sychologists study this kind of question, as you might expect. [Here's a paper](http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00250/abstract) (behind a paywall, sorry) where they asked people to name random digits. You don't get uniform distribution on 0,..,9.


I learned a little about this stuff when I was writing [a blog post](http://quomodocumque.wordpress.com/2009/06/24/more-iranian-election-statistics/) about detecting election fraud by looking for digits which looked more like "numbers made up by humans" than "numbers arrived at randomly."


**Update:** I spoke to my colleague Gary Lupyan, a cognitive psychologist here who studies such things. There are lots of interesting results, although he hasn't done the precise experiment suggested in the question. If you ask people to name a number between 1 and 100, the modal responses are between 1 and 10, with maybe a slight continuing dropoff afterwards. People disprefer even numbers and multiples of 5 and 10. He also replicated the folk belief that if you ask people to name a number between 1 and 20, the modal response is 17.


It doesn't look to me like the results he's getting are well-modeled by any particularly natural distribution, though you could certainly fit some kind of decay to it.


