Say there is a competition to guess how many jelly beans are in a jar, with the winner being whoever gets closest, and that the actual number of jelly beans is 100.
If I guessed 110 and you guessed 91, you would of course win, no question.
But what if I guessed 150 and you guessed 51… you would still win, right? According to simple person’s logic [and probably the rules of most such competitions] yes, of course you would.
Ok, now what if I guessed 200 and you guessed 1. By the logic of the above, you would still win, being off by 99 while I am out by 100. But when you look at it, this would be a rather absurd outcome– I mean, what sort of idiot would mistake 100 jelly beans for 1, right?
The reason is that what’s important when estimating an amount, population or size is the factor by which you are out, not just the difference between your guess and the true number.
In the first example above the guess of 91 is indeed better than 110 by this measure, but only just.
In the second the guess of 51 is off by a factor of nearly 2, whereas the guess of 150 is only off by a factor of 1.5.
In the third example we have an error factor of 100 vs 2! I wonder how such a result would be judged in a guessing competition? Assuming they stick with evaluating the winner by the simple numerical difference then one would be well advised to try to underestimate the count in such a challenge, because you will gain an unfair statistical advantage by doing so.
One reason I am thinking about such things is in response to a simple but infuriating puzzle question from Richard Wiseman’s blog:
Imagine that you live on the moon. One day you see a number 14 bus. What is the most likely number of bus routes on the moon?
(assume bus routes are numbered consecutively, ie there must be at least 14 routes)
He claims the best answer is in fact 14 (his explanation), but my answer is 27 and I’m sticking with it, due to the logic discussed above combined with my rationale as described in the comment I left here.
Feel free to read the various answers and comments in his post and then come back here and tell me I’m wrong– I dare you.

Pictured here is Chinese artist Liu Bolin’s
Here’s a quote from Ray,