Select n records at random from a set of N

Question

I need to select n records at random from a set of N (where 0 < n < N).

A possible algorithm is:

Answer 1

Although the algorithm described is technically correct, it depends on having an algorithm to return a bool with arbitrary probability determined by the ratio of two ints. For example, how do you select this item with a probability of 7/22? For the point of talking, let's call it the bool RandomSelect(int x, int y) method, or just the RS(x,y) method, designed to return true with probability x/y. If you're not very concerned about accuracy, the oft-given answer is to use return Random.NextDouble() < (double)x/(double)y; which is inaccurate because Random.NextDouble() is imprecise and not perfectly uniform, and the division (double)x/(double)y is also imprecise. The choice of < or <= should be irrelevant (but it's not) because in theory it's impossible to randomly pick the infinite precision random number exactly equal to the specified probability. While I'm sure an algorithm can be created or found, to implement the RS(x,y) method precisely, which would then allow you to implement the described algorithm correctly, I think that to simply answer this question as "yes the algorithm is correct" would be misleading - as it has misled so many people before, into calculating and choosing elements using double, unaware of the bias they're introducing.

Don't misunderstand me - I'm not saying everyone should avoid using the described algorithm - I'm only saying that unless you find a more precise way to implement the RS(x,y) algorithm, your selections will be subtly biased in favor of some elements more frequently than other elements.

If you care about fairness (equal probability of all possible outcomes) I think it is better, and easier to understand, to use a different algorithm instead, as I've described below:

If you take it as given that the only source of random you have available is random bits, you have to define a technique of random selection that assures equal probability, given binary random data. This means, if you want to pick a random number in a range that happens to be a power of 2, you just pick random bits and return them. But if you want a random number in a range that's not a power of 2, you have to get more random bits, and discard outcomes that could not map to fair outcomes (throw away the random number and try again). I blogged about it with pictoral representations and C# example code here: https://nedharvey.com/blog/?p=284 Repeat the random selection from your collection, until you have n unique items.