I've added this as an exception, but I've also considered doing this as a warning, since the issue is

• easy to encounter - one case occured in user_guide
• hard to explain within a short error message - requires specific equation and some level of understanding of probability
• has minimal effect on majority of use cases - as long as the variance isn't huge, the bias this error introduces is minimal, and for very specific cases e.g. the village sampling from the op warning should suffice

I also deviated a bit from original issue in that i'm allowing max(w) * n / sum (w) == 1. As far as I understand, it doesn't introduce any bias, and it allows some specific uses, e.g. df.sample(n=1,weights=[1,0])

If this is implemented as an exception, I believe that there is no way for the numpy exception "Fewer non-zero entries in p than size" to occur, as:

• w - list of weights
• n - number of non-zero weights in w
• size - size of the sample to be drawn
• len - length of w

I'm assuming that

• the weights are normalized, so sum(w) = 1, as it doesn't change anything and makes the math easier
• the weights are equal, since if any of them is larger than the others, max(w) and max(w) * size will increase
• therefore w = [1/n, 1/n, ..., 1/n] or any combination like w = [1/n, 0, 1/n, 0, ..., 1/n] where n is the number of non-zero weights
• for the "Fewer non-zero entries in p than size" to occur, size > n
• for the "Invalid weights: If replace=False, " to occur, size * max(w) / sum(w) >= 1
• size * max(w) / sum(w) >= 1
• size * max(w) >= 1, as sum(w) = 1
• size * 1/n >= 1, as max(w) = 1/n
• size >= n