Why is the Wasserstein distance between [0, 1] and [1, 0] zero?

Question

Isn't the Wasserstein distance supposed to be a non-zero number since the probabilities are not equivalent?

In [1]: scipy.stats.wasserstein_distance([0, 1], [1, 0])
Out[1]: 0.0

Answer 1

It is because

scipy.stats.wasserstein_distance

expects 1D distributions in the first and second argument. It doesn't matter in which order you obtained the (same) observations, the distribution is the same. Check that for instance

scipy.stats.wasserstein_distance([3, 1, 2, 4, 5], [1 ,4 ,5 ,3 ,2])

is also

0.0

for the same reason.