# Why does an L2 penalty prefer smaller and more diffuse weight vectors?

For instance, why is it that it is more favourable for a weight of [0.25, 0.25, 0.25, 0.25] (for which the L2 penalty is 0.25) instead of simply [1, 0, 0, 0] (for which an L2 penalty is 1)?

In this case, both weights would give the same dot product when using W.T * X