  We consider an issue of much current concern: could fairness, an issue that
is already difficult to guarantee, worsen when algorithms run much of our
lives? We consider this in the context of resource-allocation problems, we show
that algorithms can guarantee certain types of fairness in a verifiable way.
Our conceptual contribution is a simple approach to fairness in this context,
which only requires that all users trust some public lottery. Our technical
contributions are in ways to address the $k$-center and knapsack-center
problems that arise in this context: we develop a novel dependent-rounding
technique that, via the new ingredients of "slowing down" and additional
randomization, guarantees stronger correlation properties than known before.
