And that responsibility begins today with the election of a monitor to supervise its use. What's the role of "with" A happens with B. B is in part the cause or enabler of A happening. Is there any difference between"with the election of a monitor to supervise its use" and "with the election of a monitor supervising its use"? Pretty much the same. "to supervise" works better for me. The monitor is to supervise. That is the role. "supervising" has a continuous sense that does not add anything here.