It is a combination of both Phisherman's and your own answer.
It is not the size of the humidor that matters, but rather the available volume inside, that affects the humidity regulaton. A full, or nearly full, humidor is a lot easier to maintain humidity in. I only rarely glance at the humidity of my full humidors. They don't experience spikes in humidity. Conversely, I obsess over any humidors that are half full or less.
Cigars are hygroscopic. Meaning, they both emit and absorb humidity (moisture). If your humidor has significant empty space, it is filled with air that is taking up humidity that is released and lost whenever you open your humidor. Or, if you live in a humid area, your humidor is inundated with humidity each time you open it and expose it to the outside air. A full humidor has cigars to displace that harmful air and the moist cigars work in conjunction with the cedar and humidification device of your choice to regulate your humidor's humidity level.