one question: Why do dwarf plants on the right have an upward sloping diameter as you get farther out? Isn't a dwarf defined by an absolute diameter cutoff (i.e. above which it's a true planet, below which it's not)? or is there a formula that takes into account distance from something?
I'm unsure why the further would orbits require a larger size though; my guess is something to do with longer, slower orbits needing more mass to get rid of the debris.
Stern–Levison's Λ finds a body's ability to scatter smaller masses out of its orbital region over a period of time equal to the age of the Universe scales inversely with its semi-major axis [1]. (A circle's semi-major axis is its radius [2].)
This is most simply because a wide orbit contains more volume than a small orbit.
[1] http://www.boulder.swri.edu/~hal/PDF/planet_def.pdf
[2] https://en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes