Clearing the Neighbourhood: Definition of 'Orbital Region'? I am trying to determine how wide a 'neighbourhood' a planet is expected to clear.

However, the Wikipedia article on the matter provides no clarity, simply stating that a planet is expected to clear it's 'orbital region' with no definition provided.

I suspect that the correct answer is that a planet is expected to clear a region around it's orbit equal to the radius of its Hill Sphere, but I am not certain of it.

Furthermore, for a planet of Earth mass, the Hill Sphere radius is a measly 0.01AU, which doesn't seem like much of a neighbourhood!

Is there a formal way to define the 'neighbourhood'?
The IAU gives no definition, it leaves the term somewhat vague.

Various calculations of the "planetariness" of solar system bodies use slightly different notions of the "neighbourhood"

Soter's $\mu$ considers bodies to be in the neighbourhood if they share a common radial distance (ie the orbits cross each other) and the orbital periods differ by less than an order of magnitude

Margot's $\Pi$ uses $2\sqrt 3$ times the Hill radius. 

Stern and Levinson's $\Lambda$ in the original paper consider the neighbourhood to be bodies that cross the orbit of the planet, while not in an orbital resonance, to be in its neighbourhood, in a somewhat complex way that requires knowledge of the relative inclinations and and orbital velocities of bodies that cross orbits.

Changing the details of these values doesn't change the conclusion of the calculations: There is a clear and measurable difference between bodies like Mars and Neptune that are (to use Stern and Levinson's term) uberplanets and Ceres and Pluto that are unterplanets (or dwarf planets as termed by the IAU).