  Gravitational instantons with NUT charge are magnetic monopoles upon
dimensional reduction. We determine whether NUT charge can proliferate via the
Polyakov mechanism and partially screen gravitational interactions. In
semiclassical Einstein gravity, Taub-NUT instantons experience a universal
attractive force in the path integral that prevents proliferation. This
attraction further leads to semiclassical clumping instabilities, similar to
the known instabilities of hot flat space and the Kaluza-Klein vacuum. Beyond
pure Einstein gravity, NUT proliferation depends on the following question: is
the mass of a gravitational instanton in the theory always greater than its NUT
charge? Using spinorial methods we show that the answer to this question is
`yes' if all matter fields obey a natural Euclidean energy condition.
Therefore, the attractive force between instantons in the path integral wins
out and gravity is dynamically protected against screening. Semiclassical
gravity with a compactified circle can be self-consistently quantum ordered, at
the cost of suffering from clumping instabilities.
