The (free) graviton admits, in addition to the standard Pauli-Fierz
description by means of a rank-two symmetric tensor, a description in which one
dualizes the corresponding (2,2)-curvature tensor on one column to get a
(D-2,2)-tensor, where D is the spacetime dimension. This tensor derives from a
gauge field with mixed Yound symmetry (D-3,1) called the "dual graviton" field.
The dual graviton field is related non-locally to the Pauli-Fierz field (even
on-shell), in much the same way as a p-form potential and its dual (D-p-2)-form
potential are related in the theory of an abelian p-form. Since the Pauli-Fierz
field has a Young tableau with two columns (of one box each), one can
contemplate a double dual description in which one dualizes on both columns and
not just on one. The double dual curvature is now a (D-2,D-2)-tensor and
derives from a gauge field with (D-3, D-3) mixed Young symmetry, the "double
dual graviton" field. We show, however, that the double dual graviton field is
algebraically related to the original Pauli-Fierz field and, so, does not
provide a truly new description of the graviton. From this point of view, it
plays a very different role from the dual graviton field obtained through a
single dualization. Similar results are argued to hold for higher spin gauge
fields.