  This paper attempts to define a generalisation of the standard Einstein
condition (in conformal/metric geometry) to any parabolic geometry. To do so,
it shows that any preserved involution $\sigma$ of the adjoint bundle $\mc{A}$
gives rise, given certain algebraic conditions, to a unique preferred affine
connection $\nabla$ with covariantly constant rho-tensor $\mathsf{P}$,
compatible with the algebraic bracket on $\mc{A}$. These conditions can
reasonably be considered the generalisations of the Einstein condition, and
recreate the standard Einstein condition in conformal geometry. The existence
of such an involution is implies by some simpler structures: preserved metrics
when the overall algebra $\mf{g}$ is $\mf{sl}(m,\mbb{F})$, preserved complex
structures anti-commuting with the skew-form for $\mf{g}=\mf{sp}(2m,\mbb{F})$,
and preserved subundles of the tangent bundle, of a certain rank, for all the
other non-exceptional simple Lie algebras. Examples of Einstein involutions are
constructed or referenced for several geometries. The existence of cone
constructions for certain Einstein involutions is then demonstrated.
