  Power diagrams, a type of weighted Voronoi diagrams, have many applications
throughout operations research. We study the problem of power diagram
detection: determining whether a given finite partition of $\mathbb{R}^d$ takes
the form of a power diagram. This detection problem is particularly prevalent
in the field of information elicitation, where one wishes to design contracts
to incentivize self-minded agents to provide honest information.
  We devise a simple linear program to decide whether a polyhedral cell
decomposition can be described as a power diagram. Further, we discuss
applications to property elicitation, peer prediction, and mechanism design,
where this question arises. Our model is able to efficiently decide the
question for decompositions of $\mathbb{R}^d$ or of a restricted domain in
$\mathbb{R}^d$. The approach is based on the use of an alternative
representation of power diagrams, and invariance of a power diagram under
uniform scaling of the parameters in this representation.
