  Classical approval voting processes suffer from well-known impossibility
theorems. We consider grading-based voting, where voters give a grade rather
than a preference to each candidate. Numerous voting processes have been
proposed in this framework, such as majority judgment or range voting, showing
interesting properties. This article aims to present a unified framework for
grading-based voting processes. Our statement is that a voting process can be
seen as the finding of the innermost point of a multivariate scatterplot.
Introducing depth functions in voting theory enables to associate each voting
process to a depth notion, and enlarges the scope of procedures. We focus on a
given family of depth functions, the wL p depths, to highlight the behavior of
the depth-based approach.
