  The process by which jet algorithms construct jets and subjets is inherently
ambiguous and equally well motivated algorithms often return very different
answers. The Qjets procedure was introduced by the authors to account for this
ambiguity by considering many reconstructions of a jet at once, allowing one to
assign a weight to each interpretation of the jet. Employing these weighted
interpretations leads to an improvement in the statistical stability of many
measurements. Here we explore in detail the statistical properties of these
sets of weighted measurements and demonstrate how they can be used to improve
the reach of jet-based studies.
