Summary: The paper studies the relations between \(\phi \)-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam's deficiency. A new and considerably simplified approach is given to the spectral representation of \(\phi\)-divergences already established in [\textit{F. Österreicher} and \textit{D. Feldman}, ``Divergenzen von Wahrscheinlichkeitsverteilungen -- integralgeometrisch betrachtet'', Acta Math. Sci. Hungar. 37, No. 4, 329--337 (2005; \url{doi:10.1007/BF01895132})] under restrictive conditions and in [the author and \textit{I. Vajda}, ``On divergences and informations in statistics and information theory'', IEEE Trans. Inform. Theory 52, No. 10, 4394--4412 (2006; \url{doi:10.1109/TIT.2006.881731}); ``\(f\)-divergences: sufficiency, deficiency and testing of hypotheses'', in: Advances in inequalities from probability theory and statistics. New York, NY: Nova Science Publishers. 113--149 (2008)] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary convex functions which are strictly convex at one point only. Bayes sufficiency is characterized with the help of a binary model that consists of the joint distribution and the product of the marginal distributions of the observation and the parameter, respectively. LeCam's deficiency is expressed in terms of \(\phi\)-divergences where \(\phi \) belongs to a class of convex functions whose curvature measures are finite and satisfy a normalization condition.