The concept of capabilities, introduced originally by Sen with the aim to provide a better basis for the theory of inequality, has inspired many researchers but has not found any simple formal representation which might be instrumental in the construction of a comprehensive theory of equality. In the present paper, we present a formalization of the concept of capabilities based on Lancasterian characteristics, whereby a functioning of an individual is a method for transforming an initial position to a final outcome. In this context, we investigate whether preferences over capabilities as sets of functionings can be rationalized by maximization of a suitable utility function over the set of functionings. Such a rationalization turns out to be possible only in cases which must be considered exceptional and which do not allow for interesting applications of the capability approach to questions of health or equality. The conclusion which can be obtained from the predominantly negative results is that a formal description of capabilities much involve ideas which go beyond the simple representation as a family of choice sets.
