  This study focuses on situations where a finite set of alternatives is
evaluated by collecting evaluations from several individuals, some of whom may
not evaluate specific alternatives. The collection of subsets of alternatives
that individuals (can) evaluate is referred to as an evaluability profile. For
a given evaluability profile, we define a collective evaluation function whose
inputs are the evaluation orders of individuals on the subsets of alternatives
that they evaluate. We investigate the properties of collective evaluation
functions, which are modifications of those introduced in previous studies. We
identify the necessary and sufficient conditions on the evaluability profile
that ensure the existence of collective evaluation functions satisfying four
different combinations of these properties.
