  This study considers the method to derive a ranking of alternatives by
aggregating the rankings submitted by several individuals who may not evaluate
all of them. The collection of subsets of alternatives that individuals (can)
evaluate is referred to as an evaluability profile. For a given evaluability
profile, we define an aggregating ranking function whose inputs are the
rankings of individuals on the alternatives they evaluate. We investigate the
properties of aggregating ranking functions, which are modifications of those
introduced in previous studies. Whether an aggregating ranking function
satisfying a combination of properties exists depends on the evaluability
profile. Thus, we identify the necessary and sufficient conditions on
evaluability profiles to ensure the existence of the functions satisfying four
different combinations of properties. Furthermore, to examine how frequently
possible or impossible evaluability profiles occur, we derive the proportion of
each type in specific cases.
