Sorting problems usually refer to absolute evaluation (the assignment of an alternative does not depend on the others), as opposed to ranking and choice problems in which the very purpose is to compare alternatives against each other. Considering constraints concerning category size lead to define a Constrained Sorting Problem which refers both to absolute and relative evaluation.
After identifying decision situations in which category size is
useful for modelling purposes, this paper defines the concept of
category size and proposes a way to compute the size of
categories, even when the set of alternatives and/or the
preference information is/are imprecisely known. We show how this
notion can be used in a preference elicitation process. Finally,
in order to illustrate the use of this concept, we propose a
procedure to infer the values for preference parameters that
accounts for specifications (provided by the DM) about the size of
categories, in the context of the UTADIS sorting model.
Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-02.ps.gz