2.1 Grouping

Topic 1: Grouping
Topic 2: Hierarchical grouping

Topic 1: Grouping

Grouping is one of the most fundamental aspects of thinking. Although it is not a reasoning activity, a solid grasp of grouping is very important for good reasoning and argument, since in complex arguments reasons ought to be properly grouped together.

The basic notion of a group is very simple and familiar:

A group is a collection of items which belong together in some way.

Grouping is just the activity of creating or specifying groups. It involves

identifying a suitable grouping principle (see below),
identifying the items which belong to the group thus defined, and
presenting the items in a clear and orderly way.

Grouping Principle

A grouping principle is an explicit statement of the essence of the group, i.e., the sense or respect in which the items belong together. It is important to articulate the grouping principle as clearly and precisely as possible. Often groups are poorly formed because the grouping principle is confused or vague.

Coherent Groups

Here ‘coherent’ just means properly thought-out and presented. A coherent group should be:

Complete:
No gaps, nothing missing; everything which belongs in the group should be present.
Internally Distinct:
No overlaps; each item in the group should be genuinely distinct or separate from all the others.
Minimal:
No outsiders; nothing should appear in the group which does not really belong.
Ordered:
Items should be listed in the most natural or appropriate order.

Figure 2.1 Countries listed in order of GDP (IMF rankings)

MECE

Sometimes the acronym MECE is used as shorthand for a properly formed group. MECE stands for ‘Mutually Exclusive, Collectively Exhaustive’ and is just a fancy way of saying ‘no overlaps, no gaps.’

The problem with MECE, however, is that it does not conform to itself; MECE is not complete as a list of the properties of a properly formed group (i.e., its two principles are not ‘collectively exhaustive’).

See also: Topic Hierarchical Grouping

Topic 2: Hierarchical grouping

We are all familiar with the notion of a hierarchy, i.e., structures of the following kind:
Figure 2.2Figure 2.3

There is a range of metaphors to describe hierarchies, including:

A hierarchy is like a tree, with one trunk, many branches, and many leaves, though in the diagrams above the trees are upside down with the topmost item being the root
Drawing on the notion of a family tree, we describe items in the hierarchy as having a parent and children.
A hierarchy sometimes resembles a pyramid, with a wide flat base and each level narrower than the one below.

A hierarchy is a nested structure of groups and subgroups, with all the children of an item constituting one group.

Hierarchical grouping is organizing items and groups into hierarchical structures.

A coherent hierarchy

A coherent hierarchy is one that is well-thought-out and well-presented. The main aspects of coherence for hierarchies are:

Coherent Groups
The hierarchy’s constituent groups should of course be themselves coherent – i.e., complete, internally distinct, minimal, and ordered.
Abstraction The main principles of abstraction for hierarchies are captured in this simple diagram: Higher = more general. The ‘higher’ in the hierarchy (closer to the root) the item, the more general or abstract it should be. Figure 2.4
- Level Consistency. Items at the same level should be at approximately the same level of abstraction, even across branches.
- Level Completeness. All appropriate levels of abstraction should be present; there should be no ‘missing rungs’.
Congruence A hierarchy is fully congruent when similar grouping principles are used throughout the hierarchy. Congruence has two aspects:
- Horizontal Congruence. Groups at the same level (e.g., B1, B2 and C1, C2) have the same grouping principle.
- Vertical Congruence. Groups have similar grouping principles to those immediately above and below them.
  Figure 2.5
Desirable, not compulsory
Ideally, a hierarchy will satisfy all principles of coherence, but in some circumstances you may want to relax some of the constraints. This is OK as long as you understand clearly what you are doing and why you are doing it.