%Nr: DS-96-04
%Author: Jeroen Bruggeman
%Title: Formalizing Organizational Ecology
Abstract:
The aims of this thesis are threefold: (1) to show to sociologists
that formalization is useful, i.e., that a great deal of informal
sociological conclusions are unsound; that formalization
subsequently leads to improved sociological theories and to new
results, provided that the theory's underlying ideas are `good'; (2)
to formalize of the sociological theory ``organizational ecology''
(OE). OE is a collection of theory fragments, of which some are being
formalized in first-order logic and others in mathematics; (3)
to present heuristics and examples to sociologists who themselves want to
formalize. As a side issue, some prejudices against
formalization are debunked (in Ch.1).
Logical formalization proceeds iteratively along a number of steps,
from a discursive theory to its formal representation. At each step,
heuristics are presented (in Ch.1). Six steps are distinguished:
(1) study of the discursive theory, (2) dictionary of important
concepts, (3) core theory cast in informal premises and theorems, (4)
semantics of the core theory, (5) formalization of the core theory,
thereby applying an automated theorem-prover, and (6) evaluation of the
formalization. This tentative formalization method has much in common
with standard software engineering.
The target theory to be formalized is organizational ecology (OE). OE
is a theory about `Darwinian selection' in populations of social
organizations (Ch.2). A population consists of organizations of a
similar form. An example of such a form is automobile manufacturers.
Individual organizations are seen as inert. According to OE, rational
adaptation of organizations to their environment plays an
insignificant role.
As an exception to many sociological theories that are less clear,
OE's inertia fragment has 10 explicit assumptions and 5 explicit
theorems, in natural language. These sentences have been formalized in
first-order logic (see Ch.3). The theorems could not otherwise be derived.
The relative clarity of this theory fragment made it possible to
derive them after making small modifications to the assumptions.
Adding a distinction between organizations under reorganization, and
organizations in normal, reorganization-free conditions, has made the
inertia fragment consistent. A couple of new theorems have been
derived from the initial set of formalized sentences.
The niche fragment's conclusions should follow from a mathematical
model. In this model, however, two dimensions have been confused by
the authors. The model does not and can not support the
conclusions. Neither can the argument in natural language. In order to
repair the niche fragment, two strategies have been applied. (1)
Making a `reverse engineering' from the conclusions to find reasonable
assumptions in OE that support them. This has been achieved by a
formalization in first-order logic (Ch.4). (2) Repairing the
mathematical model, which then makes different predictions than
intended by the authors (Ch.5).
The density dependence fragment has been formalized by its author, as
a class of mathematical models. The theorems contain typos and give
room for counterexamples, as was found by other researchers.
Furthermore, the definition of competition among organizations is not
convincingly motivated (see Ch.6). With a new definition, the intended
theorems follow. Moreover, the new definition, plus a couple of
formalized assumptions from another theory fragment - resource
partitioning - and an empirical generalization, make it possible to
derive a number of new results that are sociologically relevant. These
new results incorporate and substantially extend the claims in
resource partitioning (Ch.6).
To conclude, in all formalized fragments of OE, all conclusions
required modifications of the theory to derive them. These
modifications consisted of making implicit information explicit,
elucidating and relating basic concepts, fine-tuning assumptions,
definitions and theorems, using assumptions from one fragment in
another fragment, and developing mathematical models. Along the way,
OE has been made more parsimonious, by discarding redundant concepts
and assumptions, and by deriving some assumptions as theorems. Some
fragments have been generalized, and other fragments turned out to be
more restricted than they appeared to be at first sight. Last but not
least, a number of new propositions has been derived.
By sociological standards, OE is an advanced theory. Logical flaws,
as discussed in this thesis, are certainly not characteristic for OE
in particular, and can be found in many sociological theories, often
in more severe forms. Sociologists appreciate logical criteria, but
rarely, if at all, do they apply these criteria to their own theories.
This thesis demonstrates that logical flaws can be found and repaired,
and that thereby new insights can be gained. For this purpose a number of
heuristics and examples have been provided. Other sociological
theories, possibly in worse logical shape than OE, would possibly
benefit even more from formalization.