Modelling War
| Published date | 01 November 1999 |
| Author | Ian Bellany |
| DOI | 10.1177/0022343399036006008 |
| Date | 01 November 1999 |
| Subject Matter | Articles |
Modelling War*
IAN BELLANY
Department of Politics and International Relations, Lancaster University
A simple, general mathematical model for modern war is presented. The form of the model is
Lanchester but its derivation owes approximately equal amounts to classical operational research and to
later ideas associated with theoretical ecology – especially the concept of ‘carrying capacity’. Solutions
to the equations corresponding to stalemated, steady-state outcomes in theatre are concentrated on,
with empirical justification derived from the unduly neglected databased work of Voevodsky.
Prolongation and stalemate are seen as the default state of modern war. War termination is discussed
as a consequence of ‘mutually (but not equally) hurting stalemate’. Examples are given of how, in
certain circumstances, stalemate may be pre-empted in theatre by striking at non-battlefield targets and
light is cast on the late 20th-century strategic trend towards conducting war preponderantly from the
air.
Introduction
The principal objective of this article is to
present a simple, general, mathematical
model of war. It defines war as a contest of
long or short duration involving armed
clashes in one or more theatres between
organized units which, in turn, rest upon the
support (logistical, manpower) of a home
base or bases, and which may be in theatre or
outside, with the same home bases and their
lines of linkage to forces in theatre also liable
to armed attack.
The model is used to explain the long
duration of a number of major wars in the
past century and a half, and consequently is
applicable to the question of war termin-
ation.1If the tendency of war is towards
prolongation and ‘mutually hurting stale-
mate’, explanations of war settlement that
take no account of war weariness are
unlikely to be broadly applicable.2And, if
stalemate is the natural condition of war, the
question arises as to why it should be
resorted to, if success (at best) lies a long
way in the future.
The model is also used to explain the
shifts in military strategy in the present
century towards waging war off the battle-
field as well as on it, as well as to shed light
on the culmination of these shifts within the
past decade (Gulf War 1990–91, Kosovo
War 1999) for off-battlefield use of force to
become the principal or even sole element in
the conduct of the war.
* The author acknowledges the support of the British
Academy. He is also grateful for helpful comments made
on an earlier draft of this article by his fellow participants
at the Vienna ECPR/ISA conference in September 1998,
as well as by referees from JPR.
1For a survey of this question, which as a topic is probably
not as neglected as its author claims, see Massoud (1996).
729
journal of
peace
R
ESEARCH
© 1999 Journal of Peace Research,
vol. 36, no. 6, 1999, pp. 729–739
Sage Publications (London, Thousand
Oaks, CA and New Delhi)
[0022-3433(199911)36:6; 729–739; 010657]
2For explanations that do take into account considerations
of ‘mutually hurting stalemate’, see Mason & Flett (1996).
For the origin of the idea, such as it is, that ‘a ripe moment
for the settlement [of a war] occurs when a mutually
hurting stalemate develops’, see Zartman (1985: 9).
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