Minimalist Modeling Methodology

by Loren Cobb, PhD.

Aetheling Consultants


The "minimalist" modeling methodology is a set of concepts that has evolved during 15 years of collaborative work with Dr. A. E. R. Woodcock on military, social, and ecological modeling, since 1980. This method consists of five fundamental ideas:

  1. Structural simplicity
  2. Behavioral simplicity
  3. Mathematical elegance
  4. Statistical analysis
  5. Organic units

The purpose of minimalist modeling is to allow the analyst to focus attention and detail on one or two vital areas of interest, in which great modeling detail is used, while painting in all other areas of behavior and structure in broad strokes that are based on generic universal principles that apply to virtually all organizations, hierarchical or otherwise. The behavioral picture so created is then enhanced with statistical methods, so that in the end only the essential answer is given, and all other aspects are averaged out. In this way minimalist modeling clears away much of the fog of detail and data that plague traditional modeling.

Structural Simplicity

In common with social and biological structures that exist throughout Nature, military organizations and structures have a remarkable degree of physical and temporal coherence, and seek to maintain that coherence even in the face of assault from predators. Models of social and military structures ought to reflect this dynamic as a fundamental self-organizing principle. When this is done properly, the shapes and structures of hierarchies emerge from the dynamic itself, just as the hexagonal shape of a beehive emerges from the efforts of bees to pack honey into a rigid structure made with walls of soft wax. The alternative, to prescribe each and every component of an organization, places an enormous burden on the modeler. To take a military example, massive databases must be created and maintained that specify the exact properties of every military unit, from fire team to army group, from artillery battery to naval squadron to recon team. The volume of data is huge, its reliability questionable, and the construction effort is enormous. The minimalist method instead uses simple principles that apply universally. Continuing the military example, every military unit in the field, regardless of size or composition, deploys subunits to protect its flanks and rear areas. For another example, every modern organization attempts to limit the number of immediate subordinates that a supervisor has, so as to gain supervisory efficiency. When supervisory efficiency degrades due to accretion of subordinates, then a new layer of command is inserted to restore the balance. This dynamic principle applies to every level of all hierarchical organizations, so they only need be encoded once for all levels.

Behavioral Simplicity

Like structural simplicity, behavioral simplicity is a general modeling principle. Rather than encode the decision-making behavior of each level of an organizational hierarchy as a separate algorithm, minimalist modeling attempts to use general principles of decision-making that apply to all levels and sizes of organizations. There are many business decisions, for example, that scale to any size of corporation: merge, acquire, restructure, reorganize. Similarly, military maneuvers also scale to any size of unit: frontal attack, flank attack, envelopment, ambush, retreat.

Mathematical Elegance

At the core of all good modeling lies mathematical elegance. Whether the mathematics comes from deep but simple structural principles like symmetry and information, or from modern theories of the statistical behavior of nonlinear dynamical systems, the proper application of mathematics at critical points in a modeling exercise leads to stunning increments in efficiency and power. Wherever possible and appropriate, minimalist modeling attempts to use this natural weapon for slicing through apparent complexity and the chaos of details. As a simple but realistic example, when a component of a large war simulation involves a number of battles in which attrition, rather than manuever, is the primary factor at work, then these battles can be reduced to an application of stochastic Lanchester equations without doing violence to the overall validity of the larger simulation. The gain in speed is huge, the loss in detail is trivial.

Statistical Analysis

Minimalist modeling takes advantage of a phenomenon of Nature known as "the Law of Large Numbers." Unlike deterministic modeling, stochastic modeling does not claim the ability to foretell the outcome of specific situations. Instead, repeated simulations are used along with well known statistical methods to show trends in the outcome based on variable input data.

In deterministic modeling, a complete set of initial conditions is given, along with specific rules defining all actions to be taken when the model is run. While there are many good models of this variety, there are also many poor ones. In addition, a good deterministic model can be rendered useless by incomplete information regarding initial conditions for a simulation, or by a lack of understanding as to how variables interact. Given good and complete data about the initial conditions, and a true understanding of how variables interact, these models may very well be able to predict the outcome of specific scenarios.

Minimalist modeling makes no such claims. Under no conditions, without regard to the validity of the input conditions or truth of the situational knowledge provided by the user, can a minimalist model predict the specific outcome of an individual situation. What it can do is to provide the user with insights as to how varying the conditions will effect the outcome of battles. These effects remain unknown until the output of repeated simulations is massaged by statistical software.

The validity of the minutiae in simulation scenarios is of secondary importance. Over a large number of runs, while experimentally varying critical parameters, statistical truths will make themselves known. So, in preparing a simulation, the analyst should portray the initial conditions as accurately as possible, but not become overly concerned if some conditions are not known.

It must be said that the ability of the analyst to glean useful information from these simulations is in direct proportion to the analyst's understanding of statistical analysis. Graphic presentations made by a simulation should be used as a tool for testing the face validity of a simulation scenario. Output from the simulation should be treated as statistical data and reported as such. Whereas a determinist might say, "If you build your embassy there, a car-bomb will destroy it," minimalists will only say, "The survival probablity of embassy personnel improves in proportion to the square of the distance of the embassy to the street."

Organic Units

Organizations are composed of a myriad parts. Minimalist modeling does not attempt to describe an organization in terms of these parts, because to do so leads directly into database madness. Instead, the minimalist description of a organization is functional. Here are two examples of how this is done. The first example is governmental, the second military.

In the governmental example, instead of listing the individual agencies that exist at each level of government, with their individual organization charts, budgets, and legal responsibilities, we rely on a graph of each government's ability to regulate the transactions of all people and institutions within its boundaries, as a function of certain key variables of interest, e.g. land area, size population, size of economy, travel and communication speed, and technological development. Each level of government is treated as an organic entity, without regard for the specific details of methods and means by which its goals are attained. Since these functions have very few parameters, the entire description compresses down into an efficient format. The evolution and pathologies of government can be modeled and studied in this minimalist way without exhaustive (and largely useless) descriptions of a myriad individual agencies.

In the military example, instead of listing the range, accuracy, and number of each type of weapon that a unit has, we rely on a single graph of the unit's firepower as a function of range. Instead of listing the range, accuracy, and number of each type of sensor that a unit has, we rely on a graph of detection probability as a function of distance. Since each function has only one or two parameters, the entire description compresses down into an extremely efficient format. Compared to standard military unit descriptions, the compression factor is on the order of two, three, or even four orders of magnitude.

This functional approach works well because real military units are constructed as organic, functional entities. Insofar as humanly possible, weapons and sensors are selected to cover a range of capabilities, so that the unit is never left defenseless or blind any specific range. The specific weapon or sensor is not important, but the coverage of all weapons and sensors is. Minimalist modeling describes the coverage, not its detailed implementation with individual weapons and sensors.

Copyright © 1996 by Loren Cobb. All rights reserved. This document may be quoted or reprinted for any purpose.

Last revised: March 2001.