Reasoning And Decision Making

© Milton N. Bradley 2010



Chapter 3 - The Nature Of Problems, Problem Statements, Concept Mapping, Information Gathering



Definitions:

Problem = Recognition that the current situation (the initial state) is in some significant way different from and less desirable than a goal (the final/desired state).

Problem Context = The overall situation in which the Problem exists.

Problem Statement => Spells out:
The Nature of Problems And Their Solutions

In common with most other situations of interest, it is readily possible to conceive of the continuity of problems as being parsed in a number of different ways, each of which has special and often unique value in achieving understanding of the extremely complex underlying reality. For that reason, the reader should understand that the arbitrary and quite simple dichotomy proposed next is just one of many possible ways of characterizing that reality.

For our present purposes, we shall consider that all problems can be divided into two complementary but mutually exclusive classes:
  1. Problems with exact solutions.
  2. Problems for which exact solutions are unknown, infeasible, or impossible.

Problems with exact solutions occur largely in disciplines like mathematics and the sciences, but also can sometimes be found in the common simpler interfaces of ordinary existence. Although achieving a correct solution to the more difficult and advanced of this class of problem often requires prodigious amounts of training and the application of much hard work, ultimately, if you have those qualifications and make the requisite effort, the desired answer will be forthcoming. What happens is that you use your expertise to correctly evaluate the situation, recognize which techniques are relevant, apply due diligence in collecting and validating the requisite data, apply the appropriate technique and “turn the calculation crank”, and out pops the desired, unambiguous answer!

Problems that lack exact solutions include most of the non-trivial ones which we routinely encounter in everyday personal life, business, government, and social organizations. A major difficulty in solving these problems lies in the fact that in many cases the relevant facts are not completely known but must be estimated (at best) or “guesstimated” (at worst), and that precise solution techniques not only are often not known, but sometimes may not even exist.

Another major difficulty that we will encounter, both in this book and in applying its technologies to real world problems, is that the methods that we present and apply herein are designed to minimize the uncertainties (to the extent that’s feasible), and that we are then going to turn that same “calculation crank” to generate an answer. But although that “answer” may then have the same superficial appearance of precision as that obtained from calculation in problems with exact solutions, it’s really anything but! So falling into the mental trap of missing or ignoring that essential difference is something that the successful problem solver must studiously avoid!

In the search for real world problem solutions it’s also essential to understand and conform to the following “Guiding Principles”, most of which will not be found in any standard text. Failure to understand and be guided by them will almost necessarily result in an inability to ever develop correct solutions to an entire class of important real life problems, so they may be ignored only at your own peril! Except as otherwise noted, all are my own formulations.

Guiding Principles

 
“The validity and worth of an idea is independent of:
  1. Who proposed it.
  2. How long it has been believed.
  3. The number and importance of those who subscribe to it.
  4. The vehemence with which they support their belief.”

 



 
“It ain’t what people don’t know that hurts ‘em,
it’s what they know that ain’t so!”

 

Charles Farrar Browne, AKA Artemus Ward, 4/23/1834 - 3/6/1867, American Philosopher and Humorist



 
“ Facts have no agenda.”

 



 
“Truth is an Uncompromising Taskmaster.”

 



 
“Except by accident, the correct solution to a problem can only result
from accurate facts, objective analysis and Reasoning”

 



 
“The simplest explanation in accord with the facts is best.”

 

"Occam's Razor", an accepted principle of Logic.


 
“A simplistic solution to a complex problem is almost invariably wrong.”

 



 
The reliability of the answer
cannot exceed
the reliability of the input data.

 


So you must be careful in your search for problem solutions, always keeping in mind the well known caveat of computers, that:


 
GARBAGE IN, GARBAGE OUT!

 



General Problem Solution Guidelines
Underlying Problem Solution Principles


To perform a Pareto Analysis:
Applying the Pareto Principle in conjunction with each of the techniques that follow will enable greatly limiting the number of variables to be included in the analysis without significantly decreasing the validity of the decisions reached.

Principles of Cost/Benefit Analysis
Solution Search Guidelines:

Desirable Solution Development Technique Characteristics
These techniques are not mutually exclusive, and are often used sequentially or even simultaneously, to examine the various problem aspects from several different viewpoints, all with the same objective of maximizing the chances that the best possible Problem Solution will be reached.

Developing A Problem Statement

The necessary first and often most critical step in arriving at an adequate Problem Solution is developing an appropriate Problem Statement, and this is sometimes so difficult to accomplish that it may not be possible to be certain that it’s been accomplished until you’ve actually succeeded in solving the Problem!

Creating a Problem Statement involves 8 essential steps:


Now let’s investigate each of these steps in detail.


In this book we shall restrict our attention to Concept Mapping and Venn Diagrams, which are the simplest and most generally applicable of the many alternative methods for performing this essential task. Concept Mapping requires no special preparation, so we shall discuss it first. Applying Venn Diagrams requires some knowledge of Formal Symbolic Logic, and that was the main reason that subject was introduced in the previous chapter.

Concept Mapping

This is a technique designed to make it easier to understand the interplay between ideas, by creating a visual picture of their relationships and interconnections. It allows you to better:
Caution!

A Concept Map is not a goal in itself! Rather it’s a tool whose use in accurately representing and understanding the current situation can enable you to produce a better Problem Statement, and ultimately a maximally useful Problem Solution!

The Advantages of Concept Mapping
The Structural Elements of a Concept Map
The Four Major Categories of Concept Map:

The Hierarchy Concept Map presents related information in descending order of importance.

In the following example, this powerful method of organizing data is applied to the Concept mapping process itself!



A standard Organization Chart like that of The US Department of Agriculture Headquarters Office shown below is another prime example of a Hierarchy Concept Map..



The Flowchart Concept Map organizes information to show the progression of the physical and/or temporal flow of materials and/or information. Originally developed to describe industrial processes, this technique soon proved to be applicable to almost any activity because of the simplicity and universality of its basic descriptors:



Adding a Diamond to this basic 5 symbol set to represent the asking of a question (usually requiring a “yes” or “no” answer) to determine which alternative path to follow, it is possible to accurately and concisely describe almost any realistic situation. As an example, shown next is a simple Flow Chart I created to describe the process of deciding whether or not to repair or replace a broken TV set.



The "Spider" Concept Map is organized by placing the central theme or unifying factor in the center of the map, then surrounding it with outwardly radiating sub-themes and supporting details.



The Systems Concept Map organizes information with focus on inputs and outputs. In this formulation the information is usually presented in hierarchical fashion, and in that limited sense it’s similar to the Hierarchy and Organization Charts. The simplified examples below describing the automotive manufacturing process were prepared by me especially for this book.





Steps In Constructing A Concept Map

The following are the steps in building a concept map manually. (A number of commercially available software programs exist for this task, and the steps are essentially the same in each case.)


Revising/Refining Concept Maps

Good maps are like good writing; and are usually the product of several drafts and revisions. The best possible result will usually require differing perspectives and insights, so showing your map to knowledgeable others like teachers, classmates, coworkers and friends to get feedback is an excellent strategy.

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