Quantifying the UnquantifiedQuantifying the Unquantified

Jim Burns

How to IncludeHow to Include

Customer Satisfaction Market Attractiveness Quality of Life Consumer Confidence Faculty Morale Material Standard of Living IN YOUR MODEL

Often these are UnquantifiedOften these are Unquantified

Begin by defining what one unit of any of these would be

Consider Quality of Life One unit of Quality of Life might be the level

of quality enjoyed in the year 1999 Define this to be a Parameter called Quality

of Life Normal Quality of Life Normal = QLN = 1

What sort of things affect What sort of things affect Quality of Life on a global Quality of Life on a global scale?scale?

Pollution Material Standard of Living Food Population density

For each of these, construct a For each of these, construct a ratioratio

Pollution ratio = Pollution normal/Pollution Here pollution normal is the amount of pollution experienced in the year

1999, in pollution units MSL ratio = MSL/MSL normal

Here, MSL normal is the amount of MSL experienced in the year 1999, in MSL units

Food ratio = Food/ Food normal Again, Food normal is the amount of food available in the year 1999, in

Food units Crowding ratio = Population density normal/Population density

again, Population density normal is the population density in the year 1999, say

What about Units?What about Units?

For some of our soft variables the units are undefined We have to define them For example, one unit of pollution could be defined

as “the average aggregate level of pollution experienced by a “typical” earthling in the year 1999”

One unit of Quality of Life could be “the average aggregate level of quality of life experienced by a ‘typical’ earthling in the year 1999.”

Under Normal Conditions,Under Normal Conditions,

What is true about all of these ratios? What is the dimensionality of these ratios?

We can now construct our We can now construct our Quality of Life FormulaQuality of Life Formula

Quality of Life = QLN * Pollution ratio * MSL ratio * Food ratio * Crowding ratio

Is this formula dimensionally consistent? Under normal conditions, Quality of Life = ?? If pollution gets higher than normal, what happens to

quality of life, assuming everything else remains the same?

If food is higher than normal, what happens to quality of life, assuming everything else is the same?

The VENSIM RepresentationThe VENSIM Representation

Quality of Life

Quality of Life Normal

Pollution Ratio

Food Ratio

MSL Ratio

Crowding ratio

What if we felt that Material What if we felt that Material Standard of Living affected Standard of Living affected birth and death rates?birth and death rates?

BR = BRN * POPULATION *MSL ratio MSL ratio = MSL / MSL Normal Does this change the dimensionality of the

BR formula? Under “normal” conditions what effect does

Material Standard of Living have on BR, birth rate?

Similarly for death rate

We could do something We could do something similar for food...similar for food...

BR = BRN * POPULATION * MSL ratio * Food ratio

And for pollution…. BR = BRN * POPULATION * MSL ratio *

Food ratio * Pollution Ratio And for crowding…. BR = BRN * POPULATION * MSL ratio *

Food ratio * Pollution Ratio * Crowding Ratio

Suppose that we believe that Suppose that we believe that the effect on births of an the effect on births of an increase in food is less than increase in food is less than the ratio would suggestthe ratio would suggest

We can amplify or attenuate the effect of non-normal conditions with the use of TABLE FUNCTIONS

We call these multipliers They are also dimensionless

Quality of Life

Quality of Life Normal

Pollution Ratio

Food Ratio

MSL Ratio

Crowding ratio

Pollution Multiplier

Food Multiplier

MSL Multiplier

Crowding Multiplier

Ratios vs. MultipliersRatios vs. Multipliers

The new formula is:The new formula is:

Quality of Life = QLN * quality pollution multiplier * quality material multiplier * quality food multiplier * quality crowding multiplier

It must be accompanied by the following equations quality pollution multiplier = TABLE(pollution ratio) quality material multiplier = TABLE(MSL ratio) quality food multiplier = TABLE(Food ratio) quality crowding multiplier = TABLE(Crowding ratio)

Similarly for Birth rateSimilarly for Birth rate

BR = BRN * POPULATION * births material multiplier * births food multiplier * births pollution multiplier * births crowding multiplier

It must be accompanied by the following equations births pollution multiplier = TABLE(pollution ratio) births material multiplier = TABLE(MSL ratio) births food multiplier = TABLE(Food ratio) births crowding multiplier = TABLE(Crowding ratio)