To understand the importance of the choice of model representation for a model, I present an example of distortion of geographical representation. 
We all more or less in mind a geographical representation of the world, whatever the form of projection used (Mercator, Lambert ...) with a size and shape for each country.

But what happens if he "distorts" the geographical representation by replacing the weight of square kilometers of other elements (change of ownership of an item of geographical pattern: the surface)?

It reaches a different perception of reality. Differ according to the new property is chosen.

Let the example developed by the newspaper: Telegraph.

It represents the World Atlas in this form:

What is shown here is the importance of countries by number of tourists visiting them. The representative keeps more or less the shape of the country and stretches or reduces it according to the amount of tourists visiting it annually.
Besides the fact that it is always nice to see a map of the world where France is the largest country , And that Europe has the heaviest weight, we see that the Central Africa region almost completely disappears from the map.

We have thus, in my opinion, this type of representation, an immediate and total points will pass this important model.

Another example, if there is now a map representative of the number of miles traveled in the year

by aircraft of each country, we see very clearly the return of the weight of the USA, the rise of Japan and even smaller for Africa ....

The same type of representation, ATLAS can be used to transmit information quality and quantity in a few seconds to display if you change its main component, which is the area of each country into another element.

This type of representation may be particularly suited to Marketing Models, Military and decision.

Another example:

Taken from Telegeography.com, although I can not find the exact reference, here is the same representation model used on another topic: Postal rates.

Reminder:

A model can be represented by several "models" of different representation. They may switch from one model representation to another without restriction. There is no better model of representation itself. Each model is best expressed in some performances. And often this perception of better representation is simply due to cultural habits or usage or technical constraints.

Iconography:

The TELEGRAPH for the link.

Those who have really worked 

• The Atlas of the Real World: Mapping the Way We Live by Daniel Dorling, Mark Newman and Anna Barford
• Published by Thames & Hudson (£ 29.95)
• Telegeography.com

Sources:

• The Atlas of the Real World: Mapping the Way We Live by Daniel Dorling, Mark Newman and Anna Barford
• Published by Thames & Hudson (£ 29.95)

• Telegeography.com

• Metanormes.