Following the criticism of the pillar models, a triangle model has been developed to illustrate the dimensions of sustainable development with their links. The basic form of the triangle is shown in Figure 6. Measures and their effects can be allocated to either a point on the lines of the triangle, thus affecting only two dimensions, or any point within the triangle if all three dimensions are affected.
Figure 6: Basic sustainability triangle
(own depiction, model is used widely in scientific and popular publications in similar form)
The triangle is also endorsed by the german network for sustainable economics on the premise that the triangle is embedded within the boundary of the ecological limits (Netzwerk Nachhaltige Okonomie 2012a). The german government recently also turned away from the three pillar model and towards a triangle model that includes the absolute limit that the network for sustainable economics asks for.
Figure 7: Sustainability triangle with absolute ecological limits
(SRU 2011, p. 5)
The sustainability triangle suggested by the German Council of Environmental Advisors (cf. Figure 7) is similar to the triangle used by the german government. It does stress the absolute ecological limit more clearly though and shows that sustainable development can only be realized within those absolute limits.
Another version of a Sustainability Triangle has been developed by VON Hauff and Kleine who favor a “magical” integrative triangle of sustainable development in an attempt to see the dimensions of sustainable development not as juxtaposing, but as an integrative concept that aims to harmonize the key aspects of sustainable development (cf. Figure 8) (Kleine 2009).
Figure 8: Integrative sustainability triangle
(Hauff, Kleine 2009)
The magical in the title of Kleine’s depiction can be considered analogous to the so called magical square of German economic policy based on the German Stability Law that postulates in §1 that the federal government and the states have to choose their political measures to ensure stability of the level of prices, high employment, a balance in foreign trade and steady and adequate economic growth (StabG). These four requirements are often depicted as corners of a square and then called the magical square because the legally mandatory concurrence all four dimensions is impossible to reach due to incongruity of the aims. While in some circumstances there is congruity, there is incongruity in other situations.
-  cf., e.g., OKUN’s law that states that economic growth leads to a high level of employment ormore exactly, a 2% increase of GDP will lead to a 1% decrease of the unemployment rate.OKUN’s law has been disputed and has been called a rule of thumb rather than a law as it is anempirical observation and not based on a theory.
-  cf., e.g., the Phillips curve that states that a decrease of the unemployment rate is correlated withan increased rate of inflation. This observation has been proved empirically for short term relations between the factors, but has been disputed for long-run predictions as both factors are influenced by many other parameters.