Big is Fragile


by Atif Ansar1, Bent Flyvbjerg, Alexander Budzier, Daniel Lunn

What Is Big?

Whether something is big seems obvious enough. Yet the construct of big and the related ideas of large, large-scale, major, mega, or huge etc. prove deceptively elusive when subjected to scrutiny. A literature review of definitions of big and related words reveals a non-exhaustive list of multiple dimensions of the construct of big such as:

  • Physical proportions measured in height, length, mass, weight, area, or volume;
  • Inputs required to build and run the thing measured in terms of quantities (and quality) of land, labor, or equipment required;
  • Financial outlay measured in upfront capital expenditure (Flyvbjerg, 2014), recurrent operational expenditure, or end-of-life costs (Clark & Wrigley, 1995, 1997);
  • Supply measured in the units of output that the thing can produce (Samuelson, 1948; Stigler, 1958) or the multiplicity of outputs (Chandler, 1990);
  • Demand being served measured not only in terms of units of demand but also the quality, speed, and functionality (Weinstock & Goodenough, 2006);
  • Temporality measured in time it takes to build the thing or the length of its life span (Gomez-Ibanez, 2003);
  • Spatial fixity or immobility and the cost of moving an asset—big tends to “spatial fixity” (Ansar, 2012);
  • Complexity measured, for example, with a focus on the technical aspects of the asset or its delivery (Simon, 1962); or with a focus on the social and political complexity (Liu et al., 2007);

Impact measured in number of people who might benefit or be harmed; number of functions enabled or disabled; or the magnitude and pace of change the thing can cause in its environment.

The relationships among these multiple dimensions—and even the indicators within each dimension—are seldom straightforward. For instance, it is often taken for granted that in order to reduce the amount of time required to complete a venture, e.g. a software IT project, a manager would need to mobilize more programmers, which will also increase the capital expenditure of the venture (for a discussion see Atkinson, 1999; Williams, 2005).

Bigness entails multiple and unpredictable interactions across the dimensions we have listed with which theories of big—such as the notion of economies of scale—have not meaningfully engaged. The risk of big is reflected in these interactions, which we turn to now.

What Is Fragility?

Taleb (2012) proposes the construct of fragility, and its antonym antifragile, to capture the type of randomness and risk we talk about here. Taleb’s inspiration for the concept came from his observation that there is no random event that can benefit a porcelain cup resting on a table yet a wide range of uncertain events – such as earthquakes or human clumsiness – that can pose harm (Taleb 2012, p. 268). Fragile things, like the porcelain cup, are vulnerable to members of the “disorder family” such as randomness, uncertainty, volatility, variability, disturbance, or entropy—terms we use interchangeably belowi to explore the fragility of big capital investments.

Fragility as a construct has found increasing use in diverse fields such as construction (Shinozuka et al., 2000; Choi et al., 2004); human bones (Seref- Ferlengez et al., 2015); global financial and banking crises (Davis et al., 1995; Taleb et al., 2012; Klemkosky, 2013; Calomiris & Haber, 2014); mathematics (Taleb & Douady, 2013); ecology and ecosystems (Nilsson & Grelsson, 1995; Sole & Montoya, 2001); interdependent networks (Callaway et al., 2000; Buldyrev et al., 2010; Vespignani, 2010; Parshani et al., 2011; Gao et al., 2012;

Morris & Barthelemy, 2013); material sciences, e.g. in assessing properties of glass forming liquids (Scopigno et al., 2001; Mauro et al, 2014; Martinez- Garcia et al., 2015); conflict-prone countries (USAID, 2005; Ziaja, 2012); democratic political systems (Mitchell, 1995; Issacharoff, 2007); and even personal ethics (Nussbaum, 2001). Despite its diverse uses, fragility has certain common meanings across these fields. Taking our point of departure in Taleb’s work, because this is the most comprehensive, and supplementing this with other sources, we first distill a general definition of fragility. Second, we use this to develop a more specific concept called “investment fragility,” which we apply to big capital investments.

Fragility describes, “how [a] system suffers” when it encounters disorder (Taleb and Douady, 2012, p. 1677, italics in the original). The outcome of fragility is typically an irreversible loss of functionality. Our preliminary proposition, which we’ll refine below, is as follows:

Proposition 1. Fragility is typically irreversible. Once broken the fragile cannot be readily restored to its original function.

Fragility as a material property is signified by a material’s breaking point (Scopigno et al., 2003; Martinez-Garcia et al., 2015). Mauro et al. (2014) call this unique intrinsic fragility threshold a “structural signature”. Buldyrev et al. (2010) conducted similar structural analysis on networks such as electricity grids (also see Vespignani, 2010). They find that intrinsic structural features of networks—such as number of nodes; whether a network is isolated or interdependent; and number of interconnections with other networks—can help determine the “critical threshold” at which the various networks break downii. As a more generalizable proposition:

Proposition 2. A thing (material, system, process, or network) has a unique “fragility threshold”, which careful structural analysis and experimentation can reveal, at which it will break down under influence from stressor(s). All other things being equal, the lower the preset threshold the greater the fragility.

An assumed benefit of big is that the fragility threshold increases with size. However, Taleb (2012, pp. 278-80) argues that larger organisms such as elephants tend to have a lower fragility threshold as a proportion of their size than smaller organisms. Thus, for example, it might take a stone twice the body weight of a cat to cause a fatal outcome. But a boulder only half the bodyweight of an elephant might suffice for its fragility threshold. The source of this disproportionally greater fragility of bigger systems is to be found in Anderson’s (XXXX) notion of “more is different.” As a more generalizable proposition, we advance:


Proposition 3. As a system grows bigger, the relative size of a stressor required to break it will decline disproportionately.

As suggested before another source of fragility is the interconnectedness of systems. In other words “inherited fragility.” Inherited fragility helps to map out the diffusion of harm in the event of fragility in a corner of an interconnected system of systems. As a generalizable proposition:

Proposition 4. In an interdependent system of systems with no redundancy the threshold of fragility for the whole system of systems is the same as the threshold of the system’s weakest component.

Systems with a low fragility threshold and low function recoverability (Quadrant 4) require a great deal of cushioning to protect them from breaking.

below suggests a composite way to map different things on the spectrum of greater to lesser fragility. This constitutes two dimensions: First, on the vertical axis is how easily something breaks, i.e. a high or low preset “fragility threshold.” Second, on the horizontal axis is how easily can the broken thing be recovered to its self-same functional state once the fragility threshold is crossed, i.e. high or low “function recoverability.”

However, not all things are as unlucky as Humpty the egg. A multi-use electric fuse also breaks easily but can also be easily restored to perform its sacrificial function (Quadrant 3). In contrast, a diamond has a high fragility threshold but once broken the damage is irreversible (Quadrant 2). Finally, fungi—and many systems in nature (Taleb, 2012)—do not break easily and easily recover (Quadrant 1). Incidentally, as our discussion on scalability in the next section shows, systems in Quadrant 1 share many properties with highly scalable systemsiii.


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