Economic Development and the Death of the Free Market

Fix, Blair Article — Manuscript Version (Preprint) Economic Development and the Death of the Free Market Evolutionary and Institutional Economic Review Provided in Cooperation with: The Bichler & Nitzan Archives Suggested Citation: Fix, Blair (2021) : Economic Development and the Death of the Free Market, Evolutionary and Institutional Economic Review, ISSN 2188-2096, Springer, Berlin, Iss. Latest Articles, pp. --, https://doi.org/10.1007/s40844-021-00224-2 , https://bnarchives.yorku.ca/705/ This Version is available at: https://hdl.handle.net/10419/242969 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/4.0/ Economic Development and the Death of the Free Market Blair Fix August 20, 2021 Abstract According to neoclassical economics, the most efficient way to organize human activity is to use the free market. By stoking self interest, the theory claims, individuals can benefit society. This idea, however, conflicts with the evolutionary theory of multilevel selection, which proposes that rather than stoke individual self interest, successful groups must suppress it. Which theory better describes how human societies develop? I seek to answer this question by studying the opposite of the market: namely hierarchy. I find evidence that as human societies develop, they turn increasingly to hierarchical organization. Yet they do so, paradoxically, at the same time that the language of free markets becomes more common, and culture becomes more individualistic. This evidence, I argue, contradicts free-market theory, but only if we treat it as a scientific doctrine. If instead we treat free-market theory as an ideology, the pieces come together. Free-market thinking, I speculate, may stoke the formation of hierarchy by cloaking power in the language of ‘freedom’. Keywords: hierarchy; hierarchical power; free market; economic development; sociality; cultural evolution; multilevel selection; energy [email protected] Free-market theory in an evolutionary context 2 1 Free-market theory in an evolutionary context There is perhaps nothing more central to mainstream economics than the belief in free markets. The idea is seductively simple. Guided only by self-interest, individuals can act through the market to benefit the whole of society. This notion of the ‘invisible hand’ (Smith,1776) has become foundational to neoclassical economics. The theory proposes that in a perfectly competitive market, the autonomous actions of selfish individuals will lead to an outcome that is ‘Pareto optimum’ (Mas-Colell et al.,1995). In this situation, no person can be made better off without making at least one person worse off. The neoclassical theory of free markets is not without critics. Heterodox political economists have pointed out many flaws, mostly related to the theory’s unrealistic assumptions (Hunt,2011;Keen,2001;Keen and Standish,2006; Lee and Keen,2004;Means,1992;Mirowski,1991;Nitzan and Bichler,2009; Pullen,2009;Robinson,1962;Sraffa,1960;Veblen,1898). My goal here, however, is not to revisit this debate, but instead to broaden it. The neoclassical theory of free markets is, at its core, a theory of how human groups should organize. It postulates that groups can organize effectively using decentralized competition, and that the selfish actions of individuals can benefit the group. Yet this theory contradicts, in almost every detail, the modern evolutionary understanding of how social organisms function. According to the theory of multilevel selection, social organisms face a fundamental dilemma. Actions that are best for the group rarely maximize relative fitness of individuals within the group (Sober and Wilson,1999;Wilson and Gowdy,2015;Wilson and Sober,1989,1994;Wilson and Wilson,2007). This creates a tension between the self-interest of individuals and the interest of the group. To resolve this tension, social organisms find ways to suppress the selfinterest of individuals. How they do so is an open question. But evolutionary history reveals a common trend. As groups become larger and more complex, they tend to become more hierarchical (Sec. 2). In this evolutionary context, the theory of free markets is an outlier. It posits that, contrary to what we observe among other social organisms, humans need not suppress self-interest to organize in large groups. And we need not use hierarchical organization. We can build complex societies, the theory claims, using decentralized competition. Free-market theory in an evolutionary context 3 My goal here is to test this claim. I look for evidence that human societies remain decentralized as they industrialize (Sec. 3). I find little evidence that this is true. Instead, the data suggests that to industrialize, human societies turn to hierarchical organization. As energy use increases, governments tend to get larger and the relative number of managers tends to grow (Sec. 3.4). To explain this evidence, I develop a formal model of institutional hierarchy (Sec. 3.5). The model assumes that institutions are hierarchically organized, and that they grow larger as energy use increases. After validating this ‘energyhierarchy’ model, I use it to infer how the ‘degree of hierarchy’ (Sec. 3.2) within societies varies with economic development. The results are unambiguous: as societies consume more energy, they appear to become more hierarchical (Sec. 3.6). This growth of hierarchy seems to contradict the neoclassical theory of free markets. Societies do not (as the theory claims they should) use small-scale competition to develop. Still more puzzling, I find that the growth of hierarchy may be associated with the spread of free-market ideas (Sec. 4). Looking at the United States, I find that as government grew and the number of managers increased, free-market jargon became more popular (Sec. 4.1). Moreover, international evidence suggests that cultures that are more individualistic and more tolerant of deviant behavior are, at the same time, more hierarchical (Sec. 4.3). To make sense of this paradox, I speculate that free-market theory may actually stoke the growth of hierarchy. It does so, I propose, by treating firms (not individuals) as the unit of competition. This focus legitimizes the firm as an autonomous unit, while leaving the firm’s internal structure as a ‘black box’. By championing firm autonomy, free-market theory may legitimize the firm’s internal chain of command, thereby justifying the accumulation of power. If this idea is correct, it leads to a radical way of integrating free-market ideas with the theory of multilevel selection. The two schools may not be competing scientific hypotheses. Instead, neoclassical economics may be best treated as abelief system whose existence should be explained using the tools of cultural evolution. The great debate: hierarchy vs. the free market 4 2 The great debate: hierarchy vs. the free market Hierarchy is to free markets what light is to darkness: namely, the polar opposite. Free markets decentralize control. Hierarchies centralize it. Free markets promote autonomy. Hierarchies promote subservience. The two forms of organization, it seems, could not be more different. Economists have long recognized this fact. But rather than study the differences between hierarchy and the market, mainstream economists have opted instead to pass judgment. The dominant school in economics — neoclassical theory — claims that outcomes from perfectly competitive markets are ‘optimal’, whereas outcomes from centralized control are ‘inefficient’ (Acemoglu and Robinson,2001). I find this response problematic. It is much like if biologists deemed singlecelled organisms to be ‘optimal’, but deemed multicellular organisms ‘inefficient’. This conclusion misses the point. The two forms of life are simply different. What is interesting is not whether one form is ‘better’ than the other, but why the two forms of life exist, how they evolved, and where evolution is headed. I propose that by taking this wider evolutionary perspective, we can better understand the debate between free markets versus hierarchy. The question we should ask is — what is the direction of human social evolution? Towards less hierarchy? Or towards more of it? 2.1 Hierarchy in an evolutionary context Before we look at the direction of hierarchy among human societies, we should look first at the big picture. Let’s review the role of hierarchy in the evolution of life on Earth. Hierarchical structure is ubiquitous in the natural world — so much so that the social scientist Herbert Simon proposed that hierarchy is the ‘architecture of complexity’ (1991). The idea is that complex systems are built by merging simpler components, creating a hierarchy of sub-systems (Annila and Kuismanen,2009). Along with this hierarchy of structure, Simon argued, comes a hierarchy of control. Complex biological systems are generally not composed of autonomous subcomponents. Instead, as complexity grows, subcomponents The great debate: hierarchy vs. the free market 5 surrender autonomy to a centralized system of command and control. The evolution of life on Earth supports Simon’s idea that hierarchy is the ‘architecture of complexity’. Through a series of ‘major evolutionary transitions’, life has grown more complex (Smith and Szathmary,1997). Although different in form, each transition appears to obey the same principle: complex structure grows from the merger of simpler sub-units. Life began, we presume, when organic molecules assembled into larger entities. The basic structure that emerged — and remains to this day — is that of the prokaryotic cell. In the next major transition, eukaryotic cells evolved (we believe) from the merger of two prokaryotic cells — a bacterium and an archaeon (López-García et al.,2017;López-García and Moreira,1999;Margulis, 1981;Sagan,1967). The bacterium became the mitochondria of modern eukaryotes, while the archaeon became the cytoplasm and nucleus. In the next transition, eukaryotic cells evolved into multicellular organisms — a symbiosis that seems to have happened multiple times (Grosberg and Strathmann,2007). In the last major transition, solitary organisms evolved into ‘eusocial’ species that cooperate in large groups (Nowak et al.,2010;West et al.,2015;Wilson and Hölldobler,2005). With their large colonies and intricate caste structure, the social insects (ants, bees, termites) are the most conspicuous example of this eusociality. Some scientists believe that modern humans may be the latest addition to the eusocial club (Gowdy and Krall,2013,2014;Richerson and Boyd, 1998;Turchin,2013). Looking at these major transitions, we see that they obey the two principles of hierarchy. First, more complex structure is built from simpler components. Second, the growth of complexity seems to involve the centralization of control. Let’s begin with the nesting aspect of hierarchy, which we see everywhere in life. Eukaryotic cells, for instance, are built from simpler organelles (i.e. the nucleus and mitochondria). Multicellular organisms, in turn, are built from simpler cells. And eusocial colonies are built from individual organisms. Each new layer of complexity, it seems, is assembled by merging simpler components. This nested hierarchy, Herbert Simon proposes, occurs through a process of evolutionary problem solving (Herbert,1962). Structures evolve that solve specific problems. The cell, for instance, solves the problem of separating ‘living’ matter from ‘non-living’ matter. Once this problem is solved, the newly created The great debate: hierarchy vs. the free market 6 structure serves as the building block to solve new problems. Eukaryotic cells built on the structure of prokaryotes to solve a new problem — one of energetics. When bacterium evolved into eukaryotic mitochondria, they shed most of their DNA, freeing up more energy for protein synthesis (Lane,2011;Lane and Martin,2010). This free energy may be what allowed eukaryotes to grow more complex than their prokaryotic counterparts (Lane,2014,2015). In addition to hierarchy in the ‘nesting’ sense, the evolution of life also follows the principle of hierarchy in the sense of centralized control. Large, complex organisms are not composed of autonomous units. Instead, the growth of complexity seems to involve the gradual loss of autonomy among sub-units, and the growth of centralized control. The eukaryotic cell, for instance, is not composed of autonomous organelles. Instead, sub-units are governed by a ‘command and control center’ — the nucleus (Pennisi,2004). Similarly, multicellular animals have evolved centralized control in the form of the nervous system (Arendt et al., 2008). Eusocial insects have elaborate caste systems in which most individuals surrender their reproductive capacity to a single queen (although the queen does not, in turn, directly control workers) (O’Donnell,1998;Shimoji et al.,2014). Humans (who are possibly the latest eusocial species) also organize using hierarchy. Evidence suggests that as societies become more populous, they add new layers of administrative hierarchy (Turchin,2010;Turchin and Gavrilets,2009). The use of centralized control may arise for two (related) reasons. First, assembling a larger system from many smaller components requires coordination. Although decentralized coordination may be possible, it seems that organization within (and among) living things usually involves some degree of centralization. Second, there is the problem of the ‘self-interest’ of sub-units. The major evolutionary transitions happened by merging sub-units that were previously autonomous. According to the theory of multilevel selection, this merger is not possible unless the ‘self-interest’ of sub-units is suppressed (Okasha,2005;Wilson,1997;Wilson et al.,2008). That is because there is often an evolutionary conflict between the ‘interest’ of the group versus the ‘interest’ of individuals within the group (Sober and Wilson,1999;Wilson and Gowdy,2015;Wilson and Sober,1989,1994;Wilson and Wilson,2007).1 1Note that the words ‘interest’ and ‘self-interest’ do not indicate intent. Rather, they are a Darwinian metaphor for actions that increase relative ‘fitness’ (differential reproduction). Also, multilevel selection theory notes that the ‘suppression’ of self interest (when it occurs) is always partial and never complete. The great debate: hierarchy vs. the free market 7 To understand this conflict, recall that natural selection rewards differential reproduction — what biologists call ‘fitness’. In many scenarios, what is ‘fit’ for individuals is not ‘fit’ for the group. Take human warfare as an example. For the group (an army), it is best if all soldiers charge into battle cohesively. But for an individual within the group, the best strategy is to run away from the frontline (Fix,2019b). So here we have a conflict between levels of selection. By deserting, an individual soldier can reduce their chance of death (hence, increase their fitness). However, if too many soldiers desert, the army collapses (hence, the group’s fitness decreases). To succeed in battle, the group must therefore suppress the self-interest (relative fitness) of deserters.2 Multilevel vs. gene-centric selection The theory of multilevel selection argues that successful groups must suppress natural selection at lower levels of organization. Since this claim remains controversial, it is worth discussing problems with the alternative view. According to orthodox Darwinism, all aspects of evolution can be reduced to competition between genes. Popularized by Richard Dawkins (1976), the gene-centric argument is convincingly simple. If an organism outbreeds its competitors, the organism’s genes also win. It seems, therefore, that higher levels of selection are not needed to explain the evolution of organized groups. Instead, complex structure arises solely from the ‘self-interest’ of genes. While at first convincing, this argument makes a subtle philosophical mistake. It assumes that a successful reduction (breaking a system into parts) implies a successful resynthesis (using the parts to rebuild the system). Often, however, reduction is a one-way street. Given a complex system, we can break it into parts. But we cannot take the parts (alone) and rebuild the system. As an example of this asymmetry, consider human travel. If I board an airplane to Tokyo, we know that the atoms in my body did the same thing. To paraphrase Richard Feynman, we can state unequivocally that ‘everything that 2Armies often suppress the motive to desert by making it a capital crime. The certain threat of capital punishment makes the possible threat of battlefield death the lesser of two evils. The great debate: hierarchy vs. the free market 8 I do, my atoms do’.3Unfortunately, this reduction tells us nothing about why I went to Tokyo. It turns out that I had a job interview — something that is easy to understand by looking at a higher level of organization (the individual). But if we try to derive ‘job interviews’ from atomic physics, we will get nowhere. The same principle holds in evolution. We can always reduce evolution to competition among genes. Often, however, we cannot start with genes (alone) and resynthesize the evolution of higher-level structure. Interestingly, this asymmetry is evident in Richard Dawkin’s exposition of gene-centric theory. He notes that organisms are ‘vehicles’ for genes. But he does not explain how these vehicles came to exist. On that front, how did multicellular organisms evolve? From the gene’s eye view, we are faced with a paradox. Given atomistic competition between cells, one would expect that natural selection would suppress the evolution of multicellularity, and instead favor the evolution of cancer. That is because cancerous cells outreproduce normal cells. Cancer should therefore be favored by natural selection. So multicellularity (as we know it) should not exist. Since multicellular organisms do exist, this logic must have a flaw. To see it, however, we need to leave the gene’s eye view and instead look at higher levels of selection. When cells began to organize in groups, selection at the multicellular level began to override selection at the cell level. That created pressure to suppress cancer. The reason is simple: cancer tends to kill multicellular organisms. Hence at the organism level, cancer is selected against. This higher-level selection allowed mechanisms (such as the immune system) to evolve that suppress somatic (cell-level) evolution (Aktipis,2016). In this light, cancer is not a ‘disease’ so much as a failure of the organism — a “failure of multicellular systems to suppress somatic evolution” (Nedelcu,2020). To wrap up this discussion, orthodox Darwinism reduces evolution to the spread of genes — something that can always be done in hindsight. In contrast, multilevel selection theory tries to resynthesize complex systems by understanding the tug-of-war between different levels of selection. The key insight of multilevel selection theory is that high-level organization requires high-level selection that suppresses selection at lower levels. Among multicellular animals, 3Speaking about the importance of the atomic theory of matter as the basis of other fields, Richard Feynman remarked: “The most important hypothesis in all of biology, for example, is that everything that animals do, atoms do” (Feynman et al.,2013, emphasis in original). The growth of hierarchy with economic development 15 Returning to Figure 1, let’s calculate CRfor the red individual. This person has 6 subordinates within a network of N=31 people. Their local reaching centrality is therefore CR=6/30 =0.2. The ‘global reaching centrality’ (GRC) of the network is then defined as the sum of the differences between the local reaching centrality of each person and the maximum reaching centrality (Cmax R) of the network: GRC =Pn i=1Cmax R−CR(i) N−1(4) The GRC can range from 0 (no hierarchy) to 1 (absolute hierarchy). As an example, the network in Figure 1has a GRC =0.92, suggesting that it is quite hierarchical. 3.3 Measuring economic development Having defined how I measure hierarchy, I turn now to how I measure economic development. When economists speak of ‘development’, they usually mean the growth of ‘real GDP’. In this paper, however, I use a different metric. I measure economic development in terms of energy use per person. I have two reasons for using energy to measure development. First, there are many ‘aggregation problems’ inherent in the calculation of real GDP (Fix,2019a; Fix et al.,2019). These problems occur largely (but not exclusively) because real GDP is based on the unit of prices, which are unstable. This instability introduces ambiguity in the value of real GDP. Second, I use energy consumption to measure ‘economic development’ because I want a method that generalizes beyond human societies. If the growth of human hierarchy is an extension of a general evolutionary process, then we want a metric of ‘development’ that is universal. Since real GDP has no meaning outside the human economy, it is not helpful. Energy, however, is a ‘universal currency’ in the natural sciences (Chaisson,2005). The importance of energy stems from basic thermodynamics. It is the flow of energy that makes complex structure possible. Without energy flows, natural systems converge to equilibrium — a state where nothing happens on the macro scale. But when there is an energy gradient, macro-level structures tend The growth of hierarchy with economic development 16 to emerge — structures that dissipate energy more rapidly (Kondepudi and Prigogine,1998). A convection cell, driven by a temperature gradient within a fluid, is a simple example of such a ‘dissipative structure’. Living organisms are a more complex example, driven by the energy flow from the sun (Annila and Annila,2008; Boltzmann,2011;Chaisson,2002;Schrodinger,1992). The human economy is still more complex, but obeys the same principle. It is a dissipative structure driven by flows of energy (Georgescu-Roegen,1971;Giampietro et al.,2012). Because of its role in driving complex systems, I use energy consumption as a measure of economic development.5 3.4 Evidence for the growth of hierarchy My goal is ultimately to use my metrics of hierarchy (Sec. 3.2) to measure how the ‘degree of hierarchy’ varies with economic development. Unfortunately, the data needed to achieve this goal does not yet exist. As such, I will take an indirect route to measuring hierarchy. I will first review evidence suggesting that hierarchy varies with economic development. In the section that follows, I show that as societies use more energy, governments tend to get larger and the number of managers tends to increase. I then use this evidence to build a formal model of hierarchy (Sec. 3.5), which I use to infer how the ‘degree of hierarchy’ varies with economic development (Sec. 3.6). The size of government In neoclassical economics, government is a necessary evil. It is a form of hierarchical organization that must exist, but should not grow too large. Government must exist, Milton Friedman observes, to “do something that the market cannot do for itself, namely, to determine, arbitrate, and enforce the rules of the game” (1962). But while government is a prerequisite for markets, 5If one is skeptical of this choice, note that there is strong correlation between energy use and real GDP (Brown et al.,2011). As such, should we measure economic development using real GDP, the results in this paper would likely remain unchanged. The growth of hierarchy with economic development 17 it is also the market’s enemy. That is because, as Franklin Fisher notes, “the principal policy insight of economics [is]that a competitive price system produces desirable results and that government interference will generally lead to an inefficient allocation of resources” (1987). In neoclassical theory, then, government is a necessary form of hierarchy, but one that should remain as small as possible. It seems, however, that real-world societies do not listen to this ‘small government’ principle. Instead, economic development goes hand in hand with larger governments. Figure 2shows the evidence across (and within) countries. I plot here the employment share of government as it relates to energy use per capita. (‘Government’ is defined as the entire public sector. Each line in Fig. 2represents the path through time of a specific country.) While country-level trends vary, the overall pattern is clear. As energy use increases, governments tend to get larger. From a neoclassical standpoint, this result is unexpected. If markets are ‘efficient’, why does economic development involve government encroachment on the private sector? One possibility is that governments are not heeding economists’ advice, and that societies would be better off if government remained small. If so, then it is politics that are driving the growth of government. To investigate the role of politics, let us turn to Figure 3. Here I replot the data from Figure 2, but this time I differentiate between two types of countries: 1. Countries that have (or once had) a communist government 2. Countries that have never had a communist government It is easy to see the difference between the two types of countries. Those that have had communist regimes tend to have larger governments than those that have not.6 Given the intense 20th-century battle between capitalism and communism, it is unsurprising that politics affect the size of government. What is surpris- 6On a historical note, the data in Figure 3captures the collapse of the Soviet Union in action. The data begins in 1990, just when the Soviet Union disbanded. Former Soviet states like the Ukraine, Estonia, Moldova and Armenia begin (in 1990) with almost 100% government employment — a relic of their communist history. But over the next decade, governments in these countries shrank drastically, collapsing to levels similar to their non-communist counterparts. With this government collapse came a decline in energy use. The growth of hierarchy with economic development 18 ● ● ● ● ● ● ALB ARM AUT BGR BLR BRA CAN CHN CRI CYP DEU ECU ESP EST GBR GRC HKG HRV IRL JOR KAZ KGZ LTU LVA MDA MKD MNG MYS NOR PAN PHL PRY RUS SVK SVN SYR TTO TZA USA ZWE Smoothed Trend 1 2 5 10 20 50 100 5 10 20 50 100 200 500 1000 Energy use per capita (GJ) Government share of total employment (%) Figure 2: Government’s share of employment vs. energy use per capita I define ‘government’ here as employment in the entire public sector. Lines represent the path through time of individual countries (from 1990 to the present). Points represent countries with a single observation. Select countries are labeled with alpha-3 codes. The black line shows the trend across all countries, smoothed with a LOESS regression. For data sources, see Section 6. The growth of hierarchy with economic development 19 1 2 5 10 20 50 100 5 10 20 50 100 200 5001000 Energy use per capita (GJ) Gov. share of emp. (%) Smoothed Trends ALB ARM AZE BEN BGR BIH BLR CHN CUB CZE EST ETH GEO HRV HUN KAZ KGZ LTU LVA MDA MNG POL ROU RUS SVK SVN UKR VNM YEM 1 2 5 10 20 50 100 5 10 20 50 100 200 500 1000 Energy use per capita (GJ) Government share of total employment (%) Communist and Former Communist Countries Non−Communist Countries Figure 3: Government’s share of employment vs. energy use per capita by political spectrum I reproduce here the data in Fig. 2, but now distinguish between communist and noncommunist countries. ‘Communist countries’ are those that have (or once had) a communist regime. Lines represent the path through time of individual countries. Communist countries are labeled with alpha-3 codes. The inset panel shows the smoothed trends, calculated with a local polynomial regression. For data sources, see Section 6. The growth of hierarchy with economic development 20 ing, however, is that regardless of politics, governments tend to get larger as energy use increases. The inset panel in Figure 3shows this fact. Here I smooth the raw data (within each type of country) using a local polynomial regression. The results are interesting. In both communist and non-communist countries, governments tend to grow larger with energy use. So yes, politics do affect the size of government. But there is also a secular trend that is independent of political ideology — a fact that does not sit well with the neoclassical theory of free markets. As societies develop, government tends to grow larger. The number of managers Let’s turn now from the public sector to the whole economy. When describing the economy, neoclassical economists see competition between firms. But what about within firms? There, competition seems less salient. Once an employee has a position within a firm, they are expected to cooperate with their coworkers. And that usually involves taking and/or giving orders — a sign of hierarchy. If we were to grossly simplify the structure of a firm’s hierarchy, we might reduce it to two classes: those who take orders and those who give orders. The order givers are usually called managers. Their job is to command the activity of other people — a job that is unique to hierarchies. I propose, then, that the relative number of managers in a society provides a window into the degree of hierarchy. A society with no managers has no hierarchy. A society with many managers has lots of hierarchy. With this thinking in mind, Figure 4plots the evidence. Here, I look at how the relative number of managers (within countries) varies with energy use per capita. As with the size of government, I find that the number of managers tends to increase with economic development. This evidence seems to contradict the neoclassical theory of free markets. As societies develop, they turn increasingly to top-down management. It could be, though, that this trend is ultimately political. In that case, politics induce the growth of hierarchy, which then ‘distorts’ free-market efficiency. To investigate the role of politics, let us look at Figure 5. Here I replot the trend between the number of managers and energy use per capita. But this The growth of hierarchy with economic development 21 AGO ARG AZE BGD BLR BRN CHE CMR COM CZE DOM ERI ETH GBR GRC HND IDN IRN ITA KAZ KHM LBY LUX MEX MMR MYS NIC NPL PAN POL QAT SDN SLV SVN TGO TON TZA USA YEM ZWE Smoothed Trend 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 5 10 20 50 100 200 500 1000 Energy use per capita (GJ) Managers' share of total employment (%) Figure 4: Managers’ share of employment vs. energy use per capita I plot here the international trend between the number of managers in a country (as a share of total employment) and energy use per capita. Lines represent the path through time of individual countries (from 1990 to the present). I have labeled select countries with alpha-3 codes. The black line shows the trend across all countries, smoothed with a LOESS regression. For data sources, see Section 6. The growth of hierarchy with economic development 22 1 2 5 10 5 10 20 50 100 200 500 1000 Energy use per capita (GJ) Managers share of emp. (%) Smoothed Trends AGO ALB ARM AZE BEN BGR BIH BLR CHN COG CUB CZE EST ETH GEO HRV HUN KAZ KGZ KHM LTU LVA MDA MNE MNG MOZ POL PRK ROU RUS SRB SVK SVN TJK TKM UKR UZB VNM YEM 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 5 10 20 50 100 200 500 1000 Energy use per capita (GJ) Managers' share of total employment (%) Communist and Former Communist Countries Non−Communist Countries Figure 5: Managers’ share of employment vs. energy use per capita by political spectrum I reproduce here the data in Fig. 4, but now distinguish between communist and noncommunist countries. ‘Communist countries’ are those that have (or once had) a communist regime. Lines represent the path through time of individual countries. Communist countries are labeled with alpha-3 codes. The inset panel shows the smoothed trends, calculated with a local polynomial regression. For data sources, see Section 6. The growth of hierarchy with economic development 23 time I differentiate between communist/non-communist politics. The results are telling. Unlike with the size of government, politics seem to have no effect on the number of managers. The inset panel in Figure 5emphasizes this nondistinction. Here I show the smoothed trend across countries, differentiated by political regime. There is virtually no difference between communist and noncommunist countries. So whatever is driving the growth of managers, it is not overtly political. 3.5 An energy-hierarchy model As societies consume more energy, governments tend to get larger and the number of managers increases. This evidence hints that economic development involves the growth of hierarchy. To gain more insight into these changes, I now develop a formal model of how social hierarchy varies with energy consumption (my measure of economic development). The model is based on two assumptions: 1. Human institutions are hierarchically organized 2. These institutions tend to grow larger as energy use increases I first formalize these assumptions into a numerical model of how social hierarchy changes with energy consumption. Then I use the model to predict how the size of government and the number of managers should grow with energy use. The Simon-Lydall model of hierarchy A half century ago, Herbert Simon (1957) and Harold Lydall (1959) independently developed a model of the hierarchical structure of firms. In this model, hierarchies have a fixed ‘span of control’, meaning all superiors control the same number of subordinates. I will call this the ‘Simon-Lydall’ model of hierarchy’. When Simon and Lydall first proposed the model, little was known about how firms were actually structured. Today, we know more about firm hierarchies, and we can say that Simon and Lydall were on the right track. While the span of control is not actually constant in real-world firms, assuming it is constant is The growth of hierarchy with economic development 24 Figure 6: The ‘Simon-Lydall’ model of hierarchy I show here two examples of the Simon-Lydall model of hierarchy. The model assumes that the span of control (the number of direct subordinates controlled by each superior) is constant within a given hierarchy. The span then determines the hierarchy’s ‘shape’. A large span creates a ‘flat’ hierarchy — one with relatively few hierarchical ranks (left). A small span creates a ‘steep’ hierarchy that has many ranks (right). a reasonable simplification.7 To get a sense for the Simon-Lydall model of hierarchy, let’s look at Figure 6. Here I visualize two modeled hierarchies, each with 31 members. The ‘shape’ of the hierarchy is determined by the span of control (which is fixed within the hierarchy). When the span is large (left), the hierarchy is ‘flat’. When the span is small (right), the hierarchy is ‘steep’. The Simon-Lydall model has 3 equations. (For their derivation, see Section 6.) Consider a hierarchy with span of control sthat has NTmembers. The number of ranks (n) in the hierarchy is: n=log[1+NT(s−1)] log(s)(5) Here bc denotes rounding down to the nearest integer. Next, we define the number of people in the bottom hierarchical rank as: 7For case studies of firm hierarchy, see Audas et al.,2004;Baker et al.,1993;Dohmen et al., 2004;Grund,2005;Lima,2000;Morais and Kakabadse,2014;Treble et al.,2001. For aggregate studies of firm hierarchy, see Ariga et al.,1992;Bell and Van Reenen,2012;Eriksson,1999; Heyman,2005;Leonard,1990;Main et al.,1993;Mueller et al.,2016;Rajan and Wulf,2006; Tao and Chen,2009. For a summary of these studies, see the Appendices in Fix,2018,2019c.) The growth of hierarchy with economic development 31 Table 2: Free parameters in the energy-hierarchy model Parameter Symbol Role Power-law exponent α Determines the size distribution of institutions (Eq. 9) Span of control sDetermines the ‘shape’ of each hierarchy (Eqs. 5–7) Number of ‘firms’ in government nAffects government share of employment (Eq. 11) Table 3: Observables predicted by the energy-hierarchy model Observable Description/method Energy use per capita Modeled as a function of mean institution size (Eq. 10) Managers’ share of employment Employment share of hierarchical ranks 3 and greater (Eq. 8) Government share of employment Employment share of top ninstitutions (Eq. 11) Concentration of hierarchical power (CHP) A measure of the degree of hierarchy — the Gini index of the hierarchical-power distribution (Eqs. 1–2) Global reaching centrality (GRC) A measure of the degree of hierarchy (Eqs. 3–4) The growth of hierarchy with economic development 32 Figure 9: The modeled growth of government with energy use This figure compares empirical and modeled trends between the government share of employment and energy use per person. Each colored dot represents an iteration of the energy-hierarchy model. Color indicates the number of ‘firms’ in modeled government (the model’s sole parameter). Black points represent real-world data, with select countries labeled with alpha-3 codes. The inset panel shows the smoothed trends for the empirical data and the best-fit model. For sources and methods, see Section 6. The growth of hierarchy with economic development 33 Figure 10: The modeled growth of management with energy use This figure compares empirical and modeled trends between the management share of employment and energy use per person. Each colored point represents an iteration of the energy-hierarchy model, with color indicating the span of control. Black points represent real-world data, with select countries labeled with alpha-3 codes. The inset panel shows the smoothed trends for the empirical data and the best-fit model. For sources and methods, see Section 6. The growth of hierarchy with economic development 34 million). The best-fit model closely predicts the growth of government during initial stages of development. For large energy use, however, the model diverges from the real-world trend. This may be because the model is wrong. Or it could be that political preferences (for government) change with energy use. I leave it for future research to better understand this discrepancy. Let’s switch now to how the relative number of managers varies with energy use (Fig. 10). The energy-hierarchy model predicts that as societies use more energy, they should accumulate managers. The trend, however, is non-linear. In the limit of high energy use, the managers’ share of employment plateaus. This is a characteristic feature of the energy-hierarchy model. As societies accumulate hierarchy, the relative number of managers approaches an asymptote of 1/s2 (where sis the span of control). This limit corresponds to a society organized in a single hierarchy. In the energy-hierarchy model, the managers’ share of employment is affected by the span of control. A smaller span of control produces ‘steeper’ hierarchies with more managers. A larger span of control produces ‘flatter’ hierarchies with fewer managers. Since the span is a free parameter, it is important to verify that fitted values are consistent with empirical data. In Figure 10, virtually all of the empirical data can be fitted with a span of control between 2 ≤s≤7. I show in Fig. 14 (Sec. 6) that this range is consistent with the existing studies of firm hierarchy. The inset panel in Figure 10 compares the best-fit model (which has a span of control of s=3.5) to the smoothed trend in real-world data. (For fitting methods, see Sec. 6.) The fit is quite close, departing only at extremes of energy use, where the empirical sample size is small. To summarize, the energy-hierarchy model predicts (with reasonable accuracy) the growth of government and managers’ employment with energy use. 3.6 Inferring how the degree of hierarchy varies with energy use Having validated the energy-hierarchy model, I now use it to infer how the ‘degree of hierarchy’ varies with energy use. The inference procedure is as follows. For each empirical observation (a country in a given year), I find the model iteration that best reproduces the Discussion: Rethinking free-market theory 35 observed level of energy use and managers’ share of employment. (For fitting methods, see Sec. 6.) I then take this model iteration, and input its simulated data into the two metrics of hierarchy — the CHP and the GRC (Sec. 3.2). The result is an inferred relation between energy use and the ‘degree of hierarchy’ within each country. The model-based inferences are shown in Figure 11. Here I plot the inferred trend between energy use per capita and the ‘degree of hierarchy’ within each country. The main panel measures hierarchy using the concentration of hierarchical power (CHP), while the inset panel uses global reaching centrality (GRC). Both metrics indicate that the degree of hierarchy tends to increase with energy use. Because this is a model-based inference, we should treat it with appropriate uncertainty. Still, the results are provocative and not at all what neoclassical economics predicts. If these estimates are correct, they suggest that societies develop by replacing small-scale competition with large-scale hierarchy. In other words, economic development involves the gradual death of the free market. 4 Discussion: Rethinking free-market theory To interpret the inferred growth of hierarchy with economic development, let’s return to the competing perspectives of multilevel selection theory and the neoclassical theory of free markets. Which theory is consistent with the evidence? I will start with multilevel selection theory, which argues that successful groups must suppress the self-interest of individuals. The theory does not stipulate how this suppression occurs, but evidence from evolutionary biology suggests that hierarchy is a common solution. The idea is that the control structure of hierarchy suppresses the fitness-seeking behavior of subunits, thus increasing the fitness of the group. Perhaps something similar happens in human societies as they develop? If so, we can treat economic development as a type of group selection in which larger (hierarchical) groups beat out smaller (less-hierarchical) groups. How and why this happens is an open question (Bichler and Nitzan,2020). Still, the (inferred) fact that economic development involves the growth of hierarchy is consistent with the theory of multi-level selection. 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capita (GJ) Inferred concentration of hierarchical power (Gini index) Figure 11: The inferred degree of hierarchy vs. energy use This figure uses the energy-hierarchy model to infer how the degree of hierarchy varies with energy use per capita in real-world societies. The main panel measures hierarchy using the concentration of hierarchical power. Colored lines indicate the path through time of a country. Select countries are labeled with alpha-3 codes. The black line shows the smoothed trend, calculated with a local polynomial regression. The inset panel measures hierarchy using global reaching centrality. For sources and methods, see Section 6. Discussion: Rethinking free-market theory 37 The same evidence, however, is difficult to interpret using the neoclassical theory of free markets. According to this theory, small-scale competition is the optimal form of social organization. The idea is that by stoking self-interest, free markets maximize the welfare of society. But if this is true, why do societies turn to hierarchy to develop? We can rescue neoclassical theory by supposing that societies would be better off if they reduced hierarchy. The problem is that this scenario requires a remarkable degree of collusion. Most developed countries seem to organize in a way that neoclassical theory says is ‘non-optimal’. But why would they do that? It could be that politics ‘distort’ the free-market. Yet we saw in Figure 5that political regimes have no effect on the relative number of managers. That leaves free-market theory in an uncomfortable situation. For unknown reasons, countries of the world are pursuing a path to development that neoclassical theory says is ‘inefficient’. We can always appeal to ‘distortions’ to rescue neoclassical theory. But this is what philosophers of science call an auxiliary hypothesis — an idea that is used solely to rescue a theory from falsification (Lakatos,1976;Popper,1959). Worse still, the concept of ‘distortion’ is almost impossible to test. What evidence would show that developed economies are not distorted? According to neoclassical theory, finding a perfectly competitive market would suffice. But that leads to tortuous logic. Either free-market theory is both true and consistent with the evidence, in which case we find perfect competition. Or free-market theory is still true but inconsistent with the evidence, in which case we infer that the economy is distorted. Either way, the theory wins. A less tortuous alternative is to conclude that the evidence is inconsistent with neoclassical theory. Rather than develop via the free market, societies turn to hierarchy. 4.1 The two sides of a social-science theory Were we studying non-human animals, we could leave the discussion at that. The evidence favors multilevel selection theory over the neoclassical theory of free markets. The problem, though, is that we are studying humans — an animal whose behavior is shaped not just by instinct, by also by beliefs. Discussion: Rethinking free-market theory 38 This entangling of beliefs and behavior means that doing social science is more complicated than doing natural science. When we evaluate a social-science theory, not only must we study its factual merit, we must also study the theory’s effect on behavior. Importantly, the two components of the theory need not be consistent. Put simply, a social-scientific theory can be factually incorrect and yet ideologically potent. Take, as an example, Karl Marx’s theory of capitalism (Marx, 1867). Many critics think the theory has gaping flaws (Keen,2001;Nitzan and Bichler,2009;Robinson,1962;Samuelson,1971). And yet virtually no one disputes Marx’s impact on history. Without Marx’s ideas, there may have been no communist revolutions. So regardless of its scientific merit, Marx’s theory had a strong influence on human behavior. When social-science theories are obscure, of course, we need not worry about their ideological effect. But when a theory becomes popular — as in the case of Marxism — we must pay attention to its effect on behavior. In the case of Marxism, the effect was straightforward. Marx claimed that the injustices of capitalism could be solved only by communist revolution (Marx and Engels,1967). Inspired by Marx’s ideas, revolutionaries like Lenin and Mao did precisely what Marx proposed — they led communist revolutions to overthrow capitalism. When it comes to free-market theory, however, the ideological component is less easily understood. On the face of it, free-market theory advocates atomistic competition. Yet the theory became popular (during the 20th century) at precisely the time when small-scale competition was being replaced by large-scale hierarchy. Figure 12 shows this trend in the United States. Here I plot the relative word frequency (in American written English) of four free-market terms: ‘small business’, ‘free market’, ‘competitive market’ and ‘perfect competition’. I take this word frequency as a measure of the prevalence of free-market ideas. Against this word frequency, I plot our two proxies for hierarchy: the government share of employment and the management share of employment. Over the last century, it seems that at the same time that hierarchy grew, free-market jargon became more common. How should we interpret this trend? One possibility is that the spread of free-market language was a reaction to the growth of hierarchy. After witnessing Discussion: Rethinking free-market theory 39 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1890 1890 1890 1890 2008 2008 2008 2008 0.2 0.5 1 2 5 10 20 50 100 200 500 2 5 10 20 Government share of US employment (%) Word frequency (occurrence per million words) ● ● ● ● 'Small Business' 'Free Market' 'Competitive Market' 'Perfect Competition' A. Frequency of free−market terminology vs. government employment ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1860 1860 1860 1880 2008 2008 2008 2008 0.2 0.5 1 2 5 10 20 50 100 200 500 1 2 5 10 Management share of US employment (%) Word frequency (occurrence per million words) ● ● ● ● 'Small Business' 'Free Market' 'Competitive Market' 'Perfect Competition' B. Frequency of free−market terminology vs. management employment Figure 12: Frequency of free-market terminology in American English vs. trends in hierarchy This figure shows the relative frequency in American English of four free-market terms. Panel A compares this word frequency to the government share of US employment. Panel B compares it to the management share of employment. From 1860–2000, the time interval is decadal. From 2000 onward, the time interval is annual. For sources and methods, see Section 6. Discussion: Rethinking free-market theory 40 the growth of government and large firms, free-market proponents reacted by writing more frequently about the merits of small-scale competition. But despite the increasing prevalence of their ideas, free-market thinkers were unable to stop the growth of government and large firms. If this interpretation is correct, then free-market ideas do have an atomistic effect. It is just that this thinking failed to catch hold. There is, however, another interpretation of the evidence. When we separate a theory into a scientific and ideological component, there is no reason that the two sides must connect. In other words, the ideological effect of a theory (its effect on human behavior) can be different from the theory’s factual claims. Free-market theory argues that small-scale competition is the most effective form of social organization. But when put into action, perhaps free-market ideas do the opposite of what they claim. Might free-market thinking foster the growth of hierarchy? The evidence in Figure 12 suggests that this possibility is worth exploring. 4.2 Belief systems as ‘massive fictions’ According to multilevel selection theory, social animals face a fundamental dilemma. To be successful, social groups must suppress the selfish behavior of individuals. The problem is that within the group, selfish behavior is advantageous. David Sloan Wilson and E.O. Wilson call this dilemma the ‘fundamental problem of social life’ (Wilson and Wilson,2007). The existence of sociality, they argue, is predicated on solving this problem. Humans, it seems, have developed a way to motivate altruism that is unique. We rely, at least in part, on the power of beliefs. Successful groups adopt belief systems that motivate group cohesion (Turchin,2016). Importantly, these beliefs need not be scientifically true. As long as they motivate pro-social actions, beliefs can be factually inaccurate — sometimes wildly so. For this reason, David Sloan Wilson argues that belief systems are often ‘massively fictional’: Groups governed by belief systems that internalize social control can be much more successful than groups that must rely on external forms of social control. For all of these (and probably other) reasons, we can expect many belief systems to be massively fictional in their portrayal of the world. Sources and methods 47 6 Sources and methods All data and code for this paper are available at the Open Science Framework: https://osf.io/gbvnh/. Code for the hierarchy model is available at github: https://github.com/blairfix/energy_hierarchy_mod. R versions of the hierarchy-model functions are available at https://github.com/blairfix/hmod. 6.1 Data sources Communist/non-communist status. I classify a country as ‘communist’ if it has, or once had, a regime that claimed to be Marxist–Leninist. See the supplementary materials for a detailed list of sources. Cultural tightness Data for cultural ‘tightness’ comes from Gelfand et al. (2020) and can be downloaded from the Open Science Framework: https: //osf.io/pc4ef/ Gelfand’s data was first reported in a 2010 paper. I assume that this was the date of data gathering. I match Gelfand’s data (in Fig. 13) with the average of the managers’ share of employment (within each country) over the period 1990-2010. Energy use per capita. Data for energy use per capita comes from the World Bank, series EG.USE.PCAP.KG.OE. To these values I add an estimate for energy consumed through food (2000 kcal per day). Firm size. Data for firm size comes from the Global Entrepreneurship Monitor (GEM), series ‘omnowjob’. To calculate firm size, I merge all data over the years 2001-2014. Because the GEM data over-represents large firms, I use only firms with 1000 or fewer employees. For method details, see the Appendix in (Fix, 2017). Power-law exponents for firm-size distributions are estimated using the R PoweRlaw package (Gillespie,2014). Free-market word frequency. Word frequency of free-market jargon is from the Google Ngram corpus for American English. Sources and methods 48 Government employment. Data for government employment comes from ILOSTAT series GOV_LVL_PSE (all public sector employees). I divide this series by the size of the labor force reported in World Bank series SL.TLF.TOTL.IN. Data for US government employment share (Fig. 12A) comes from: • 1890 to 1928: Historical Statistics of the United States, Table Ba 470-477 • 1929 to present: Bureau of Economic Analysis series 6.8A-D (total persons engaged in production) Individualism Index. Data for the ‘individualism index’ comes from Hofstede et al. (2010). In addition to measures for specific countries, Hofstede reports measures for the following regions: (1) Arab countries; (2) East Africa; and (3) West Africa. Based on Hofstede’s notes, I disaggregate these regions as follows: • Arab countries =Egypt, Iraq, Kuwait, Lebanon, Libya, Saudi Arabia, United Arab Emirates • East Africa =Ethiopia, Kenya, Tanzania, Zambia • West Africa =Ghana, Niger, Sierra Leone, Togo I assign each country Hofstede’s metric for the region. According to Hofstede, most of his data was gathered in the late 1960s and early 1970s (the dataset does not specify years). However, data for the management share of employment does not begin until 1990. To match Hofstede’s data with the management data (Fig. 13), I average the latter (within each country) over the period 1990-2010. Managers’ employment. International data for the management share of employment is from ILOSTAT Table TEM_OCU, series EMPoc1P. Data for the United States (Fig. 12B) comes from: • 1860 to 1990: Historical Statistics of the United States, Table Ba 1033- 1046 Sources and methods 49 • 1990 to present: Bureau of Labor Statistics Current Population Survey series LNU02032453 (management employment) divided by Bureau of Economic Analysis series 6.8D (total persons engaged in production) 6.2 Hierarchy-model equations The hierarchy model used in this paper is based on equations derived independently by Herbert Simon (1957) and Harold Lydall (1959). In this model, hierarchies have a constant span of control. We assume that there is one person in the top rank. The total membership in the hierarchy is then given by the following geometric series: NT=1+s+s2+...+sn−1(12) Here nis the number of ranks, sis the span of control, and NTis the total membership. Summing this geometric series gives: NT=1−sn 1−s(13) In my model of hierarchy, the input is the hierarchy size NTand the span of control s. To model the hierarchy, we must first estimate the number of hierarchical ranks n. To do this, we solve Eq. 13 for n: n=log[1+NT(s−1)] log(s)(14) Here bc denotes rounding down to the nearest integer. Next we need to calculate N1— the employment in the bottom hierarchical rank. To do this, we rewrite Eq. 12, this time building the hierarchy from the bottom up. Starting with the bottom rank N1, membership in each consecutive rank declines by a factor of 1/s. That means the hierarchy’s total membership (NT) is given by the following geometric series: NT=N11+1 s+1 s2+...+1 sn−1(15) Sources and methods 50 Summing this series gives: NT=N11−1/sn 1−1/s(16) Solving for N1gives: N1=NT1−1/s 1−1/sn(17) Given N1, membership in each hierarchical rank his: Nh=N1 sh−1(18) Sometimes rounding errors cause total employment of the modeled hierarchy to depart slightly from the size of the original inputted institutions. When this happens I add/subtract members from the bottom rank to correct the error. The model is implemented numerically in C++, using the Armadillo linear algebra library (Sanderson and Curtin,2016). 6.3 Modeling Managers I model managers as all individuals in and above rank 3. In a firm with nhierarchical levels, the number of managers is equivalent to the membership in a hierarchy with n−2 levels. Using Eq. 13, we find that the number of managers Mis: M=1−sn−2 1−s(19) By dividing Eq. 19 by Eq. 13, we can find the management share of employment (M/NT) in the firm: M NT =1−sn−2 1−sn(20) Sources and methods 51 6.4 Finding the best-fit energy-hierarchy model To find the model parameters that best fit the trends in empirical data (inset Fig. 9and Fig. 10), I first group the model results in log-spaced bins by energy use. (This smooths the stochastic noise that is built into the model.) In each bin, I calculate the average energy use and the average of the statistic of interest (either the management share of employment or the government share of employment). I then interpolate linearly between these averaged points, creating a function that relates energy use to the government/management share of employment. I use this numerical function to compute the error between the model and the raw empirical data. The error function is: ε= (logSr−logSm)2(21) Here Sris the real-world statistic (either government or management share of employment) and Smis the model statistic. The best-fit model minimizes this error. 6.5 Fitting the energy-hierarchy model to individual countries To infer the degree of hierarchy within countries (Fig. 11), I first fit the energyhierarchy model to data for individual countries. For each country-year observation, I chose the model iteration that minimizes the following error function: ε= (logEr−logEm)2+(logMr−logMm)2(22) Here Erand Emare energy use per capita in the real-world country and the model, respectively. Mrand Mmare the management share of employment in the real-world country and model, respectively. Because the energy-hierarchy model is stochastic, I choose the 10 best-fit iterations, and average the measured degree of hierarchy across these models. I then infer that the degree of hierarchy found in the real-world country is the same as found in the model. Sources and methods 52 6.6 Calculating the degree of hierarchy in the energy-hierarchy model To calculate the degree of hierarchy in the energy-hierarchy model, I assume that power relations exist only within institutions. In other words, there are no power relations between institutions. It is worth noting that this assumption is not realistic. Studies of corporate ownership suggest that between firms, there is an interlocking network of power (Fichtner et al.,2017;Glattfelder and Battiston,2009;Vitali et al.,2011). I ignore this complexity here for two reasons. First, it is beyond the scope of the energy-hierarchy model to simulate the network of power between firms. Second, this network is ignored by the neoclassical theory of free markets. In the neoclassical model, firms interact only by buying and selling, so there are no power relations between them. In my energy-hierarchy model, then, I give neoclassical theory the benefit of the doubt. I assume that power-relations exist only within firms, not between them. Were we to add power relations between firms, the inferred degree of hierarchy would increase. One more caveat. The energy-hierarchy model does not directly simulate the chain of command within hierarchies. Instead, it simulates aggregate hierarchical structure — the number of people in each rank. To calculate the number of subordinates controlled by an individual, I assign each modeled person the average number of subordinates below their rank, defined as: Ns(h) = Ph−1 1Ni Nh (23) Here his the hierarchical rank, Nis the membership in each rank, and Nsis the average number of subordinates. I then input the distribution of Nsinto the formulas for the concentration of hierarchical power (Eqs. 1–2) and global reaching centrality (Eqs. 3–4). Sources and methods 53 6.7 Differences between CHP and GRC My two metrics of hierarchy — the concentration of hierarchical power (CHP) and global reaching centrality (GRC) — both agree that the ‘least hierarchical’ network is one in which nobody has subordinates. But the two metrics disagree about what type of network is the ‘most hierarchical’. The GRC assumes that the most hierarchical network is one in which all people are directly under the command of a single person. This is a society consisting of a single hierarchical firm, in which the CEO directly commands everyone else. Whether such a society is indeed the ‘most hierarchical’ is a matter of definition. In an engineering scenario (where the GRC is derived), it makes sense to define the most hierarchical network as one in which a single node directly controls all other nodes. But in human networks, this idea makes less sense. The problem is that in practice, as humans accumulate more direct subordinates, their ability to actually command any single person diminishes. An army general may easily command 10 officers. But can the same general manage 10,000 soldiers directly? Unlikely. As humans try to directly manage more people, their subordinates become more autonomous. We have a word for this tendency. As the span of control increases, we say that the hierarchy becomes ‘flatter’. To many people, a flatter organization is ‘less hierarchical’. But the GRC assumes the reverse is true. That is why my other metric — the ‘concentration of hierarchical power’ (CHP) — is useful. In contrast to the GRC, the CHP views a steeper organization as more hierarchical. Because the CRC and CHP disagree about what constitutes the ‘most hierarchical network’, they could give conflicting results for the trend in social hierarchy. One metric might increase while the other decreases. Fortunately, I do not find such a conflict (Fig. 11). The reason the two metrics agree is because their differing definitions matter only when societies approach a single hierarchy. Since no real-world society is close to this limit, the CHP and GRC show a consistent trend. Sources and methods 54 6.8 Verifying the energy-hierarchy model’s span of control In the energy-hierarchy model, the span of control is a free parameter that varies between model iterations. One way to test the model is to see if the fitted values for the span of control are consistent with observations from real-world firms. To conduct this test, I use Eq. 22 to find the model iteration that best fits the observed relation (within countries) between energy use and the management share of employment. I then take the fitted values for the span of control and compare them to real-world studies of hierarchy within firms. Figure 14 shows the results. The model’s estimates for the span of control have a range that is consistent with the real-world observations. A t-test (p=0.77) and ks-test (p= 0.08) both indicate that the two distributions are statistically indistinguishable at the 5% level. Funding This research was funded in part by John Medcalf, Mike Tench, Robin Shannon, Brent Gulanowski, Tom Ross, Steve Keen, Hilliard MacBeth, Joe Clarkson, Grace and Garry Fix, Pierre, Norbert Hornstein, and Ed Zimmer. Conflicts of Interest The author has no conflicts of interest to declare that are relevant to the content of this article. 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