Quantifying Value with Effective Complexity

Introduction

Every coherent economic system must be underpinned by a theory of value. A theory of value axiomatically impacts what is or is not considered valuable, helps to facilitate the exchange of disparate goods, shapes the formulation of public policies and affects the income distribution under that system. Historical theories of value include the labour theory of value, the marginal theory of value, the Sraffian theory of value, etc. (Dobb, 1975; Taylor, 2001).

In recent decades, economic inequality has reached extreme levels in the United States and a number of other advanced economies (Dabla-Norris et al., 2015), prompting prominent thinkers to question the efficacy of current market systems, underlying rules of engagement and conventional theories of value (Deaton, 2019; Stiglitz, 2015; Yunus, 2017). In particular, the presumed correspondence between compensation and value creation (under capitalism) has been called into question, with the implication being that prices and value regularly diverge from one another (Graeber & Cerutti, 2018).

Some implementations of capitalism more closely resemble a system wherein money is ransomed rather than earned. Here, the word ‘ransomed’ is not intended to insinuate violence or unethical behaviour rather it is used to imply that money is only meted out when one’s value can be reasonably withheld until an exchange is completed. This property is key. Value that cannot be systematically withheld has no protections and is unlikely to receive just recompense. (Note that an exchange may occur at a single point in time or spread out over an extended timeframe.)

Accordingly, a number of constructs have been devised and deployed to protect specific forms of value, and render them ‘ransomable’. These protections are both de jure and de facto, arising from laws, regulations, corporate policies and societal norms. Some such protections are easy to observe (e.g., copyrights, patents and property rights). However, at the scale necessitated by the vast, entangled economy, these protections and their supporting structures fan out into a ubiquitous web of rules, both visible and invisible. We call these and other such rules the ‘market rules of engagement’. The importance of these exogenous rules in determining prices has been highlighted by Douglass North and other economists (North, 1991, 1992).

Designing and enforcing protections that render value appropriately ‘ransomable’ is a nonobvious process. However, it is a critical process. Corporations and individuals alike live and die by the specifics of these protections. In some cases, the value produced is well protected. In other cases, presumably, only a fraction of the value produced can be ransomed if any at all.

At present, the protections that arise from laws, regulations, corporate policies and societal norms are moulded by democracy, public opinion, special interests and other such forces. All of these forces are subject to biases (both conscious and unconscious) and their intuitions and desires can fail to reflect a deeper reality (even when operating under the best of intentions). Often, these biases are rooted in historical precedents, which may no longer align with contemporary reality. Consequently, market prices and values are expected to diverge from one another habitually. This divergence is counterproductive to the greater economic goal of maximising value (which is distinct from maximising monetary wealth). At issue is not simply the question of whether the correlations between market prices and inherent values are strong or weak, the problem is far deeper. The problem is that at present, we lack a suitable quantitative means to even assess whether these correlations are strong or weak. We lack a robust alternative metric of value to benchmark against.

Utilising Frameworks

One goal in the pursuit of quantifying value is to design a fairer economic system. At first glance, ‘fairness’ represents a large and nebulous concept that is often ill-constrained and ill-posed. However, serious attacks have been mounted to open up fronts and make rigorous and meaningful progress on the question of fairness, most notably the work of John Rawls and his ‘veil of ignorance’ (Rawls, 1971). In his theory, Rawls asks us to imagine going back to a time before we were born, before we had any inkling of our own unique circumstances, talents, susceptibilities or preferences. Only from this vantage point, behind a veil of ignorance, Rawls argues, could we reasonably come to a consensus about fair rules of engagement for the world at large. This framework allows us to move towards more objectively decidable resolutions on the seemingly subjective question of ‘fairness’.

In general, a goal of science is to reparameterise seemingly subjective questions into more objectively addressable subcomponents by introducing new frameworks (e.g., veil of ignorance). An insightful framework can break down seemingly subjective phenomena into smaller, more objectively decidable questions that nonetheless shed light on the larger phenomenon when logically reassembled. Here, we define an ‘objective question’ as one whose answer is perspective (or mind) independent and a ‘subjective question’ as one whose answer is perspective (or mind) dependent. These two extremes form opposite ends of a spectrum, with likely no firm dividing line, only gradations between the two. As such, we posit that the best way to measure the objectivity of a specific question is to measure the strength of the consensus among individuals competently providing answers. For these purposes, competence depends on the scope of information available to the individual and his or her ability to comprehend and reason from that information. (In some cases, this competence may only exist in theory.) As an example, a question regarding the outcome of a specific coin flip is highly objective because once all of the information regarding the outcome has been conveyed to and understood by the observers, there exists a strong consensus on the outcome (regardless of prior uncertainty while the coin was in the air). Even if the relevant information is never collected or disseminated, the question is still highly objective due to the hypothetical possibility that the information could have been collected and a strong consensus achieved.

In order to illustrate how science makes use of insightful frameworks to break down seemingly subjective phenomena into more objectively decidable subquestions, we consider the following hypothetical scenario. Some ancient peoples might have believed that the coolness of an object to the touch was a purely subjective sensation. Today, however, we have rigorous means of objectively quantifying the temperature and thermal conductivity of an object in order to better address this question. First, the sensory experience of warmth or coolness had to be mapped to concepts of temperature and thermal conductivity (defined within frameworks of thermodynamics and heat transfer). Further quantifying these concepts required, for instance, mapping units of temperature to the expansion of mercury or mapping units of time to the motion of a pendulum. These physical observations are more easily measured and agreed upon with a simple visual inspection. In this manner, scientific frameworks have rendered questions regarding the coolness of an object to the touch more objective. Science produces frameworks that can reparameterise large and slippery questions into more objectively agreed-upon fragments (e.g., thermometer readings from mercury levels).

Following suit, we propose a framework to render the seemingly subjective concept of economic value more objective by analysing value through the lens of complexity theory. By definition, economics studies the distribution, allocation, consumption and production of wealth. However, wealth takes many disparate forms, which are difficult to reconcile and sum without deferring to market prices. Unfortunately, market prices cannot measure a good’s inherent value. Market prices can only claim to correlate with inherent value in the context of a number of untested assumptions. One such assumption is a belief in the validity and efficacy of the market rules of engagement. As previously discussed, faulty rules of engagement will cause a divergence between market prices and inherent value. Accordingly, conventional economics tools cannot be used to robustly evaluate the market rules of engagement, the rules’ abilities to accurately assess value or even the overall growth of value in a society. Any attempt to evaluate the market rules of engagement by tracking only market prices is inherently circular. Conventional economics tools can only produce naïve assessments of the growth of a society’s economic value. For example, conventional tools may be able to measure an increase in the quantity of a certain class of goods but could not accurately assess the quality or other important properties of those goods (Benedikt & Oden, 2011).

Reparameterising Value

On examination, we divide value along three dimensions: Progress, Qualia and Truth. The dimension of value that we label as ‘Progress’ pertains to the advancement of the world. Heuristically, it encompasses development, innovation and production in technology, infrastructure, art, ideas, culture, etc. Progress measures how each decade has improved upon the last. Later we will argue that the Progress dimension of value best represents economic value on the whole and can be quantified with effective complexity (EC). Others have hinted that value and complexity are correlated (Daly, 1973; Romer, 1996), and Benedikt and Oden (2011) explicitly argued for a valorisation of complexity. In this work, we make a distinct argument for the intrinsic (as opposed to instrumental) value of complexity and propose a framework by which complexity-based valuations can be hypothetically computed.

The dimension of value that we label as ‘Qualia’ pertains to the feelings and experiences of conscious beings. In the philosophy of mind, ‘Qualia’ denotes the subjective experiences and sensations that are unique to conscious beings. Unlike non-conscious computers, which only operate on data in a mechanistic sense, humans experience colour, taste, sound, pleasure, pain, etc. These experiences undoubtedly impact the subjective well-being of conscious individuals and cannot be dismissed as factors in determining desires, demands and certain forms of value.

Finally, the dimension of value that we label as ‘Truth’ explores any inherent value in gaining knowledge and understanding of reality, as it is. For example, it may be argued that gaining knowledge of a new fundamental particle in physics or of an occurrence in ancient history has value in of itself (and is therefore worth seeking), independent of any potential impact on Progress or Qualia.

As a general model, these three dimensions of value are taken to be orthogonal to one another and can be thought of as a useful set of basis vectors that span a three-dimensional value space. Any specific action or object may have positive or negative value along one dimension, independent of its value along another dimension. For example, a horrible truth may have value by virtue of its accuracy in describing the world (Truth) but contribute to pain along the Qualia dimension. Alternatively, a pleasurable activity (Qualia) might contribute to the deterioration of Progress, while having no impact along the Truth dimension. In general, intentioned actions are undertaken with the fundamental motive of effecting change in at least one of these three dimensions. While higher-level motives may be formulated (e.g., love, friendship, loyalty, honour, etc.), at base, these higher-level motives can usually be deconstructed into component vectors that lie along one or more of the three fundamental dimensions (Progress, Qualia, Truth).

A specific action or object (in a given context) can have its value-point plotted on a three-dimensional graph as shown in Figure 1. Furthermore, a specific individual’s current location within a three-dimensional value space may be determined from past actions and objects (vectors) that affect that individual. An individual’s current distance from the origin in one of the dimensions (e.g., Qualia) may affect that individual’s ability to move along a different dimension of value (e.g., Progress). For instance, a person who has experienced a great deal of pain and depression (Qualia) might find it difficult to produce works of Progress. Conversely, a person who has experienced too much bliss (Qualia) might also be dissuaded from working towards Progress. Consequently, moving from one value-point to another may be thought of as analogous to moving a particle in a non-conservative, three-dimensional force field. The difficulty of moving from one point to another point in the three-dimensional space is path dependent. The ability to traverse one of the dimensions can be impacted by the starting location in the other two dimensions, even while all three dimensions are in fact orthogonal to one another.

OPEN IN VIEWER

Figure 1.

Source: The authors.

Some philosophers, such as Epicurus, favoured Qualia as preferential and dismissed the other dimensions of value (Wilson, 1951). However, this perspective does not reflect the ideals of contemporary capitalistic societies. At a policy level, capitalistic societies tend to favour progress and accomplishments, lauding these endeavours as most economically valuable and to some extent rewarding them accordingly. The most profitable companies tend to peddle in Progress, whether through production, improved distribution, efficiency or innovation in physical goods, technology, infrastructure, culture, relationships, information, ideas, etc. (Murphy et al., 2019). Fundamentally, all of these activities are engaged in the process of complexifying the world (whether directly or indirectly).

Moreover, when actions are pleasurable but pose a hindrance or detriment to Progress (herein measured by complexity), they are disincentivised with laws, regulations, taxes or social stigma. Examples of such activities may include using hard drugs, smoking cigarettes, activities that pose a fire risk, vandalism, pollution, dropping out of high school, laziness, etc. Conversely, actions that may be considered difficult, painful or lacking in pleasure are generally commended if their results yield Progress (complexity). Examples of such activities may include maintaining physical fitness, painful medical procedures, putting a man on the moon, home maintenance, volunteer work, dedication to a craft, acts of heroism, work ethic, etc. In other cases, activities have no impact on Progress (complexity) and are therefore neutral in terms of economic value. Intuitively, capitalism would rate a society where people lounge in pleasure but do very little, as inferior to a society where people endure pain and hard work but achieve great accomplishments. Moreover, while Truth may contain its own inherent value, capitalistic societies tend to favour truths that pay out by facilitating Progress (e.g., scientific truths that lead to new inventions). For these reasons, economic value is most suitably measured along the dimension of Progress.

Progress (or economic value) cannot be easily measured with simple physical properties such as mass, volume, composition or substance. Rather, economic value arises out of embodied information, typically in the form of a hierarchical arrangement of an object’s fundamental parts. For example, a coherent novel is more valuable than an equally large stack of papers that have been printed on with the same amount of ink in a random gibberish pattern. Food is more valuable before it has been digested (a process that breaks down a great deal of its molecular structure). A structured computer is more valuable than its unstructured raw materials. The same could be said of life. While the specific atoms in a living body are continually flushed out and replaced (as individual cells die), the embodied information (from DNA down to electrons) preserves a living being’s individuality and potential value (both intrinsic and instrumental). In fact, most any valuable object could be rendered valueless by burning it to ash in a high-temperature furnace, thereby erasing its embodied information. Even pure metals like platinum can have their embodied information and value destroyed by nuclear processes that rearrange their fundamental particles.

The second law of thermodynamics ensures that on a grand scale, organised information is continually randomised and degraded. However, on a local scale, something beautiful is afoot. Humans are born creative and with the potential to be productive. Great civilisations arise from human minds and hands. Interpersonal relationships and networks flourish. Technology progresses. Culture abounds. These measures of progress (and others) make life worth living and are, as a rule of thumb, ‘valuable’. Moreover, they all share a common denominator; they all embody (or engender) abundant complexity in a universe that tends towards disorder.

Whereas entropy measures ignorance, information is the opposite of ignorance. In a naïve sense, we could choose to measure embodied information either in units of entropy (Shannon information) or by using algorithmic information content (AIC; also called Kolmogorov complexity; Chaitin, 1990; Kolmogorov, 1963). However, meaningful information (that which contributes to economic value) is better quantified by operating on the AIC to tease out the contributions attributable to regularities. The information measure known as effective complexity (EC) does precisely this (as will be discussed later in detail) and therefore provides a powerful proxy metric for measuring economic value.

While most of the universe marches towards a high-entropy state, living beings and their creations not only embody enormous complexity but also continually give rise to even greater complexity. EC is a characteristic largely engendered by life and the inventions of living beings (Bar-Yam, 2002; Capra, 2005), which both harness and fight the increase of entropy on a local scale. The creation and preservation of net EC are what humans strive for every day as they work to keep their bodies healthy and living, maintain their cars and houses, build and nurture relationships, produce writing, art, ideas, and culture. The creation and preservation of EC are built into a human’s raison d’être and can be interpreted as a measure of what humans have and have created of value.

However, often humans treasure things for their simplicity, not their complexity. They seek simplified tax codes, tools that are simple but effective and highly purified silicon for use in transistors. Measuring the currently embodied EC of an object does not capture its full value. Instead, we must consider an object’s intrinsic value and instrumental value. The EC currently embodied by an object functions as a proxy for its intrinsic value. However, the object may also serve as a raw material, tool or other factor in the production of still greater complexity in the future. This future complexity is the object’s instrumental value and must be incorporated into any calculation of the object’s overall value. For example, in a hypothetical chain of events, highly purified silicon is used to produce transistors, which are assembled into computers, which produce abundant future complexity through vast calculations. While purified silicon may appear to have little value (due to its minimal embodied EC), the sum of its intrinsic and instrumental value is quite large. Often an object’s future EC contributions will dwarf its presently embodied EC. When humans seek things that are simple, it is with the ultimate purpose of using this simplicity to facilitate even greater complexity in the future.

As a further spot check on the correlation between economic value and effective complexity, consider both the value and EC of an individual human. Human life and well-being are prized by general consensus. Simultaneously, the human brain, with its nearly 100 billion neurons (Allen & Barres, 2009), each making up to 10,000 connections, is highly complex (perhaps the most complex object in our known solar system). Furthermore, thinking individuals (with well-functioning brains) engender enormous future EC through their creativity, decisions, actions and secondary effects. Therefore, under complexalism, actions that ultimately promote the survival and well-being of humans have a large positive value, while those that ultimately destroy human life have a large negative value.

Measuring Complexity

Complexity theory is a rich field, and a number of diverse complexity measures have been proposed (Lloyd, 2001). However, the measure known as effective complexity best formalises our intuitive notions of complexity in a general format (Gell-Mann & Lloyd, 2010). Other measures of complexity (e.g., self-dissimilarity; Wolpert & Macready, 2002) can typically be formulated as special cases of EC. EC makes use of AIC, which measures the length of a highly compressed description of a bit string. Formally, the AIC of a bit string is the length of the shortest computer programme that can print the bit string and then halt (on a universal Turing machine). As an informal example, the bit string ‘1010101010101010101010101010101010101010’ could be compressed and described as ‘“10” repeated 20 times’. Therefore, the AIC of this bit string is given by the length of its compressed description, not the length of the full bit string. Conversely, a bit string that is truly random cannot be compressed, and its shortest description is at least as long as the bit string itself. For this reason, AIC is sometimes called ‘algorithmic randomness’ as it assigns higher values to random bit strings than to bit strings containing patterns, which allow for compression.

Therefore, AIC is not a viable measure of what we intuitively consider embodied information. The AIC of a random bit string is large, whereas its embodied information is small. For example, in literature, a novel composed by randomly selecting words from a dictionary is considered to contain very little meaningful information, despite its large AIC.

EC, on the other hand, only measures the AIC of the regularities in a bit string. In doing so, EC closely approximates our intuitive notion of embodied information. EC separates a bit string into a subset containing its regular features and a subset containing its incidental (or random) features. It then measures the AIC of just the regularities.

Regular features are distinguished from incidental features by using a procedure from the literature that embeds the bit string in a set of similar bit strings and assigns a probability to each member of the set (Gell-Mann & Lloyd, 1996). Each member of the set must share the regularities of the original bit string but otherwise can vary in its details. For instance, the bit string ‘1010101010101010101010101010101010101010’ could be typed out in various fonts wherein the symbols ‘1’ and ‘0’ are perceived as the regularities, and the stylistic differences between each font are perceived as the incidental features.

An assembled set of similar entities, where each member has an assigned probability, can be considered an ensemble (wherein the regularities are constraints to be held constant). This ensemble mirrors ensembles used in statistical mechanics (e.g., the microcanonical ensemble wherein the total energy imposes a constraint or the canonical ensemble wherein the temperature imposes a constraint). By analogy, the regular features correspond to macrostate features while the incidental features correspond to microstate features. The EC is given by the AIC of the ensemble. EC is thus distinct from AIC in that it conceptually separates the bit string into two subsets, one containing the regularities and the other containing the incidental features. EC only measures the information content of the regularities in the bit string.

One notable criticism levelled at EC is that it is not uniquely determined for a given bit string (in the absence of externally imposed constraints; McAllister, 2003). The EC of a bit string depends on subjective decisions (constraints) such as on which computing machine the AIC is calculated, the choice of an encoding scheme and how regularities are defined. The first two subjective decisions (choice of a computing machine and an encoding scheme) can be largely dismissed as long as protocols are established and followed which standardise both decisions (thereby minimising any resulting subjectivity or ambiguity).

The third necessary and subjective decision, defining regularities (also denoted ‘coarse-graining’), has been addressed by Céspedes and Fuentes, who argue that EC can be uniquely determined (or at least reasonably bounded) as long as the ‘cognitive and practical interests’ concerning the bit string are determined a priori (Céspedes & Fuentes, 2020). Under these conditions, EC is compatible with scientific practices and can be applied robustly as an information measure. As a hypothetical example, Céspedes and Fuentes imagine a bit string that records the earth’s atmospheric temperature over time. This bit string may be considered on the basis of a period of one day or on the basis of a period of 21,000 years yielding different patterns over different timescales and hence different potential regularities. If, however, the various researchers using this bit string agree to use the same basis (presumably based on a shared research agenda), then they will arrive at the same (or at least a similar) EC result. If there is consensus on the ‘cognitive and practical interests’ among the parties (i.e., agreement on the coarse-graining practice for determining regularities), then EC can be uniquely determined.

Under complexalism, EC is used as a proxy metric for the economic value of goods. In order for EC to serve as the basis for a rigorous economic theory of value, the EC of the goods being evaluated must be uniquely determined (given a specific context). As discussed, uniquely determining the EC of an object (or bit string) requires that the parties involved come to a consensus on how to identify regularities (i.e., coarse-graining). While this process inherently involves some subjectivity, we contend that it can be resolved in a more objective fashion than other nebulous approaches to assessing value.

Complexalism reparameterises large and slippery questions of value into sub-questions about the coarse-graining procedure. Each of these sub-questions, on its own, can more easily garner a consensus resolution. Once reassembled, the agreed-upon answers to the sub-questions enable a robust quantification of value. The purpose of this reparameterisation is analogous to the purpose of rendering an object’s coolness to the touch more objective by slicing it into more objectively addressable subcomponents (e.g., the expansion of mercury and the swinging of a pendulum).

Finding the best coarse-graining procedures for complexalism remains an open question left for future work, but we list a few conceivable approaches. In one approach, the regularities in a physical object might be constrained by a ‘minimum intentional feature size’. For instance, the minimum intentional feature size could be defined as the smallest unit of detail (voxel) that the creator would reproducibly incorporate into his or her work under standard operating procedures. A 3D-printed part might have a minimum intentional feature size of 1 mm. If asked to produce a dozen identical prints, each print would be reproduced with an all-around precision of 1 mm. Smaller features would be irreproducible, unintentional and considered noise. Likewise, two pristine cars of the same make, model, year, colour and accessories that have just come off of the same assembly line are identical for all practical valuation purposes. Complexalism should not concern itself about the precise arrangement of atoms and dislocations within the metal itself (so long as they do not affect other important materials properties), lest these atomic-scale regularities drown out the regularities of interest. More generally, a diverse set of ‘minimum intentional feature parameters’ may be selected. For a 3D-printed part, these may include the selected set of colours (quantified by wavelength), compositions, mechanical properties, etc. For a highly designed object like a car, each aspect is designed to within certain intentional specifications (e.g., manufacturing tolerances). These specifications set error bars on the parameter precision necessary for each feature to maintain its purpose. Accordingly, these specifications could be used to guide the coarse-graining procedures.

Alternatively, ‘minimum consequential feature parameters’ could be determined. These feature parameters favour consequence over intent. For example, an object might be overdesigned (in intent) at a feature scale that cannot be practically distinguished from a less designed object. One could argue that if both objects are indistinguishable, they should have the same valuation from a consequence perspective. The minimum consequential feature parameter could accordingly be constrained by physical limitations on a human’s ability to distinguish between colours, hardness, mechanical properties, etc. Furthermore, if the causal relationship interrelating features at different hierarchical levels is known (e.g., how microscale features impact bulk mechanical properties), a more complete picture of the consequences resulting from each scale could be assessed and accounted for. Deciding on a coarse-graining procedure might additionally be aided by machine learning techniques or generative adversarial networks. As Gell-Mann and Lloyd have pointed out, the coarse-graining procedure does not necessarily need to be decided by humans or even living beings (Gell-Mann & Lloyd, 2010).

We contrast complexalism with the current state of affairs in assigning valuations. At present, market prices are the default proxy for economic value. This approach is riddled with fundamental weaknesses. Market prices are dictated (in part) by the equilibrium between supply and demand. However, demand is readily manipulated and often too nebulous to evaluate directly and rigorously (Becher & Feldman, 2016). While demand operates on a market scale, it derives from individual desires (whether simple or multifaceted). There is little reason to believe that following the desires of individuals (even averaged en masse) is an efficient route for pursuing or assessing Truth or Progress. For this reason, questions in philosophy, science, mathematics, medicine, engineering, etc., cannot be viably resolved by a popular vote. Instead, these questions must be resolved with expertise, specialised training and rigorous studies. While demand may indirectly drive Progress (or at least motivate it), the connection between the two is tenuous. Generally, policy interventions are additionally necessary (e.g., government funding for research in the basic sciences).

If anything, desires may more aptly reflect the Qualia dimension of value. Qualia are, after all, subjective internal experiences most readily accessed by the individual experiencing them. However, here too, manipulations arise. In his theory of Mimetic Desire, René Girard argues that most all desires arise from the copying of others (Livingston, 1992). While inner desires may appear highly personal and seem to elucidate something deeper about one’s true self, they are often, in fact, foreign entities implanted through advertising, media and other sources.

Furthermore, market prices depend on market rules of engagement, which, as discussed, cannot be robustly evaluated using conventional economics tools. In many cases, market prices may result from a combination of demand and poorly designed rules of engagement. For these reasons, market prices are unlikely to accurately reflect Progress or economic value. Simultaneously, communism (as an opposing economic system) is rife with fundamental weaknesses, not least of which is its dependence on the highly subjective discernments and opinions of bureaucrats in planning the economy. Complexalism, on the other hand, provides an alternative and potentially more objectively decidable metric of value that circumvents many of the shortcomings inherent to ‘demand’.

To be clear, complexalism does not take power out of the hands of the people. Rather, it is meant to empower people in their value assessments by providing a more potent and palpable framework for valuations. This is accomplished by first differentiating between three independent dimensions of value: Progress, Qualia and Truth. Next, a systematic approach for quantifying Progress using EC is explored (as detailed below). By breaking down large and nebulous questions of value into more addressable sub-questions, complexalism allows individuals to develop consensuses at a more fundamental level, far removed from the biases and susceptibilities inherent to desires.

Simulating Valuations

The process of quantitatively assessing value under complexalism is most easily explained by starting with three idealised assumptions: (a) the universe is deterministic, (b) we have access to unlimited computing power and (c) we have access to all initial state information. These assumptions can later be relaxed through approximations. Instead of following Revenue and Cost (e.g., to decide levels of production), complexalism tracks the tension between two new terms, ‘total complexity’ (TC) and ‘complexity opportunity cost’ (COC).

TC is a measure of the EC both embodied within (intrinsic) and engendered by (instrumental) an object of interest. Here we use the term ‘object’ in a broad sense, encompassing physical items, ideas, services, etc. First, the object of interest (e.g., my yellow bicycle) and its surroundings are encoded as information in a simulation. The EC presently embodied in both the simulated object and its simulated surroundings is quantified and this number is stored. Next, the simulation is run forward in time, with the embodied EC (of both the object and surroundings) computed and stored at each timestep. For example, my yellow bicycle is utilised to perform daily tasks, each of which increases the net complexity of the surroundings. Any secondary effects are also simulated, quantified and captured in an expanding chain of causal events, each contributing to the embodied EC of the simulated surroundings for that timestep. Overall, the EC of the entire simulation is integrated with respect to time (stepwise, assuming infinitesimal timesteps) from the present (t_o) up to a specified point in the future (t_f). This integrated result is stored as ‘result A’.

Now the whole process is repeated in simulation B with a single difference; in simulation B, my yellow bicycle is absent (while the surroundings begin in the same initial state). The simulation will obviously run a different course in the absence of my yellow bicycle. Once again, the EC is integrated with respect to time up to the same future point and stored as ‘result B’. The difference between ‘result A’ and ‘result B’ is the difference in complexity between two worlds, one with the yellow bicycle and one without it (Equation 1).

T C = ∫ t o t f C o s d t − ∫ t o t f C s d t

(1)

The term C_os represents the instantaneous EC of the object of interest and its surroundings, while C_s represents the instantaneous EC of just the surroundings. TC measures the impact (i.e., complexalism benefit) of my yellow bicycle. However, the impact alone does not dictate value. Additionally, value is contextual. In complexalism contextuality is built in by virtue of the simulations themselves being contextual. These simulations incorporate not only the object of interest but also its potentially affected surroundings. This context can incorporate time, place, cultural norms, etc.

Consider a simple hypothetical example of a farmer, Jane, with four identical buckets of water and four potential uses for water: hydrate herself, hydrate her animals, wash her body and water her garden. When deciding how to use the first bucket of water, each activity has a distinct level of priority, as measured by the associated TC. Hydrating herself in order to remain alive is a high priority as it has high TC. The staggering interconnectivity of the human brain along with its creative potential is an enormous source of complexity (both intrinsic and instrumental). Therefore, fostering human life, well-being and thinking are highly valuable activities under complexalism. Watering the garden has much lower priority as it has lower TC. However, each potential use case has diminishing marginal TC as more water is allotted to that potential use case. As the farmer drinks more water, she becomes less thirsty, and the TC added with each additional sip decreases. Under complexalism, we assume that the farmer will act reasonably and spread the available water over the potential use cases so as to maximise its impact (TC).

In some cases, equivalent goods are not equally accessible. For instance, some water may be readily available, while other water must first be pumped from a distant well and carried back. These different sources of water entail different complexity opportunity costs. COC is the TC that could have otherwise been added to the system, had time and resources not been expended elsewhere (e.g., in acquiring the replacement goods). For example, the water that is readily available has nearly zero COC, whereas the water that must first be pumped from a distant well and carried back expends worker energy and time, which could have otherwise been spent producing additional TC in other tasks. In general, the marginal COC of obtaining an additional unit of a good increases with consumption (at least at high levels of consumption). This is because the most easily available goods are consumed first, and additional goods must be scrounged for in increasingly taxing ways. Note that the COC can entail the raw materials, manufacturing, labour, and transportation, etc., associated with obtaining an equivalent replacement unit (not necessarily the efforts that went into the original unit in question).

Whereas the marginal TC generally decreases with increased consumption, the marginal COC generally increases with increased consumption. When the marginal TC and marginal COC are calculated as functions of consumption (using simulations) and plotted on the same graph (Figure 2), they intersect at a break-even point where marginal TC equals marginal COC. This break-even point sets a boundary on the simulation that limits further scrounging/production for additional units of that good. Obtaining additional units (beyond the break-even point) would actually decrease overall complexity and would constitute an unreasonable behaviour.

OPEN IN VIEWER

Figure 2.

Source: The authors.

Establishing a meritocratic correspondence between one’s compensation (or price) and one’s positive impact is a philosophical question with at least three distinct possible approaches. Should compensation be proportional to: (a) the benefit the individual produces, (b) the hypothetical loss that would be incurred by the absence of the individual or (c) the cost to replace the individual?

We contend that option (b) best represents a meritocracy. In order to highlight the differences between option (a) and option (b), we return to the simple example of the farmer with four buckets of water (instead of individuals). Let us posit that in this circumstance, the farmer uses the first bucket of water (bucket #1) to hydrate herself, bucket #2 to hydrate her animals, bucket #3 to wash her body and bucket #4 to water her garden, in order to maximise TC. Under option (a), bucket #1 has tremendous TC or value (by virtue of keeping the farmer alive), while bucket #4 has minimal TC or value (by virtue of keeping her garden alive). However, in a practical sense (due to the interchangeability of the identical buckets of water), if bucket #1 went missing (e.g., stolen), the farmer would not die of thirst. Rather she would promote buckets 2–4 to serve use cases 1–3 (in order of priority). Therefore, the value lost is the TC associated with keeping the garden alive. This more pragmatic assessment of value is reflected in option (b).

Option (c) closely mirrors current market principles and shares in its weaknesses. For example, the cost to replace a worker is typically assessed via market forces (supply and demand establishing an equilibrium price). However, a market-derived price can only be interrogated after the rules of engagement have been set for the market. The rules of engagement (e.g., regulations on monopolies, monopsonies, unions, minimum wage, contract law, etc.) impact the relative negotiating power of every party involved and therefore impact the resulting price. For these reasons, option (c) is not suitable for meta-level evaluations of the rules of engagement (a goal of complexalism). Alternatively, if the ‘cost’ of option (c) is interpreted to mean the COC, then in general option (c) reduces to option (b) due to the equivalence between marginal TC and marginal COC at the break-even point.

In complexalism simulations (for determining TC), when one unit of a good is removed, other units of that same good, previously allocated to lower priority uses, are shifted to fulfil the highest priority uses first. The overall effect is that removing a unit from any use case always results in a loss of TC equivalent to the marginal TC of that good at the break-even point. Therefore, under complexalism a good or activity’s value (along with its price or level of compensation) is proportional to the marginal TC of that object at the break-even point.

This described procedure gives complexalism-derived valuations that can, in theory, be applied to anything or any profession. It is important to note that under complexalism, the calculated values of specific objects may or may not resemble current market prices. In some cases, the contrast between the two will be stark. These differences should be taken as features, not bugs. The utility of any new framework derives from its areas of disagreement with prior frameworks. Furthermore, complexalism is an economic theory of value, not a moral theory of value. Other moral restrictions (e.g., deontological) should be considered in addition to the valuations prescribed by complexalism.

At present, the available computational resources and data sets are not large enough to implement complexalism simulations on a broad scale. Nonetheless, complexalism can be wielded as a potent theoretical framework. As an example by analogy, Rawl’s ‘veil of ignorance’ framework cannot be physically put into practice but has nonetheless served as a conceptual foundation and guiding light in important policy decisions (Kukathas & Pettit, 1990). In a similar fashion, complexalism might help to systematically contextualise economic policy decision-making.

Furthermore, a number of simplifying assumptions might be employed to render complexalism more computationally tractable. First, in order to eliminate excess unknowns about the future, complexalism could use recent historical data to make retrodictions about the recent past (as opposed to predictions about the future). These retrodictions (made at set time intervals) could establish valuations for specific goods and occupations to compare against market-derived prices. These comparisons would benchmark where prices and value have diverged and by how much. For instance, a representative basket of goods and occupations could be simulated in order to establish valuation anchor points for use in a course-correcting feedback loop (when steering the economy). Furthermore, mean-field approximations might be used to provide generalised (though context relevant) surroundings in the simulations, as opposed to highly specialised surroundings with unique minutia. Although Chaitin proved that AIC is technically undecidable (Chaitin, 1990), a number of approaches to bound and/or estimate AIC have been proposed (Bloem et al., 2014; Cilibrasi & Vitanyi, 2005; Delahaye & Zenil, 2012; Soler-Toscano & Zenil, 2017; Soler-Toscano et al., 2014). Gell-Mann and Lloyd simply propose setting a finite maximal computation time in order to produce a decidable AIC proxy when computing EC (Gell-Mann & Lloyd, 2010). Historically, a number of frameworks and algorithms have been proposed before the computational power to widely implement them existed (e.g., Newton’s method, machine learning; Nilsson, 1965). Likewise, complexalism may benefit from recent and future advances in exascale computing and quantum computing (Arute et al., 2019).

Conclusions

Complexalism provides an independent and potentially more objective metric for assessing the value impact of objects and occupations when evaluating policy decisions. Computed value-anchoring points may serve as targets to aim for when steering the economy (by tuning its underlying rules of engagement). Monetary wealth or economic growth measured by market prices cannot be used for these meta-level evaluations. Value and market prices often diverge precisely because of poorly designed rules of engagement. In the current absence of a more objective measure of value, the mechanisms for determining prices and wages cannot be cross-examined. This sets up a blind feedback loop that is more likely to conjure a simulacrum than reflect reality. Complexalism offers an alternative and potentially more objective benchmark of value by which to judge the efficacy of rules and their outcomes.